commalist.txt

= Amity family

=== Amity
Subgroup: 2.3.5
Comma list: 1600000/1594323
Mapping: {{mapping|legend=1| 1 3 6 | 0 -5 -13 }}

==== Overview to extensions

=== Septimal amity
Subgroup: 2.3.5.7
Comma list: 4375/4374, 5120/5103
Mapping: {{mapping|legend=1| 1 3 6 -2 | 0 -5 -13 17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4375/4374, 5120/5103
Mapping: {{mapping| 1 3 6 -2 21 | 0 -5 -13 17 -62 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 625/624, 729/728
Mapping: {{mapping| 1 3 6 -2 21 17 | 0 -5 -13 17 -62 -47 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 375/374, 540/539, 729/728
Mapping: {{mapping| 1 3 6 -2 21 17 -1 | 0 -5 -13 17 -62 -47 18 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 256/255, 324/323, 352/351, 375/374, 400/399, 456/455
Mapping: {{mapping| 1 3 6 -2 21 17 -1 15 | 0 -5 -13 17 -62 -47 18 -38 }}

==== Hitchcock
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2200/2187
Mapping: {{mapping| 1 3 6 -2 6 | 0 -5 -13 17 -9 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 176/175, 325/324
Mapping: {{mapping| 1 3 6 -2 6 2 | 0 -5 -13 17 -9 6 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 169/168, 176/175, 273/272
Mapping: {{mapping| 1 3 6 -2 6 2 -1 | 0 -5 -13 17 -9 6 18 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
Mapping: {{mapping| 1 3 6 -2 6 2 -1 0 | 0 -5 -13 17 -9 6 18 15 }}

==== Stalagmite
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 4375/4374
Mapping: {{mapping| 1 3 6 -2 -7 | 0 -5 -13 17 37 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 4375/4374
Mapping: {{mapping| 1 3 6 -2 -7 -11 | 0 -5 -13 17 37 52 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 | 0 -5 -13 17 37 52 18 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 -13 | 0 -5 -13 17 37 52 18 61 }}

==== Hemiamity
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5120/5103
Mapping: {{mapping| 2 1 -1 13 13 | 0 5 13 -17 -14 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 3025/3024
Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}

=== Accord
Subgroup: 2.3.5.7
Comma list: 126/125, 100352/98415
Mapping: {{mapping|legend=1| 1 3 6 11 | 0 -5 -13 -29 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 896/891
Mapping: {{mapping| 1 3 6 11 6 | 0 -5 -13 -29 -9 }}

=== Houborizic
Subgroup: 2.3.5.7
Comma list: 225/224, 1250000/1240029
Mapping: {{mapping|legend=1| 1 3 6 13 | 0 -5 -13 -36 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 1250000/1240029
Mapping: {{mapping| 1 3 6 13 -9 | 0 -5 -13 -36 44 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 2200/2197
Mapping: {{mapping| 1 3 6 13 -9 2 | 0 -5 -13 -36 44 6 }}

==== Houbor
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 2200/2187
Mapping: [{{val| 1 3 6 13 6 }}, {{val| 0 -5 -13 -36 -9 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 325/324
Mapping: [{{val| 1 3 6 13 6 2 }}, {{val| 0 -5 -13 -36 -9 6 }}]

=== Paramity
Subgroup: 2.3.5.7
Comma list: 65625/65536, 1600000/1594323
Mapping: {{mapping|legend=1| 1 3 6 -17 | 0 -5 -13 70 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 19712/19683, 41503/41472
Mapping: {{mapping| 1 3 6 -17 36 | 0 -5 -13 70 -115 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
Mapping: {{mapping| 1 3 6 -17 36 17 | 0 -5 -13 70 -115 -47 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
Mapping: {{mapping| 1 3 6 -17 36 17 -31 | 0 -5 -13 70 -115 -47 124 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
Mapping: {{mapping| 1 3 6 -17 36 17 -31 15 | 0 -5 -13 70 -115 -47 124 -38 }}

=== Bamity
Subgroup: 2.3.5.7
Comma list: 245/243, 64827/64000
Mapping: {{mapping|legend=1| 2 1 -1 3 | 0 5 13 6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 441/440
Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 245/243, 441/440
Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}

=== Hamity
Subgroup: 2.3.5.7
Comma list: 2430/2401, 4000/3969
Mapping: {{mapping|legend=1| 1 8 19 15 | 0 -10 -26 -19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 2200/2187
Mapping: {{mapping| 1 8 19 15 15 | 0 -10 -26 -19 -18 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 275/273, 572/567
Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}

=== Gamity
Subgroup: 2.3.5.7
Comma list: 1029/1024, 1071875/1062882
Mapping: {{mapping|legend=1| 1 13 32 -1 | 0 -15 -39 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 1071875/1062882
Mapping: {{mapping| 1 13 32 -1 -11 | 0 -15 -39 5 19 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 10985/10976
Mapping: {{mapping| 1 13 32 -1 -11 -10 | 0 -15 -39 5 19 18 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
Mapping: {{mapping| 1 13 32 -1 -11 -10 -2 | 0 -15 -39 5 19 18 8 }}

=== Trinity
Subgroup: 2.3.5.7
Comma list: 703125/702464, 1600000/1594323
Mapping: {{mapping|legend=1| 1 8 19 46 | 0 -15 -39 -101 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 19712/19683
Mapping: {{mapping| 1 8 19 46 18 | 0 -15 -39 -101 -34 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
Mapping: {{mapping| 1 8 19 46 18 64 | 0 -15 -39 -101 -34 -141 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
Mapping: {{mapping| 1 8 19 46 18 64 -22 | 0 -15 -39 -101 -34 -141 61 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 | 0 -15 -39 -101 -34 -141 61 -114 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 | 0 -15 -39 -101 -34 -141 61 -114 -104 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 72 | 0 -15 -39 -101 -34 -141 61 -114 -104 -157 }}

=== Amicable
Subgroup: 2.3.5.7
Comma list: 2401/2400, 1600000/1594323
Mapping: {{mapping|legend=1| 1 3 6 5 | 0 -20 -52 -31 }}

==== Amical
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 131072/130977, 1600000/1594323
Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}

==== Amorous
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 6250/6237, 19712/19683
Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}

==== Pseudoamical
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 1600000/1594323
Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 1375/1372, 19773/19712
Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}

==== Pseudoamorous
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 980000/970299
Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440, 1875/1859
Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}

==== Floral
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 14641/14580
Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}

==== Humorous
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 1600000/1594323
Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
Mapping: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}

=== Calamity
Subgroup: 2.3.5.7
Comma list: 1600000/1594323, 2100875/2097152
Mapping: {{mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 12005/11979, 131072/130977
Mapping: {{mapping| 1 13 32 -15 -18 | 0 -25 -65 39 47 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979
Mapping: {{mapping| 1 13 32 -15 -18 -31 | 0 -25 -65 39 47 76 }}

=== Familia
Subgroup: 2.3.5.7
Comma list: 16875/16807, 1600000/1594323
Mapping: {{mapping|legend=1| 1 8 19 20 | 0 -25 -65 -67 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 1600000/1594323
Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372, 2205/2197
Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}


= Whitewood family

=== Whitewood
Subgroup: 2.3.5
Comma list: 2187/2048
Mapping: {{mapping|legend=1| 7 11 0 | 0 0 1 }}

=== Septimal whitewood
Subgroup: 2.3.5.7
Comma list: 36/35, 2187/2048
Mapping: {{mapping|legend=1| 7 11 0 36 | 0 0 1 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 2079/2048
Mapping: {{mapping| 7 11 0 36 8 | 0 0 1 -1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44, 512/507
Mapping: {{mapping| 7 11 0 36 8 26 | 0 0 1 -1 1 0 }}

=== Redwood
Subgroup: 2.3.5.7
Comma list: 525/512, 729/700
Mapping: {{mapping|legend=1| 7 11 0 52 | 0 0 1 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 385/384, 729/700
Mapping: {{mapping| 7 11 0 52 8 | 0 0 1 -2 1 }}

=== Mujannab
Subgroup: 2.3.5.7
Comma list: 54/49, 64/63
Mapping: {{mapping|legend=1| 7 11 0 20 | 0 0 1 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 54/49, 64/63
Mapping: {{mapping| 7 11 0 20 8 | 0 0 1 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 52/49, 64/63
Mapping: {{mapping| 7 11 0 20 8 26 | 0 0 1 0 1 0 }}

=== Greenwood
Subgroup: 2.3.5.7
Comma list: 405/392, 1323/1280
Mapping: {{mapping|legend=1| 7 11 1 12 | 0 0 2 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 1323/1280
Mapping: {{mapping| 7 11 1 12 9 | 0 0 2 1 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 640/637
Mapping: {{mapping| 7 11 1 12 9 26 | 0 0 2 1 2 0 }}


= Archytas clan

=== Archy
Subgroup: 2.3.7
Comma list: 64/63
Mapping: {{mapping|legend=2| 1 0 6 | 0 1 -2 }}
Mapping: {{mapping|legend=3| 1 0 0 6 | 0 1 0 -2 }}

==== Overview to extensions

===== 7-limit extensions

===== Subgroup extensions

==== Supra
Subgroup: 2.3.7.11
Comma list: 64/63, 99/98
Mapping: {{mapping| 1 0 6 13 | 0 1 -2 -6 }}

===== Supraphon
Subgroup: 2.3.7.11.13
Comma list: 64/63, 78/77, 99/98
Mapping: {{mapping| 1 0 6 13 18 | 0 1 -2 -6 -9 }}

=== Superpyth
Subgroup: 2.3.5.7
Comma list: 64/63, 245/243
Mapping: {{mapping|legend=1| 1 0 -12 6 | 0 1 9 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 245/243
Mapping: {{mapping| 1 0 -12 6 -22 | 0 1 9 -2 16 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 0 -12 6 -22 -17 | 0 1 9 -2 16 13 }}

===== Uberpyth
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 144/143, 245/243
Mapping: {{mapping| 1 0 -12 6 -22 26 | 0 1 9 -2 16 -14 }}

===== Thomas
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 169/168, 245/243
Mapping: {{mapping| 1 1 -3 4 -6 4 | 0 2 18 -4 32 -1 }}

==== Suprapyth
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 99/98
Mapping: {{mapping| 1 0 -12 6 13 | 0 1 9 -2 -6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 65/63, 99/98
Mapping: {{mapping| 1 0 -12 6 13 18 | 0 1 9 -2 -6 -9 }}

=== Quasisuper
Subgroup: 2.3.5.7
Comma list: 64/63, 2430/2401
Mapping: {{mapping|legend=1| 1 0 23 6 | 0 1 -13 -2 }}

==== Quasisupra
Subgroup: 2.3.5.7.11
Comma list: 64/63, 99/98, 121/120
Mapping: {{mapping| 1 0 23 6 13 | 0 1 -13 -2 -6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 78/77, 91/90, 121/120
Mapping: {{mapping| 1 0 23 6 13 18 | 0 1 -13 -2 -6 -9 }}

==== Quasisoup
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 2430/2401
Mapping: {{mapping| 1 0 23 6 -22 | 0 1 -13 -2 16 }}

=== Ultrapyth
Subgroup: 2.3.5.7
Comma list: 64/63, 6860/6561
Mapping: {{mapping|legend=1| 1 0 -20 6 | 0 1 14 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 2401/2376
Mapping: {{mapping| 1 0 -20 6 21 | 0 1 14 -2 -11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 91/90, 1573/1568
Mapping: {{mapping| 1 0 -20 6 21 -25 | 0 1 14 -2 -11 18 }}

==== Ultramarine
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 3773/3645
Mapping: {{mapping| 1 0 -20 6 -38 | 0 1 14 -2 26 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 91/90, 100/99, 847/845
Mapping: {{mapping| 1 0 -20 6 -38 -25 | 0 1 14 -2 26 18 }}

=== Quasiultra
Subgroup: 2.3.5.7
Comma list: 64/63, 33614/32805
Mapping: {{mapping|legend=1| 1 0 31 6 | 0 1 -18 -2 }}

=== Schism
Subgroup: 2.3.5.7
Comma list: 64/63, 360/343
Mapping: {{mapping|legend=1| 1 0 15 6 | 0 1 -8 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 64/63, 99/98
Mapping: {{mapping| 1 0 15 6 13 | 0 1 -8 -2 -6 }}

=== Beatles
Subgroup: 2.3.5.7
Comma list: 64/63, 686/675
Mapping: {{mapping|legend=1| 1 1 5 4 | 0 2 -9 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 686/675
Mapping: {{mapping| 1 1 5 4 10 | 0 2 -9 -4 -22 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 91/90, 100/99, 169/168
Mapping: {{mapping| 1 1 5 4 10 4 | 0 2 -9 -4 -22 -1 }}

==== Ringo
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63, 540/539
Mapping: {{mapping| 1 1 5 4 2 | 0 2 -9 -4 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 78/77, 91/90
Mapping: {{mapping| 1 1 5 4 2 4 | 0 2 -9 -4 5 -1 }}

==== Beetle
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 686/675
Mapping: {{mapping| 1 1 5 4 -1 | 0 2 -9 -4 15 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 91/90, 169/168
Mapping: {{mapping| 1 1 5 4 -1 4 | 0 2 -9 -4 15 -1 }}

=== Progress
Subgroup: 2.3.5.7
Comma list: 64/63, 392/375
Mapping: {{mapping|legend=1| 1 0 5 6 | 0 3 -5 -6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63, 77/75
Mapping: {{mapping| 1 0 5 6 4 | 0 3 -5 -6 -1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 66/65, 77/75
Mapping: {{mapping| 1 0 5 6 4 0 | 0 3 -5 -6 -1 7 }}

===== Progressive
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 56/55, 64/63, 77/75
Mapping: {{mapping| 1 0 5 6 4 9 | 0 3 -5 -6 -1 -10 }}

=== Fervor
Subgroup: 2.3.5.7
Comma list: 64/63, 9604/9375
Mapping: {{mapping|legend=1| 1 -1 7 8 | 0 5 -9 -10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63, 1350/1331
Mapping: {{mapping| 1 -1 7 8 4 | 0 5 -9 -10 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 78/77, 507/500
Mapping: {{mapping| 1 -1 7 8 4 12 | 0 5 -9 -10 -1 -16 }}

=== Sixix
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/2916
Mapping: {{mapping|legend=1| 1 3 4 0 | 0 -5 -6 10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 125/121
Mapping: {{mapping| 1 3 4 0 6 | 0 -5 -6 10 -9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 55/54, 64/63, 125/121
Mapping: {{mapping| 1 3 4 0 6 4 | 0 -5 -6 10 -9 -1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 40/39, 55/54, 64/63, 85/84, 125/121
Mapping: {{mapping| 1 3 4 0 6 4 1 | 0 -5 -6 10 -9 -1 11 }}


= Archytas family

=== Archytas
Subgroup: 2.3.5.7
Comma list: [[64/63]]
Mapping: {{mapping|legend=1| 1 0 0 6 | 0 1 0 -2 | 0 0 1 0 }}
Mapping to lattice: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]

=== Ares
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99
Mapping: {{mapping|legend=1| 1 0 0 6 2 | 0 1 0 -2 -2 | 0 0 1 0 2 }}
Mapping to lattice: [{{val| 0 1 1 -2 0 }}, {{val| 0 0 -1 0 -2 }}]

=== Vulcan
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63
Mapping: {{mapping|legend=1| 1 0 0 6 9 | 0 1 0 -2 -2 | 0 0 1 0 -1 }}


= Augmented family

=== Augmented
Subgroup: 2.3.5
Comma list: 128/125
Mapping: {{mapping|legend=1| 3 0 7 | 0 1 0 }}

==== Overview to extensions

=== Septimal augmented (augene)
Subgroup: 2.3.5.7
Comma list: 64/63, 126/125
Mapping: {{mapping|legend=1| 3 0 7 18 | 0 1 0 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63, 100/99
Mapping: {{mapping| 3 0 7 18 20 | 0 1 0 -2 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 56/55, 64/63, 66/65
Mapping: {{mapping| 3 0 7 18 20 16 | 0 1 0 -2 -2 -1 }}

===== Ogene
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 91/90, 100/99
Mapping: {{mapping| 3 0 7 18 20 -8 | 0 1 0 -2 -2 4 }}

===== Agene
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 78/77, 100/99
Mapping: {{mapping| 3 0 7 18 20 35 | 0 1 0 -2 -2 -5 }}

==== Eugene
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 77/75
Mapping: {{mapping| 3 0 7 18 -4 | 0 1 0 -2 3 }}

=== August
Subgroup: 2.3.5.7
Comma list: 36/35, 128/125
Mapping: {{mapping|legend=1| 3 0 7 -1 | 0 1 0 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 56/55
Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44, 56/55
Mapping: {{mapping| 3 0 7 -1 1 -3 | 0 1 0 2 2 3 }}

===== Augustus
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 36/35, 45/44, 56/55
Mapping: {{mapping| 3 0 7 -1 1 11 | 0 1 0 2 2 0 }}

=== Inflated
Subgroup: 2.3.5.7
Comma list: 28/27, 128/125
Mapping: {{mapping|legend=1| 3 0 7 -6 | 0 1 0 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 55/54, 128/125
Mapping: {{mapping| 3 0 7 -6 -4 | 0 1 0 3 3 }}

=== Deflated
Subgroup: 2.3.5.7
Comma list: 21/20, 128/125
Mapping: {{mapping|legend=1| 3 0 7 13 | 0 1 0 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 21/20, 33/32, 128/125
Mapping: {{mapping| 3 0 7 13 15 | 0 1 0 -1 -1 }}

=== Hexe
Subgroup: 2.3.5.7
Comma list: 50/49, 128/125
Mapping: {{mapping|legend=1| 6 0 14 17 | 0 1 0 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 56/55, 125/121
Mapping: {{mapping| 6 0 14 17 21 | 0 1 0 0 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 56/55, 66/65, 105/104
Mapping: {{mapping| 6 0 14 17 21 13 | 0 1 0 0 0 1 }}

=== Triforce
Subgroup: 2.3.5.7
Comma list: 49/48, 128/125
Mapping: {{mapping|legend=1| 3 0 7 6 | 0 2 0 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 77/75
Mapping: {{mapping| 3 0 7 6 8 | 0 2 0 1 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 66/65, 77/75
Mapping: {{mapping| 3 0 7 6 8 4 | 0 2 0 1 1 3 }}

===== Semitriforce
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 77/75, 507/500
Mapping: {{mapping| 6 0 14 12 16 27 | 0 2 0 1 1 -1 }}

=== Hemiaug
Subgroup: 2.3.5.7
Comma list: 128/125, 245/243
Mapping: {{mapping|legend=1| 3 1 7 -1 | 0 2 0 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125, 243/242
Mapping: {{mapping| 3 1 7 -1 1 | 0 2 0 5 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 91/90, 128/125, 243/242
Mapping: {{mapping| 3 1 7 -1 1 13 | 0 2 0 5 5 -1 }}

=== Hemiug
Subgroup: 2.3.5.7
Comma list: 128/125, 1323/1250
Mapping: {{mapping|legend=1| 3 1 7 14 | 0 2 0 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125, 1323/1250
Mapping: {{mapping| 3 1 7 14 16 | 0 2 0 -3 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 66/65, 105/104, 507/500
Mapping: {{mapping| 3 1 7 14 16 13 | 0 2 0 -3 -3 -1 }}

=== Oodako
Subgroup: 2.3.5.7
Comma list: 128/125, 2401/2400
Mapping: {{mapping|legend=1| 3 3 7 8 | 0 4 0 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125, 2401/2400
Mapping: {{mapping| 3 3 7 8 10 | 0 4 0 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 128/125, 507/500
Mapping: {{mapping| 3 3 7 8 10 12 | 0 4 0 1 1 -2 }}

=== Hemisemiaug
Subgroup: 2.3.5.7
Comma list: 128/125, 12005/11664
Mapping: {{mapping|legend=1| 6 1 14 4 | 0 2 0 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125, 3773/3645
Mapping: {{mapping| 6 1 14 4 8 | 0 2 0 3 3 }}

=== Trisected
Subgroup: 2.3.5.7
Comma list: 128/125, 1029/1000
Mapping: {{mapping|legend=1| 3 0 7 10 | 0 3 0 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125, 1029/1000
Mapping: {{mapping| 3 0 7 10 12 | 0 3 0 -1 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 91/90, 128/125, 1029/1000
Mapping: {{mapping| 3 0 7 10 12 0 | 0 3 0 -1 -1 7 }}

=== Niner
Subgroup: 2.3.5.7
Comma list: 128/125, 686/675
Mapping: {{mapping|legend=1| 9 0 21 11 | 0 1 0 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125, 540/539
Mapping: {{mapping| 9 0 21 11 17 | 0 1 0 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 128/125
Mapping: {{mapping| 9 0 21 11 17 19 | 0 1 0 1 1 1 }}

=== Trug
Subgroup: 2.3.5.7
Comma list: 128/125, 360/343
Mapping: {{mapping|legend=1| 3 1 7 6 | 0 3 0 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125, 360/343
Mapping: {{mapping| 3 1 7 6 8 | 0 3 0 2 2 }}

=== Subgroup extensions

==== Augmented (2.3.5.19 subgroup)
Subgroup: 2.3.5.19
Comma list: 76/75, 96/95
Mapping: {{mapping|legend=2| 3 0 7 8 | 0 1 0 1 }}

=== External links


= Avicennmic temperaments

=== Submerged
Subgroup: 2.3.5.7
Comma list: 525/512, 3125/3087
Mapping: {{mapping|legend=1| 1 -6 3 9 | 0 11 -1 -9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 525/512
Mapping: {{mapping| 1 -6 3 9 0 | 0 11 -1 -9 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 105/104, 121/120, 441/440
Mapping: {{mapping| 1 -6 3 9 0 | 0 11 -1 -9 5 }}


= Breed family

=== Breed
Subgroup: 2.3.5.7
Comma list: 2401/2400
Mapping: {{mapping|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }}
Mapping to lattice: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}]

=== Jove
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440
Mapping: {{mapping|legend=1| 1 1 1 2 2 | 0 2 1 1 5 | 0 0 2 1 0 }}

==== Jovial
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440
Mapping: {{mapping| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 441/440, 595/594
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}

===== Heartlandia
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 441/440, 1452/1445
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 171/170, 243/242, 324/323, 364/363, 441/440
Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}

==== Jovis
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 441/440
Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}

==== Jofur
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 243/242
Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}

=== Agni
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372
Mapping: {{mapping|legend=1| 1 1 1 2 5 | 0 2 1 1 0 | 0 0 2 1 -3 }}
Mapping to lattice: [{{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624, 1375/1372
Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}

=== Zisa
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 5632/5625
Mapping: {{mapping|legend=1| 1 1 1 2 -3 | 0 2 1 1 8 | 0 0 2 1 8 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 4096/4095
Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}

=== Lif
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 131072/130977
Mapping: {{mapping|legend=1| 1 1 1 2 8 | 0 2 1 1 -12 | 0 0 2 1 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095
Mapping: {{mapping| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}

==== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 1216/1215, 1729/1728, 2080/2079, 2401/2400
Mapping: {{mapping| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}

=== Baldur
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800
Mapping: {{mapping|legend=1| 2 0 1 3 7 | 0 2 1 1 -2 | 0 0 2 1 3 }}

==== Greenland
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715
Mapping: {{mapping| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}

===== Midnatssol
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 442/441, 561/560, 676/675
Mapping: {{mapping| 2 0 1 3 7 -1 5 | 0 2 1 1 -2 4 2 | 0 0 2 1 3 2 0 }}

=== Freya
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024
Mapping: {{mapping|legend=1| 1 1 -1 1 5 | 0 2 3 2 1 | 0 0 4 2 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2401/2400, 3025/3024, 4096/4095
Mapping: {{mapping| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}

==== Eir
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 3025/3024
Mapping: {{mapping| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400
Mapping: {{mapping| 1 1 -1 1 5 5 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 -5 12 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199
Mapping: {{mapping| 1 1 -1 1 5 5 -5 3 | 0 2 3 2 1 6 6 -2 | 0 0 4 2 -3 -5 12 3 }}

==== Heimlaug
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 3025/3024
Mapping: {{mapping| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}

=== Vili
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 391314/390625
Mapping: {{mapping|legend=1| 1 1 -1 1 -4 | 0 2 3 2 6 | 0 0 6 3 14 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 4225/4224
Mapping: {{mapping| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}

=== Frigg
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 644204/643125
Mapping: {{mapping|legend=1| 1 1 -7 -2 -7 | 0 2 3 2 4 | 0 0 10 5 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 10648/10647
Mapping: {{mapping| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}

=== Ennealimmic
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374
Mapping: {{mapping|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4375/4374
Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}


= Breedsmic temperaments

=== Tertiaseptal
Subgroup: 2.3.5.7
Comma list: 2401/2400, 65625/65536
Mapping: {{mapping|legend=1| 1 -19 7 0 | 0 22 -5 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 65625/65536
Mapping: {{mapping| 1 -19 7 0 -48 | 0 22 -5 3 55 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 441/440, 625/624, 3584/3575
Mapping: {{mapping| 1 -19 7 0 -48 43 | 0 22 -5 3 55 -42 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575
Mapping: {{mapping| 1 -19 7 0 -48 43 49 | 0 22 -5 3 55 -42 -48 }}

==== Tertia
Subgroup:2.3.5.7.11
Comma list: 385/384, 1331/1323, 1375/1372
Mapping: {{mapping| 1 -19 7 0 -19 | 0 22 -5 3 24 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384, 625/624, 1331/1323
Mapping: {{mapping| 1 -19 7 0 -19 43 | 0 22 -5 3 24 -42 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 385/384, 561/560, 625/624, 715/714
Mapping: {{mapping| 1 -19 7 0 -19 43 49 | 0 22 -5 3 24 -42 -48 }}

==== Tertiaseptia
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 6250/6237, 65625/65536
Mapping: {{mapping| 1 -19 7 0 112 | 0 22 -5 3 -116 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400
Mapping: {{mapping| 1 -19 7 0 112 43 | 0 22 -5 3 -116 -42 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197
Mapping: {{mapping| 1 -19 7 0 112 43 49 | 0 22 -5 3 -116 -42 -48 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 625/624, 833/832, 1156/1155, 1216/1215, 2200/2197
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 | 0 22 -5 3 -116 -42 -48 105 }}

===== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 625/624, 833/832, 875/874, 1105/1104, 1156/1155, 1216/1215
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 | 0 22 -5 3 -116 -42 -48 105 -117 }}

===== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 | 0 22 -5 3 -116 -42 -48 105 -117 -60 }}

===== 31-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 }}

===== 37-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 }}

===== 41-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 -4 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 10 }}

==== Hemitert
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 65625/65536
Mapping: {{mapping| 1 -41 12 -3 -73 | 0 44 -10 6 79 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095
Mapping: {{mapping| 1 -41 12 -3 -73 85 | 0 44 -10 6 79 -84 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095
Mapping: {{mapping| 1 -41 12 -3 -73 85 97| 0 44 -10 6 79 -84 -96 }}

==== Semitert
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 65625/65536
Mapping: {{mapping| 2 -16 9 3 47 | 0 22 -5 3 -46 }}

=== Emmthird
Subgroup: 2.3.5.7
Comma list: 2401/2400, 14348907/14336000
Mapping: {{mapping|legend=1| 1 -3 -17 -8 | 0 14 59 33 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 1792000/1771561
Mapping: {{mapping| 1 -3 -17 -8 -8 | 0 14 59 33 35 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440, 2200/2197
Mapping: {{mapping| 1 -3 -17 -8 -8 -13 | 0 14 59 33 35 51 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 441/440, 595/594, 2200/2197
Mapping: {{mapping| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}

=== Hemififths
Subgroup: 2.3.5.7
Comma list: 2401/2400, 5120/5103
Mapping: {{mapping|legend=1| 1 1 -5 -1 | 0 2 25 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 896/891
Mapping: {{mapping| 1 1 -5 -1 2 | 0 2 25 13 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 243/242, 364/363
Mapping: {{mapping| 1 1 -5 -1 2 4 | 0 2 25 13 5 -1 }}

==== Semihemi
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3388/3375, 5120/5103
Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845, 1716/1715
Mapping: {{mapping| 2 0 -35 -15 -47 -37 | 0 2 25 13 34 28 }}

==== Quadrafifths
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 5120/5103
Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 2401/2400, 3025/3024
Mapping: {{mapping| 1 1 -5 -1 8 10 | 0 4 50 26 -31 -43 }}

==== Cutefourths
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4000/3993, 5120/5103
Mapping: {{mapping| 1 -1 -30 -14 -28 | 0 6 75 39 73 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1575/1573, 2401/2400
Mapping: {{mapping| 1 -1 -30 -14 -28 -20 | 0 6 75 39 73 55 }}

=== Osiris
Subgroup: 2.3.5.7
Comma list: 2401/2400, 31381059609/31360000000
Mapping: {{mapping|legend=1| 1 13 33 21 | 0 32 86 51 }}

=== Quasiorwell
Subgroup: 2.3.5.7
Comma list: 2401/2400, 29360128/29296875
Mapping: {{mapping|legend=1| 1 -7 3 1 | 0 38 -3 8 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 5632/5625
Mapping: {{mapping| 1 -7 3 1 -11 | 0 38 -3 8 64 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095
Mapping: {{mapping| 1 -7 3 1 -11 22 | 0 38 -3 8 64 -81 }}

=== Quinmite
Subgroup: 2.3.5.7
Comma list: 2401/2400, 1959552/1953125
Mapping: {{mapping|legend=1| 1 -7 -5 -3 | 0 34 29 23 }}

=== Newt
Subgroup: 2.3.5.7
Comma list: 2401/2400, 33554432/33480783
Mapping: {{mapping|legend=1| 1 1 19 11 | 0 2 -57 -28 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 19712/19683
Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095
Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}

==== 2.3.5.7.11.13.19 subgroup (neonewt)
Subgroup: 2.3.5.7.11.13.19
Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400
Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}

=== Septidiasemi
Subgroup: 2.3.5.7
Comma list: 2401/2400, 2152828125/2147483648
Mapping: {{mapping|legend=1| 1 -1 6 4 | 0 26 -37 -12 }}

==== Sedia
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 939524096/935859375
Mapping: {{mapping| 1 -1 6 4 -3 | 0 26 -37 -12 65 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 441/440, 2200/2197, 3584/3575
Mapping: {{mapping| 1 -1 6 4 -3 4 | 0 26 -37 -12 65 -3 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
Mapping: {{mapping| 1 -1 6 4 -3 4 2 | 0 26 -37 -12 65 -3 21 }}

=== Subneutral
Subgroup: 2.3.5.7
Comma list: 2401/2400, 274877906944/274658203125
Mapping: {{mapping|legend=1| 1 -41 8 -5 | 0 60 -8 11 }}

=== Maviloid
Subgroup: 2.3.5.7
Comma list: 2401/2400, 1224440064/1220703125
Mapping: {{mapping|legend=1| 1 -21 -22 -15 | 0 52 56 41 }}

=== Lockerbie
Subgroup: 2.3.5.7
Comma list: 2401/2400, {{monzo| 24 13 -18 -1 }}
Mapping: {{mapping|legend=1| 1 -25 -16 -13 | 0 74 51 44 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 766656/765625
Mapping: {{mapping| 1 -25 -16 -13 -26 | 0 74 51 44 82 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 3025/3024, 4225/4224
Mapping: {{mapping| 1 -25 -16 -13 -26 -6 | 0 74 51 44 82 27 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224
Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}

==== 2.3.5.7.11.13.17.41 subgroup
Subgroup: 2.3.5.7.11.13.17.41
Comma list: 616/615, 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224
Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 5 | 0 74 51 44 82 27 42 1 }}

=== Unthirds
Subgroup: 2.3.5.7
Comma list: 2401/2400, 68359375/68024448
Mapping: {{mapping|legend=1| 1 -13 -14 -9 | 0 42 47 34 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 4000/3993
Mapping: {{mapping| 1 -13 -14 -9 -8 | 0 42 47 34 33 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400
Mapping: {{mapping| 1 -13 -14 -9 -8 -47 | 0 42 47 34 33 146 }}

=== Neominor
Subgroup: 2.3.5.7
Comma list: 2401/2400, 177147/175616
Mapping: {{mapping|legend=1| 1 -3 -29 -14 | 0 6 41 22 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 35937/35840
Mapping: {{mapping| 1 -3 -29 -14 -8 | 0 6 41 22 15 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 243/242, 364/363, 441/440
Mapping: {{mapping| 1 -3 -29 -14 -8 -7 | 0 6 41 22 15 14 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 243/242, 273/272, 364/363
Mapping: {{mapping| 1 -3 -29 -14 -8 -7 -28 | 0 6 41 22 15 14 42 }}

=== Catafourth
Subgroup: 2.3.5.7
Comma list: 2401/2400, 78732/78125
Mapping: {{mapping|legend=1| 1 -15 -19 -12 | 0 28 36 25 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 78408/78125
Mapping: {{mapping| 1 -15 -19 -12 -38 | 0 28 36 25 70 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 441/440, 10985/10976
Mapping: {{mapping| 1 -15 -19 -12 -38 -4 | 0 28 36 25 70 13 }}

=== Cotritone
Subgroup: 2.3.5.7
Comma list: 2401/2400, 390625/387072
Mapping: {{mapping|legend=1| 1 -13 -4 -4 | 0 30 13 14 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 4000/3993
Mapping: {{mapping| 1 -13 -4 -4 2 | 0 30 13 14 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 364/363, 385/384, 625/624
Mapping: {{mapping| 1 -13 -4 -4 2 -7 | 0 30 13 14 3 22 }}

=== Fibo
Subgroup: 2.3.5.7
Comma list: 2401/2400, 341796875/339738624
Mapping: {{mapping|legend=1| 1 -27 -7 -9 | 0 46 15 19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 43923/43750
Mapping: {{mapping| 1 -27 -7 -9 -4 | 0 46 15 19 12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624, 847/845, 1375/1372
Mapping: {{mapping| 1 -27 -7 -9 -4 -5 | 0 46 15 19 12 14 }}

=== Quasimoha
Subgroup: 2.3.5.7
Comma list: 2401/2400, 3645/3584
Mapping: {{mapping|legend=1| 1 1 9 6 | 0 2 -23 -11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 1815/1792
Mapping: {{mapping| 1 1 9 6 2 | 0 2 -23 -11 5 }}

=== Mintone
Subgroup: 2.3.5.7
Comma list: 2401/2400, 177147/175000
Mapping: {{mapping|legend=1| 1 -17 -34 -20 | 0 22 43 27 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 43923/43750
Mapping: {{mapping| 1 -17 -34 -20 -43 | 0 22 43 27 55 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 441/440, 847/845
Mapping: {{mapping| 1 -17 -34 -20 -43 -36 | 0 22 43 27 55 47 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 351/350, 441/440, 561/560, 847/845
Mapping: {{mapping| 1 -17 -34 -20 -43 -36 10 | 0 22 43 27 55 47 -7 }}

=== Gorgik
Subgroup: 2.3.5.7
Comma list: 2401/2400, 28672/28125
Mapping: {{mapping|legend=1| 1 -13 8 2 | 0 18 -7 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 2401/2400, 2560/2541
Mapping: {{mapping| 1 -13 8 2 14 | 0 18 -7 1 -13 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 196/195, 364/363, 512/507
Mapping: {{mapping| 1 -13 8 2 14 11 | 0 18 -7 1 -13 -9 }}

=== Hemigoldis
Subgroup: 2.3.5.7
Comma list: 2401/2400, 549755813888/533935546875
Mapping: {{mapping|legend=1| 1 21 -9 2 | 0 24 -14 -1 }}

=== Surmarvelpyth
Subgroup: 2.3.5.7
Comma list: 2401/2400, {{monzo| 93 -32 -17 -1 }}
Mapping: {{mapping|legend=1| 1 -27 55 22 | 0 70 -129 -47 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 820125/819896, 2097152/2096325
Mapping: {{mapping| 1 -27 55 22 -19 | 0 70 -129 -47 55 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167
Mapping: {{mapping| 1 -27 55 22 -19 -11 | 0 70 -129 -47 55 36 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619
Mapping: {{mapping| 1 -27 55 22 -19 -11 78 | 0 70 -129 -47 55 36 -181 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984
Mapping: {{mapping| 1 -27 55 22 -19 -11 78 41 | 0 70 -129 -47 55 36 -181 -90 }}

=== References


= Bug family

=== Bug
Subgroup: 2.3.5
Comma list: 27/25
Mapping: {{mapping|legend=1| 1 0 0 | 0 -2 -3 }}

==== Overview to extensions

=== Beep
Subgroup: 2.3.5.7
Comma list: 21/20, 27/25
Mapping: {{mapping|legend=1| 1 0 0 2 | 0 2 3 1 }}

==== Pentoid
Subgroup: 2.3.5.7.11
Comma list: 21/20, 27/25, 33/32
Mapping: {{mapping| 1 0 0 2 5 | 0 2 3 1 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 21/20, 26/25, 27/25, 33/32
Mapping: {{mapping| 1 0 0 2 5 -1 | 0 2 3 1 -2 6 }}

==== Pento
Subgroup: 2.3.5.7.11
Comma list: 21/20, 27/25, 45/44
Mapping: {{mapping| 1 0 0 2 -2 | 0 2 3 1 7 }}

=== Mite
Subgroup: 2.3.5.7
Comma list: 27/25, 28/25
Mapping: {{mapping|legend=1| 1 0 0 -2 | 0 2 3 6 }}


= Cataharry family

=== Cataharry
Subgroup: 2.3.5.7
Comma list: [[19683/19600]]
Mapping: {{mapping|legend=1| 1 0 0 -2 | 0 2 0 9 | 0 0 1 -1 }}

=== Albus
Subgroup: 2.3.5.7.11
Comma list: 540/539, 8019/8000
Mapping: {{mapping|legend=1| 1 0 0 -2 6 | 0 2 0 9 -12 | 0 0 1 -1 3 }}

==== Madagascar
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675
Mapping: {{mapping| 1 0 0 -2 6 -1 | 0 2 0 9 -12 3 | 0 0 1 -1 3 1 }}
Mapping to lattice: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]

=== Snape
Subgroup: 2.3.5.7.11
Comma list: 441/440, 19683/19600
Mapping: {{mapping|legend=1| 1 0 0 -2 -7 | 0 2 0 9 22 | 0 0 1 -1 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 676/675
Mapping: {{mapping| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 0 0 1 -1 -3 1 }}

=== Hagrid
Subgroup: 2.3.5.7.11
Comma list: 243/242, 9801/9800
Mapping: {{mapping|legend=1| 2 0 0 -4 -1 | 0 2 0 9 5 | 0 0 1 -1 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 364/363
Mapping: {{mapping| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 0 0 1 -1 0 1 }}

=== Draco
Subgroup: 2.3.5.7.11
Comma list: 176/175, 19683/19600
Mapping: {{mapping|legend=1| 1 0 0 -2 -6 | 0 2 0 9 9 | 0 0 1 -1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 676/675
Mapping: {{mapping| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 0 0 1 -1 1 1 }}


= Cataharry temperaments

=== Swetneus
Subgroup: 2.3.5.7
Comma list: 19683/19600, 50421/50000
Mapping: {{mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375, 19683/19600
Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 676/675, 847/845
Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}

=== Majvamoid
Subgroup: 2.3.5.7
Comma list: 19683/19600, 29360128/29296875
Mapping: {{mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 19683/19600
Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 676/675, 1573/1568, 4225/4224
Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224
Mapping: {{mapping| 1 10 5 38 31 19 6 | 0 -22 -7 -92 -72 -40 -5 }}


= Diaschismic family

=== Diaschismic
Subgroup: 2.3.5
Comma list: 2048/2025
Mapping: {{mapping|legend=1| 2 0 11 | 0 1 -2 }}

==== Overview to extensions

===== 7-limit extensions

===== Subgroup extensions

==== Srutal archagall
Subgroup: 2.3.5.17
Comma list: 136/135, 256/255
Mapping: {{mapping| 2 0 11 5 | 0 1 -2 1 }}

=== Septimal diaschismic
Subgroup: 2.3.5.7
Comma list: 126/125, 2048/2025
Mapping: {{mapping|legend=1| 2 0 11 31 | 0 1 -2 -8 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 896/891
Mapping: {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 364/363
Mapping: {{mapping| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 136/135, 176/175, 196/195, 256/255
Mapping: {{mapping| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}

==== 2.3.5.7.11.13.17.23 subgroup (Na"Naa')
Subgroup: 2.3.5.7.11.13.17.23
Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255
Mapping: {{mapping| 2 0 11 31 45 55 5 63 | 0 1 -2 -8 -12 -15 1 -17 }}

=== Pajara
Subgroup: 2.3.5.7
Comma list: 50/49, 64/63
Mapping: {{mapping|legend=1| 2 0 11 12 | 0 1 -2 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 64/63, 99/98
Mapping: {{mapping| 2 0 11 12 26 | 0 1 -2 -2 -6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 64/63, 65/63, 99/98
Mapping: {{mapping| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 52/51, 64/63, 65/63, 99/98
Mapping: {{mapping| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }}

===== Pajarina
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 64/63, 78/77, 99/98
Mapping: {{mapping| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 64/63, 78/77, 85/84, 99/98
Mapping: {{mapping| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }}

===== Pajarita
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 50/49, 64/63, 66/65
Mapping: {{mapping| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 40/39, 50/49, 64/63, 66/65, 85/84
Mapping: {{mapping| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }}

==== Pajarous
Subgroup: 2.3.5.7.11
Comma list: 50/49, 55/54, 64/63
Mapping: {{mapping| 2 0 11 12 -9 | 0 1 -2 -2 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 55/54, 64/63, 65/63
Mapping: {{mapping| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 52/51, 55/54, 64/63, 65/63
Mapping: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}

===== Pajaro
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 50/49, 55/54, 64/63
Mapping: {{mapping| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 40/39, 50/49, 55/54, 64/63, 85/84
Mapping: {{mapping| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }}

==== Pajaric
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 56/55
Mapping: {{mapping| 2 0 11 12 7 | 0 1 -2 -2 0 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 45/44, 50/49, 56/55
Mapping: {{mapping| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 34/33, 40/39, 45/44, 50/49, 56/55
Mapping: {{mapping| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }}

==== Hemipaj
Subgroup: 2.3.5.7.11
Comma list: 50/49, 64/63, 121/120
Mapping: {{mapping| 2 1 9 10 8 | 0 2 -4 -4 -1 }}

==== Hemifourths
Subgroup: 2.3.5.7.11
Comma list: 50/49, 64/63, 243/242
Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 64/63, 78/77, 144/143
Mapping: {{mapping| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 64/63, 78/77, 85/84, 144/143
Mapping: {{mapping| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }}

=== Srutal
Subgroup: 2.3.5.7
Comma list: 2048/2025, 4375/4374
Mapping: {{mapping|legend=1| 2 0 11 -42 | 0 1 -2 15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 896/891, 1331/1323
Mapping: {{mapping| 2 0 11 -42 -28 | 0 1 -2 15 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 176/175, 325/324, 364/363
Mapping: {{mapping| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 169/168, 176/175, 221/220, 256/255
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 136/135, 169/168, 176/175, 190/189, 221/220, 256/255
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}

===== Srutaloo
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 256/255
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }}

====== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 232/231, 256/255
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }}

====== 31-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 217/216, 221/220, 232/231, 256/255
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 48 | 0 1 -2 15 11 8 1 20 6 27 -12 }}

=== Keen
Subgroup: 2.3.5.7
Comma list: 875/864, 2048/2025
Mapping: {{mapping|legend=1| 2 0 11 -23 | 0 1 -2 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1232/1215
Mapping: {{mapping| 2 0 11 -23 26 | 0 1 -2 9 -6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 1078/1053
Mapping: {{mapping| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 119/117, 144/143, 154/153
Mapping: {{mapping| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 1}}

===== Keenic
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 100/99, 352/351, 385/384
Mapping: {{mapping| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 100/99, 136/135, 154/153, 256/255
Mapping: {{mapping| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }}

=== Bidia
Subgroup: 2.3.5.7
Comma list: 2048/2025, 3136/3125
Mapping: {{mapping|legend=1| 4 0 22 43 | 0 1 -2 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 896/891, 1375/1372
Mapping: {{mapping| 4 0 22 43 71 | 0 1 -2 -5 -9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 325/324, 640/637, 896/891
Mapping: {{mapping| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 176/175, 256/255, 325/324, 640/637
Mapping: {{mapping| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 136/135, 176/175, 190/189, 256/255, 325/324, 640/637
Mapping: {{mapping| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 136/135, 176/175, 190/189, 253/252, 256/255, 325/324, 640/637
Mapping: {{mapping| 4 0 22 43 71 -36 10 17 -20 | 0 1 -2 -5 -9 8 1 0 6 }}

=== Shrutar
Subgroup: 2.3.5.7
Comma list: 245/243, 2048/2025
Mapping: {{mapping|legend=1| 2 1 9 -2 | 0 2 -4 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 245/243
Mapping: {{mapping| 2 1 9 -2 8 | 0 2 -4 7 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 196/195, 245/243
Mapping: {{mapping| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 136/135, 154/153, 176/175, 196/195
Mapping: {{mapping| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342
Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}

===== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 253/252, 343/342
Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 -4 | 0 2 -4 7 -1 16 2 17 12 }}

=== Shru
Subgroup: 2.3.5.7
Comma list: 392/375, 1323/1280
Mapping: {{mapping|legend=1| 2 1 9 11 | 0 2 -4 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 77/75, 1323/1280
Mapping: {{mapping| 2 1 9 11 8 | 0 2 -4 -5 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 77/75, 105/104, 507/500
Mapping: {{mapping| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}

=== Sruti
Subgroup: 2.3.5.7
Comma list: 2048/2025, 19683/19600
Mapping: {{mapping|legend=1| 2 0 11 -15 | 0 2 -4 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 243/242, 896/891
Mapping: {{mapping| 2 0 11 -15 -1 | 0 2 -4 13 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 351/350, 676/675
Mapping: {{mapping| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 144/143, 170/169, 176/175, 221/220
Mapping: {{mapping| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}

=== Anguirus
Subgroup: 2.3.5.7
Comma list: 49/48, 2048/2025
Mapping: {{mapping|legend=1| 2 0 11 4 | 0 2 -4 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 243/242
Mapping: {{mapping| 2 0 11 4 -1 | 0 2 -4 1 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 91/90, 243/242
Mapping: {{mapping| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 49/48, 56/55, 91/90, 119/117, 154/153
Mapping: {{mapping| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}

=== Echidna
Subgroup: 2.3.5.7
Comma list: 1728/1715, 2048/2025
Mapping: {{mapping|legend=1| 2 1 9 2 | 0 3 -6 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 896/891
Mapping: {{mapping| 2 1 9 2 12 | 0 3 -6 5 -7 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 364/363, 540/539
Mapping: {{mapping| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 176/175, 221/220, 256/255, 540/539
Mapping: {{mapping| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}

=== Echidnic
Subgroup: 2.3.5.7
Comma list: 686/675, 1029/1024
Mapping: {{mapping|legend=1| 2 2 7 6 | 0 3 -6 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 686/675
Mapping: {{mapping| 2 2 7 6 3 | 0 3 -6 -1 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 169/168, 385/384, 441/440
Mapping: {{mapping| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 136/135, 154/153, 169/168, 256/255
Mapping: {{mapping| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}

=== Quadrasruta
Subgroup: 2.3.5.7
Comma list: 2048/2025, 2401/2400
Mapping: {{mapping|legend=1| 2 0 11 8 | 0 4 -8 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 896/891, 2401/2400
Mapping: {{mapping| 2 0 11 8 22 | 0 4 -8 -3 -19 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 196/195, 512/507, 676/675
Mapping: {{mapping| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 170/169, 176/175, 196/195, 256/255
Mapping: {{mapping| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }}

==== Quadrafourths
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 2048/2025
Mapping: {{mapping| 2 0 11 8 -1 | 0 4 -8 -3 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 243/242, 676/675
Mapping: {{mapping| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 144/143, 170/169, 196/195, 221/220
Mapping: {{mapping| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }}


= Diaschismic rank-3 family

=== Rank-3 diaschismic
Subgroup: 2.3.5.7
Comma list: [[2048/2025]]
Mapping: {{mapping|legend=1| 2 0 11 0 | 0 1 -2 0 | 0 0 0 1 }}

=== Varda
Subgroup: 2.3.5.7.11
Comma list: 176/175, 896/891
Mapping: {{mapping|legend=1| 2 0 11 0 14 | 0 1 -2 0 -4 | 0 0 0 1 1 }}
Mapping to lattice: [{{val| 0 1 -2 2 -2 }}, {{val| 0 0 0 -1 -1 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 364/363
Mapping: {{mapping| 2 0 11 0 14 24 | 0 1 -2 0 -4 -7 | 0 0 0 1 1 1 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 176/175, 256/255, 351/350
Mapping: {{mapping| 2 0 11 0 14 24 5 | 0 1 -2 0 -4 -7 1 | 0 0 0 1 1 1 0 }}

==== Julius
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 325/324, 896/891
Mapping: {{mapping| 2 0 11 0 14 -18 | 0 1 -2 0 -4 8 | 0 0 0 1 1 0 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 176/175, 256/255, 325/324
Mapping: {{mapping| 2 0 11 0 14 -18 5 | 0 1 -2 0 -4 8 1 | 0 0 0 1 1 0 0 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 136/135, 176/175, 190/189, 256/255, 286/285
Mapping: {{mapping| 2 0 11 0 14 -18 5 -13 | 0 1 -2 0 -4 8 1 5 | 0 0 0 1 1 0 0 1 }}

=== Augustus
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1232/1215
Mapping: {{mapping|legend=1| 2 0 11 0 3 | 0 1 -2 0 3 | 0 0 0 1 -1 }}

=== Tiberius
Subgroup: 2.3.5.7.11
Comma list: 441/440, 2048/2025
Mapping: {{mapping|legend=1| 2 0 11 0 -17 | 0 1 -2 0 4 | 0 0 0 1 2 }}

=== Claudius
Subgroup: 2.3.5.7.11
Comma list: 540/539, 2048/2025
Mapping: {{mapping|legend=1| 2 0 11 0 15 | 0 1 -2 0 1 | 0 0 0 1 -2 }}


= Dicot family

=== Dicot
Subgroup: 2.3.5
Comma list: 25/24
Mapping: {{mapping|legend=1| 1 1 2 | 0 2 1 }}

==== Overview to extensions

===== 7-limit extensions

===== Subgroup extensions

==== Dicot (2.3.5.11 subgroup)
Subgroup: 2.3.5.11
Comma list: 25/24, 45/44
Mapping: {{mapping| 1 1 2 2 | 0 2 1 5 }}

===== 2.3.5.11.13 subgroup
Subgroup: 2.3.5.11.13
Comma list: 25/24, 40/39, 45/44
Mapping: {{mapping| 1 1 2 2 4 | 0 2 1 5 -1 }}

==== Eudicot (2.3.5.11 subgroup)
Subgroup: 2.3.5.11
Comma list: 25/24, 33/32
Mapping: {{mapping| 1 1 2 4 | 0 2 1 -2 }}

===== 2.3.5.11.13 subgroup
Subgroup: 2.3.5.11.13
Comma list: 25/24, 33/32, 40/39
Mapping: {{mapping| 1 1 2 4 4 | 0 2 1 -2 -1 }}

=== Septimal dicot
Subgroup: 2.3.5.7
Comma list: 15/14, 25/24
Mapping: {{mapping|legend=1| 1 1 2 2 | 0 2 1 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 15/14, 22/21, 25/24
Mapping: {{mapping| 1 1 2 2 2 | 0 2 1 3 5 }}

==== Eudicot
Subgroup: 2.3.5.7.11
Comma list: 15/14, 25/24, 33/32
Mapping: {{mapping| 1 1 2 2 4 | 0 2 1 3 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 15/14, 25/24, 33/32, 40/39
Mapping: {{mapping| 1 1 2 2 4 4 | 0 2 1 3 -2 -1 }}

=== Flattie
Subgroup: 2.3.5.7
Comma list: 21/20, 25/24
Mapping: {{mapping|legend=1| 1 1 2 3 | 0 2 1 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 21/20, 25/24, 33/32
Mapping: {{mapping| 1 1 2 3 4 | 0 2 1 -1 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 14/13, 21/20, 25/24, 33/32
Mapping: {{mapping| 1 1 2 3 4 4 | 0 2 1 -1 -2 -1 }}

=== Sharpie
Subgroup: 2.3.5.7
Comma list: 25/24, 28/27
Mapping: {{mapping|legend=1| 1 1 2 1 | 0 2 1 6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 28/27, 35/33
Mapping: {{mapping| 1 1 2 1 2 | 0 2 1 6 5 }}

=== Dichotic
Subgroup: 2.3.5.7
Comma list: 25/24, 64/63
Mapping: {{mapping|legend=1| 1 1 2 4 | 0 2 1 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 64/63
Mapping: {{mapping| 1 1 2 4 2 | 0 2 1 -4 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 40/39, 45/44, 64/63
Mapping: {{mapping| 1 1 2 4 2 4 | 0 2 1 -4 5 -1 }}

==== Dichotomic
Subgroup: 2.3.5.7.11
Comma list: 22/21, 25/24, 33/32
Mapping: {{mapping| 1 1 2 4 4 | 0 2 1 -4 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 22/21, 25/24, 33/32, 40/39
Mapping: {{mapping| 1 1 2 4 4 4 | 0 2 1 -4 -2 -1 }}

==== Dichosis
Subgroup: 2.3.5.7.11
Comma list: 25/24, 35/33, 64/63
Mapping: {{mapping| 1 1 2 4 5 | 0 2 1 -4 -5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 35/33, 40/39, 64/63
Mapping: {{mapping| 1 1 2 4 5 4 | 0 2 1 -4 -5 -1 }}

=== Decimal
Subgroup: 2.3.5.7
Comma list: 25/24, 49/48
Mapping: {{mapping|legend=1| 2 0 3 4 | 0 2 1 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 49/48
Mapping: {{mapping| 2 0 3 4 -1 | 0 2 1 1 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 45/44, 49/48, 91/90
Mapping: {{mapping| 2 0 3 4 -1 1| 0 2 1 1 5 4}}

==== Decimated
Subgroup: 2.3.5.7.11
Comma list: 25/24, 33/32, 49/48
Mapping: {{mapping| 2 0 3 4 10 | 0 2 1 1 -2 }}

==== Decibel
Subgroup: 2.3.5.7.11
Comma list: 25/24, 35/33, 49/48
Mapping: {{mapping| 2 0 3 4 7 | 0 2 1 1 0 }}

=== Sidi
Subgroup: 2.3.5.7
Comma list: 25/24, 245/243
Mapping: {{mapping|legend=1| 1 -1 1 -3 | 0 4 2 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 99/98
Mapping: {{mapping| 1 -1 1 -3 -3 | 0 4 2 9 10 }}

=== Sida
Subgroup: 2.3.5.7
Comma list: 25/24, 1323/1280
Mapping: {{mapping|legend=1| 1 -1 1 6 | 0 4 2 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 33/32, 245/242
Mapping: {{mapping| 1 3 3 1 2 | 0 -4 -2 5 4 }}


= Didymus rank-3 family

=== Didymus
Subgroup: 2.3.5.7
Comma list: 81/80
Mapping: {{mapping|legend=1| 1 0 -4 0 | 0 1 4 0 | 0 0 0 1 }}

=== Euterpe
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98
Mapping: {{mapping|legend=1| 1 0 -4 0 1 | 0 1 4 0 -2 | 0 0 0 1 2 }}

=== Clio
Subgroup: 2.3.5.7.11
Comma list: 81/80, 176/175
Mapping: {{mapping|legend=1| 1 0 -4 0 -12 | 0 1 4 0 8 | 0 0 0 1 1 }}

=== Terpsichore
Subgroup: 2.3.5.7.11
Comma list: 81/80, 540/539
Mapping: {{mapping|legend=1| 1 0 -4 0 -2 | 0 1 4 0 7 | 0 0 0 1 -2 }}

=== Polyhymnia
Subgroup: 2.3.5.7.11
Comma list: 81/80, 385/384
Mapping: {{mapping|legend=1| 1 0 -4 0 11 | 0 1 4 0 -3 | 0 0 0 1 -1 }}

=== Calliope
Subgroup: 2.3.5.7.11
Comma list: 45/44, 81/80
Mapping: {{mapping|legend=1| 1 0 -4 0 -6 | 0 1 4 0 6 | 0 0 0 1 0 }}

=== Thalia
Subgroup: 2.3.5.7.11
Comma list: 33/32, 55/54
Mapping: {{mapping|legend=1| 1 0 -4 0 5 | 0 1 4 0 -1 | 0 0 0 1 0 }}

=== Melpomene
Subgroup: 2.3.5.7.11
Comma list: 56/55, 81/80
Mapping: {{mapping|legend=1| 1 0 -4 0 7 | 0 1 4 0 -4 | 0 0 0 1 1 }}

=== Erato
Subgroup: 2.3.5.7.11
Comma list: 81/80, 126/125
Mapping: {{mapping|legend=1| 1 0 -4 -13 0 | 0 1 4 10 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 105/104, 126/125
Mapping: {{mapping| 1 0 -4 -13 0 -20 | 0 1 4 10 0 15 | 0 0 0 0 1 0 }}

=== References


= Dimcomp family

=== Dimcomp
Subgroup: 2.3.5.7
Comma list: 390625/388962
Mapping: {{mapping|legend=1| 4 0 0 -1 | 0 1 0 -1 | 0 0 1 2 }}

=== Undecimal dimcomp
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 6250/6237
Mapping: {{mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1375/1372, 2080/2079
Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}

=== Octopod
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 1375/1372, 4000/3993
Mapping: {{mapping|legend=1| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }}


= Diminished family

=== Diminished
Subgroup: 2.3.5
Comma list: 648/625
Mapping: {{mapping|legend=1| 4 0 3 | 0 1 1 }}

=== Septimal diminished
Subgroup: 2.3.5.7
Comma list: 36/35, 50/49
Mapping: {{mapping|legend=1| 4 0 3 5 | 0 1 1 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 50/49, 56/55
Mapping: {{mapping| 4 0 3 5 14 | 0 1 1 1 0 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 40/39, 50/49, 66/65
Mapping: {{mapping| 4 0 3 5 14 15 | 0 1 1 1 0 0 }}

==== Demolished
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 50/49
Mapping: {{mapping| 4 0 3 5 -5 | 0 1 1 1 3 }}

==== Cohedim
Subgroup: 2.3.5.7.11
Comma list: 36/35, 50/49, 125/121
Mapping: {{mapping| 4 1 4 6 6 | 0 2 2 2 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 50/49, 66/65, 125/121
Mapping: {{mapping| 4 1 4 6 6 7 | 0 2 2 2 3 3 }}

=== Hemidim
Subgroup: 2.3.5.7
Comma list: 49/48, 648/625
Mapping: {{mapping|legend=1| 4 0 3 8 | 0 2 2 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 77/75, 243/242
Mapping: {{mapping| 4 0 3 8 -2 | 0 2 2 1 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 77/75, 243/242
Mapping: {{mapping| 4 0 3 8 -2 -1 | 0 2 2 1 5 5 }}

=== Octonion
Subgroup: 2.3.5.7
Comma list: 245/243, 392/375
Mapping: {{mapping|legend=1| 8 0 6 -3 | 0 1 1 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 77/75, 245/243
Mapping: {{mapping| 8 0 6 -3 15 | 0 1 1 2 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 66/65, 77/75, 507/500
Mapping: {{mapping| 8 0 6 -3 15 17 | 0 1 1 2 1 1 }}

=== Subgroup extensions

==== Diminished (2.3.5.17 subgroup)
Subgroup: 2.3.5.17
Comma list: 51/50, 289/288
Mapping: {{mapping|legend=2| 4 0 3 10 | 0 1 1 1 }}

==== Diminished (2.3.5.19 subgroup)
Subgroup: 2.3.5.19
Comma list: 96/95, 513/500
Mapping: {{mapping|legend=2| 4 0 3 17 | 0 1 1 0 }}


= Ditonmic family

=== Ditonic
Subgroup: 2.3.5
Comma list: 1220703125/1207959552
Mapping: {{mapping|legend=1| 1 6 3 | 0 -13 -2 }}

=== Coditone
Subgroup: 2.3.5.7
Comma list: 225/224, 2125764/2100875
Mapping: {{mapping|legend=1| 1 6 3 13 | 0 -13 -2 -30 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 78408/78125
Mapping: {{mapping| 1 6 3 13 -3 | 0 -13 -2 -30 19 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 385/384, 847/845
Mapping: {{mapping| 1 6 3 13 -3 2 | 0 -13 -2 -30 19 5 }}

==== Coditonic
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 6655/6561
Mapping: {{mapping| 1 6 3 13 15 | 0 -13 -2 -30 -34 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 325/324, 847/845
Mapping: {{mapping| 1 6 3 13 15 20 | 0 -13 -2 -30 -34 -48 }}

=== Diton
Subgroup: 2.3.5.7
Comma list: 126/125, 8751645/8388608
Mapping: {{mapping|legend=1| 1 6 3 -4 | 0 -13 -2 20 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 2079/2048
Mapping: {{mapping| 1 6 3 -4 -3 | 0 -13 -2 20 19 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 126/125, 245/242, 1287/1280
Mapping: {{mapping| 1 6 3 -4 -3 2 | 0 -13 -2 20 19 5 }}

=== Notes


= Escapade family

=== Escapade

==== 5-limit
Subgroup: 2.3.5
Comma list: 4294967296/4271484375 ({{monzo|32 -7 -9}})
Mapping: {{mapping|legend=1| 1 2 2 | 0 -9 7 }}

==== 2.3.5.11 subgroup
Subgroup: 2.3.5.11
Comma list: 4000/3993 ({{monzo|5 -1 3 -3}}), 5632/5625 ({{monzo|9 -2 -4 1}})
Mapping: {{mapping| 1 2 2 3 | 0 -9 7 10 }}

==== 2.3.5.11.31 subgroup
Subgroup: 2.3.5.11.31
Comma list: 496/495 ({{monzo| 4 -2 -1 -1 1 }}), 961/960 ({{monzo| -6 -1 -1 0 2 }}), 4000/3993 ({{monzo| 5 -1 3 -3 0 }})
Mapping: {{mapping| 1 2 2 3 5 | 0 -9 7 10 -1 }}

== Strong extensions

=== Escaped

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 245/243, 65625/65536
Mapping: {{mapping|legend=1| 1 2 2 4 | 0 -9 7 -26 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 4000/3993
Mapping: {{mapping| 1 2 2 4 3 | 0 -9 7 -26 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 245/243, 352/351, 385/384, 625/624
Mapping: {{mapping| 1 2 2 4 3 2 | 0 -9 7 -26 10 37 }}

=== Alphaquarter

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 5120/5103, 29360128/29296875
Mapping: {{mapping|legend=1| 1 2 2 0 | 0 -9 7 61 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 5120/5103
Mapping: {{mapping| 1 2 2 0 3 | 0 -9 7 61 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 625/624, 847/845, 1575/1573
Mapping: {{mapping| 1 2 2 0 3 2 | 0 -9 7 61 10 37 }}

=== Escapist

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 225/224, 12288/12005
Mapping: {{mapping|legend=1| 1 2 2 3 | 0 -9 7 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 2560/2541
Mapping: {{mapping| 1 2 2 3 3 | 0 -9 7 -4 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 99/98, 176/175, 507/500
Mapping: {{mapping| 1 2 2 3 3 3 | 0 -9 7 -4 10 15 }}

== Weak extensions

=== Septisuperfourth

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 6144/6125, 118098/117649
Mapping: {{mapping|legend=1| 2 4 4 7 | 0 -9 7 -15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 5632/5625
Mapping: {{mapping| 2 4 4 7 6 | 0 -9 7 -15 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573, 3584/3575
Mapping: {{mapping| 2 4 4 7 6 11 | 0 -9 7 -15 10 -39 }}

===== Septisuperquad
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539, 4096/4095
Mapping: {{mapping| 2 4 4 7 6 5 | 0 -9 7 -15 10 26 }}

=== Arch

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 3136/3125, 5250987/5242880
Mapping: {{mapping|legend=1| 1 2 2 2 | 0 -18 14 35 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 4000/3993
Mapping: {{mapping| 1 2 2 2 3 | 0 -18 14 35 20 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 676/675, 3136/3125
Mapping: {{mapping| 1 2 2 2 3 4 | 0 -18 14 35 20 -13 }}


= Father family

=== Father
Subgroup: 2.3.5
Comma list: 16/15
Mapping: {{mapping|legend=1| 1 0 4 | 0 1 -1 }}

==== Overview to extensions

=== Septimal father
Subgroup: 2.3.5.7
Comma list: 16/15, 28/27
Mapping: {{mapping|legend=1| 1 0 4 -2 | 0 1 -1 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 28/27
Mapping: {{mapping| 1 0 4 -2 -3 | 0 1 -1 3 4 }}

=== Mother
Subgroup: 2.3.5.7
Comma list: 16/15, 21/20
Mapping: {{mapping|legend=1| 1 0 4 6 | 0 1 -1 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 11/10, 16/15, 21/20
Mapping: {{mapping| 1 0 4 6 5 | 0 1 -1 -2 -1 }}

=== Pater
Subgroup: 2.3.5.7
Comma list: 16/15, 126/125
Mapping: {{mapping|legend=1| 1 0 4 11 | 0 1 -1 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 100/99
Mapping: {{mapping| 1 0 4 11 10 | 0 1 -1 -5 -4 }}


= Fifive family

=== Fifive
Subgroup: 2.3.5
Comma list: 9765625/9565938
Mapping: {{mapping|legend=1| 2 2 3 | 0 5 7 }}

==== 2.3.5.13 subgroup
Subgroup: 2.3.5.13
Comma list: 325/324, 20000/19773
Mapping: {{mapping| 2 2 3 6 | 0 5 7 6 }}

==== 2.3.5.13.17 subgroup
Subgroup: 2.3.5.13.17
Comma list: 170/169, 289/288, 325/324
Mapping: {{mapping| 2 2 3 6 7 | 0 5 7 6 5 }}

=== Crepuscular
Subgroup: 2.3.5.7
Comma list: 50/49, 4375/4374
Mapping: {{mapping|legend=1| 2 2 3 4 | 0 5 7 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98, 864/847
Mapping: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 78/77, 99/98, 144/143
Mapping: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 78/77, 85/84, 99/98, 144/143
Mapping: {{mapping| 2 2 3 4 6 6 7 | 0 5 7 7 4 6 5 }}

=== Fifives
Subgroup: 2.3.5.7
Comma list: 875/864, 83349/81920
Mapping: {{mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 3969/3872
Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 1352/1331
Mapping: {{mapping| 2 2 3 7 6 6 | 0 5 7 -6 4 6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 144/143, 170/169, 221/220
Mapping: {{mapping| 2 2 3 7 6 6 7 | 0 5 7 -6 4 6 5 }}

=== Fourfives
Subgroup: 2.3.5.7
Comma list: 245/243, 235298/234375
Mapping: {{mapping|legend=1| 4 4 6 7 | 0 5 7 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 235298/234375
Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 385/384, 20000/19773
Mapping: {{mapping| 4 4 6 7 19 12 | 0 5 7 9 -11 6 }}

==== Quadrafives
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 1375/1372
Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 196/195, 245/243, 275/273
Mapping: {{mapping| 4 4 6 7 11 12 | 0 5 7 9 6 6 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 170/169, 196/195, 245/243
Mapping: {{mapping| 4 4 6 7 11 12 14 | 0 5 7 9 6 6 5 }}

=== Notes


= Gamelismic clan

=== Slendric
Subgroup: 2.3.7
Comma list: 1029/1024
Mapping: {{mapping|legend=2| 1 1 3 | 0 3 -1 }}
Mapping: {{mapping|legend=3| 1 1 0 3 | 0 3 0 -1 }}

==== Overview to extensions

===== Full 7-limit extensions

===== Subgroup extensions

==== Radon
Subgroup: 2.3.7.11
Comma list: 896/891, 1029/1024
Mapping: {{mapping| 1 1 3 6 | 0 3 -1 -13 }}

=== Mothra
Subgroup: 2.3.5.7
Comma list: 81/80, 1029/1024
Mapping: {{mapping|legend=1| 1 1 0 3 | 0 3 12 -1 }}

==== Undecimal mothra
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98, 385/384
Mapping: {{mapping| 1 1 0 3 5 | 0 3 12 -1 -8 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 99/98, 105/104, 144/143
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 99/98, 105/104, 120/119, 144/143
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 16 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 99/98, 105/104, 120/119, 144/143, 153/152
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 16 22 }}

==== Mosura
Subgroup: 2.3.5.7.11
Comma list: 81/80, 176/175, 540/539
Mapping: {{mapping| 1 1 0 3 -1 | 0 3 12 -1 23 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 144/143, 176/175, 196/195
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 144/143, 176/175, 189/187, 196/195
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 -15 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 96/95, 144/143, 153/152, 176/175, 196/195
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 -15 -9 }}

==== Cyndra
Subgroup: 2.3.5.7.11
Comma list: 45/44, 81/80, 1029/1024
Mapping: {{mapping| 1 1 0 3 0 | 0 3 12 -1 18 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 78/77, 81/80, 640/637
Mapping: {{mapping| 1 1 0 3 0 1 | 0 3 12 -1 18 14 }}

=== Rodan
Subgroup: 2.3.5.7
Comma list: 245/243, 1029/1024
Mapping: {{mapping|legend=1| 1 1 -1 3 | 0 3 17 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 441/440
Mapping: {{mapping| 1 1 -1 3 6 | 0 3 17 -1 -13 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 352/351, 364/363
Mapping: {{mapping| 1 1 -1 3 6 8 | 0 3 17 -1 -13 -22 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 154/153, 196/195, 245/243, 256/255, 273/272
Mapping: {{mapping| 1 1 -1 3 6 8 8 | 0 3 17 -1 -13 -22 -20 }}

===== Aerodactyl
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 245/243, 385/384, 441/440
Mapping: {{mapping| 1 1 -1 3 6 -1 | 0 3 17 -1 -13 24 }}

==== Aerodino
Subgroup: 2.3.5.7.11
Comma list: 176/175, 245/243, 1029/1024
Mapping: {{mapping| 1 1 -1 3 -3 | 0 3 17 -1 33 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 176/175, 245/243, 847/845
Mapping: {{mapping| 1 1 -1 3 -3 -1 | 0 3 17 -1 33 24 }}

==== Varan
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243, 1029/1024
Mapping: {{mapping| 1 1 -1 3 -2 | 0 3 17 -1 28 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 245/243, 352/351
Mapping: {{mapping| 1 1 -1 3 -2 0 | 0 3 17 -1 28 19 }}

=== Guiron
Subgroup: 2.3.5.7
Comma list: 1029/1024, 10976/10935
Mapping: {{mapping|legend=1| 1 1 7 3 | 0 3 -24 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 10976/10935
Mapping: {{mapping| 1 1 7 3 -2 | 0 3 -24 -1 28 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 729/728
Mapping: {{mapping| 1 1 7 3 -2 0 | 0 3 -24 -1 28 19 }}

=== Gorgo
Subgroup: 2.3.5.7
Comma list: 36/35, 1029/1024
Mapping: {{mapping|legend=1| 1 1 1 3 | 0 3 7 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 1029/1024
Mapping: {{mapping| 1 1 1 3 1 | 0 3 7 -1 13 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44, 507/500
Mapping: {{mapping| 1 1 1 3 1 2 | 0 3 7 -1 13 9 }}

==== Spartan
Subgroup: 2.3.5.7.11
Comma list: 36/35, 56/55, 1029/1024
Mapping: {{mapping| 1 1 1 3 5 | 0 3 7 -1 -8 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 56/55, 507/500
Mapping: {{mapping| 1 1 1 3 5 2 | 0 3 7 -1 -8 9 }}

=== Gidorah
Subgroup: 2.3.5.7
Comma list: 21/20, 144/125
Mapping: {{mapping|legend=1| 1 1 2 3 | 0 3 2 -1 }}

=== Oncle
Subgroup: 2.3.5.7
Comma list: 1029/1024, 2430/2401
Mapping: {{mapping|legend=1| 1 1 6 3 | 0 3 -19 -1 }}

=== Archaeotherium
Subgroup: 2.3.5.7
Comma list: 405/392, 1029/1024
Mapping: {{mapping|legend=1| 1 1 5 3 | 0 3 -14 -1 }}

=== Clyndro
Subgroup: 2.3.5.7
Comma list: 135/128, 360/343
Mapping: {{mapping|legend=1| 1 1 4 3 | 0 3 -9 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 352/343
Mapping: {{mapping| 1 1 4 3 4 | 0 3 -9 -1 -3 }}

=== Miracle
Subgroup: 2.3.5.7
Comma list: 225/224, 1029/1024
Mapping: {{mapping|legend=1| 1 1 3 3 | 0 6 -7 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 385/384
Mapping: {{mapping| 1 1 3 3 2 | 0 6 -7 -2 15 }}

===== Miraculous
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 243/242
Mapping: {{mapping| 1 1 3 3 2 4 | 0 6 -7 -2 15 -3 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 120/119, 144/143, 154/153, 170/169
Mapping: {{mapping| 1 1 3 3 2 4 4 | 0 6 -7 -2 15 -3 1 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 105/104, 120/119, 144/143, 154/153, 170/169, 210/209

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 105/104, 120/119, 144/143, 154/153, 161/160, 170/169, 210/209

===== Benediction
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 351/350, 385/384
Mapping: {{mapping| 1 1 3 3 2 7 | 0 6 -7 -2 15 -34 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 243/242, 273/272, 351/350, 375/374
Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 6 -7 -2 15 -34 -30 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 210/209, 225/224, 243/242, 273/272, 286/285, 375/374

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 162/161, 210/209, 225/224, 231/230, 243/242, 273/272, 286/285

===== Manna
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 325/324, 385/384
Mapping: {{mapping| 1 1 3 3 2 0 | 0 6 -7 -2 15 38 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 243/242, 273/272, 325/324, 385/384
Mapping: {{mapping| 1 1 3 3 2 0 0 | 0 6 -7 -2 15 38 42 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 210/209, 225/224, 243/242, 273/272, 325/324, 343/342

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 210/209, 225/224, 243/242, 273/272, 300/299, 325/324, 343/342

===== Semimiracle
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 243/242, 385/384
Mapping: {{mapping| 2 2 6 6 4 7 | 0 6 -7 -2 15 2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 225/224, 243/242, 273/272
Mapping: {{mapping| 2 2 6 6 4 7 7 | 0 6 -7 -2 15 2 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 210/209, 221/220, 225/224, 243/242, 273/272

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 169/168, 208/207, 210/209, 221/220, 225/224, 243/242, 273/272

===== Hemisecordite
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 385/384, 847/845
Mapping: {{mapping| 1 1 3 3 2 2 | 0 12 -14 -4 30 35 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 243/242, 273/272, 385/384, 847/845
Mapping: {{mapping| 1 1 3 3 2 2 2 | 0 12 -14 -4 30 35 43 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list:

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list:

====== Semihemisecordite
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 243/242, 289/288, 385/384, 847/845
Mapping: {{mapping| 2 2 6 6 4 4 7 | 0 12 -14 -4 30 35 12 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 209/208, 225/224, 243/242, 289/288, 361/360, 385/384
Mapping: {{mapping| 2 2 6 6 4 4 7 8 | 0 12 -14 -4 30 35 12 5 }}

======= 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 209/208, 225/224, 243/242, 289/288, 323/322, 361/360, 385/384
Mapping: {{mapping| 2 2 6 6 4 4 7 8 7 | 0 12 -14 -4 30 35 12 5 21 }}

===== Phicordial
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 385/384, 2200/2197
Mapping: {{mapping| 1 -11 17 7 -28 3 | 0 18 -21 -6 45 1 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 243/242, 273/272, 385/384, 2200/2197
Mapping: {{mapping| 1 -11 17 7 -28 3 -5 | 0 18 -21 -6 45 1 13 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 210/209, 225/224, 243/242, 273/272, 385/384, 2200/2197

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 210/209, 225/224, 243/242, 273/272, 300/299, 385/384, 1105/1104

==== Revelation
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 1029/1024
Mapping: {{mapping| 1 1 3 3 5 | 0 6 -7 -2 -16 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 99/98, 105/104, 512/507
Mapping: {{mapping| 1 1 3 3 5 4 | 0 6 -7 -2 -16 -3 }}

==== Hemimiracle
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/242, 1029/1024
Mapping: {{mapping| 1 1 3 3 4 | 0 12 -14 -4 -11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 245/242, 512/507
Mapping: {{mapping| 1 1 3 3 4 4 | 0 12 -14 -4 -11 -6 }}

==== Oracle
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 1029/1024
Mapping: {{mapping| 1 -5 10 5 4 | 0 12 -14 -4 -1 }}

=== Hemiseven
Subgroup: 2.3.5.7
Comma list: 1029/1024, 19683/19600
Mapping: {{mapping|legend=1| 1 -2 -15 4 | 0 6 29 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 19683/19600
Mapping: {{mapping| 1 -2 -15 4 16 | 0 6 29 -2 -21 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440, 676/675
Mapping: {{mapping| 1 -2 -15 4 16 -19 | 0 6 29 -2 -21 38 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 351/350, 385/384, 441/440, 676/675
Mapping: {{mapping| 1 -2 -15 4 16 -19 -21 | 0 6 29 -2 -21 38 42 }}

=== Valentine
Subgroup: 2.3.5.7
Comma list: 126/125, 1029/1024
Mapping: {{mapping|legend=1| 1 1 2 3 | 0 9 5 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 176/175
Mapping: {{mapping| 1 1 2 3 3 | 0 9 5 -3 7 }}

===== Valentino
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 176/175, 196/195
Mapping: {{mapping| 1 1 2 3 3 5 | 0 9 5 -3 7 -20 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 126/125, 154/153, 176/175, 196/195
Mapping: {{mapping| 1 1 2 3 3 5 5 | 0 9 5 -3 7 -20 -14 }}

===== Lupercalia
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 126/125
Mapping: {{mapping| 1 1 2 3 3 3 | 0 9 5 -3 7 11 }}

===== Dwynwen
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 126/125, 176/175
Mapping: {{mapping| 1 1 2 3 3 2 | 0 9 5 -3 7 26 }}

===== Semivalentine
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 169/168, 176/175
Mapping: {{mapping| 2 2 4 6 6 7 | 0 9 5 -3 7 3 }}

===== Hemivalentine
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 176/175, 343/338
Mapping: {{mapping| 1 1 2 3 3 4 | 0 18 10 -6 14 -9 }}

===== Demivalentine
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 176/175, 676/675
Mapping: {{mapping| 1 -8 -3 6 -4 -16 | 0 18 10 -6 14 37 }}

==== Hemivalentino
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 1029/1024
Mapping: {{mapping| 1 1 2 3 2 | 0 18 10 -6 45 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 243/242, 1029/1024
Mapping: {{mapping| 1 1 2 3 2 5 | 0 18 10 -6 45 -40 }}

===== Hemivalentoid
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 243/242, 343/338
Mapping: {{mapping| 1 1 2 3 2 4 | 0 18 10 -6 45 -9 }}

=== Superkleismic
Subgroup: 2.3.5.7
Comma list: 875/864, 1029/1024
Mapping: {{mapping|legend=1| 1 -5 -5 5 | 0 9 10 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 385/384
Mapping: {{mapping| 1 -5 -5 5 2 | 0 9 10 -3 2 }}

===== 2.3.5.7.11.19 subgroup
Subgroup: 2.3.5.7.11.19
Comma list: 100/99, 133/132, 190/189, 385/384
Mapping: {{mapping| 1 -5 -5 5 2 -6 | 0 9 10 -3 2 14 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 245/242
Mapping: {{mapping| 1 -5 -5 5 2 -8 | 0 9 10 -3 2 16 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 120/119, 144/143, 245/242
Mapping: {{mapping| 1 -5 -5 5 2 -8 -12 | 0 9 10 -3 2 16 22 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 120/119, 144/143, 133/132, 190/189
Mapping: {{mapping| 1 -5 -5 5 2 -8 -12 -6 | 0 9 10 -3 2 16 22 14 }}

==== Superana
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 245/242, 385/384
Mapping: {{mapping| 1 -5 -5 5 2 22 | 0 9 10 -3 2 -25 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 154/153, 196/195, 245/242, 256/255
Mapping: {{mapping| 1 -5 -5 5 2 22 18 | 0 9 10 -3 2 -25 -19 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 133/132, 154/153, 190/189, 196/195, 256/255
Mapping: {{mapping| 1 -5 -5 5 2 22 18 -6 | 0 9 10 -3 2 -25 -19 14 }}

=== Dee leap week
Subgroup: 2.3.5.7
Comma list: 1029/1024, 2460375/2458624
Mapping: {{mapping|legend=1| 1 -5 25 5 | 0 9 -31 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 2460375/2458624
Mapping: {{mapping| 1 -5 25 5 -28 | 0 9 -31 -3 43 }}

=== Unidec
Subgroup: 2.3.5.7
Comma list: 1029/1024, 4375/4374
Mapping: {{mapping|legend=1| 2 -1 -3 7 | 0 6 11 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 4375/4374
Mapping: {{mapping| 2 -1 -3 7 9 | 0 6 11 -2 -3 }}

===== Ekadash
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 625/624, 729/728
Mapping: {{mapping| 2 -1 -3 7 9 -19 | 0 6 11 -2 -3 38 }}

===== Hendec
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 364/363, 385/384
Mapping: {{mapping| 2 -1 -3 7 9 6 | 0 6 11 -2 -3 2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 273/272, 325/324, 364/363
Mapping: {{mapping| 2 -1 -3 7 9 6 4 | 0 6 11 -2 -3 2 6 }}

=== Necromanteion
Subgroup: 2.3.5.7
Comma list: 1029/1024, 5103/5000
Mapping: {{mapping|legend=1| 1 -5 -7 5 | 0 12 17 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 243/242, 1029/1024
Mapping: {{mapping| 1 -5 -7 5 -13 | 0 12 17 -4 30 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 243/242, 343/338
Mapping: {{mapping| 1 -5 -7 5 -13 7 | 0 12 17 -4 30 -6 }}

=== Restles
Subgroup: 2.3.5.7
Comma list: 1029/1024, 153664/151875
Mapping: {{mapping|legend=1| 1 -2 8 4 | 0 12 -19 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 153664/151875
Mapping: {{mapping| 1 -2 8 4 -7 | 0 12 -19 -4 35 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 676/675
Mapping: {{mapping| 1 -2 8 4 -7 4 | 0 12 -19 -4 35 -1 }}

=== Lagaca
Subgroup: 2.3.5.7
Comma list: 1029/1024, 11529602/11390625
Mapping: {{mapping|legend=1| 2 -4 15 8 | 0 9 -13 -3 }}

=== Quartemka
Subgroup: 2.3.5.7
Comma list: 1029/1024, 1250000/1240029
Mapping: {{mapping|legend=1| 1 -17 -26 9 | 0 21 32 -7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 800000/793881
Mapping: {{mapping| 1 -17 -26 9 7 | 0 21 32 -7 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 2200/2197
Mapping: {{mapping| 1 -17 -26 9 7 -14 | 0 21 32 -7 -4 20 }}

=== Tritriple
Subgroup: 2.3.5.7
Comma list: 1029/1024, 1959552/1953125
Mapping: {{mapping|legend=1| 1 -11 -7 7 | 0 27 20 -9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 43923/43750
Mapping: {{mapping| 1 -11 -7 7 -4 | 0 27 20 -9 16 }}

=== Widefourth
Subgroup: 2.3.5.7
Comma list: 1029/1024, 48828125/48771072
Mapping: {{mapping|legend=1| 1 -17 -5 9 | 0 33 13 -11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 234375/234256
Mapping: {{mapping| 1 16 8 -2 17 | 0 -33 -13 11 -31 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 625/624, 847/845
Mapping: {{mapping| 1 16 8 -2 17 12 | 0 -33 -13 11 -31 -19 }}

=== Other subgroup extensions

==== Euslendric (2.3.7.13)
Subgroup: 2.3.7.13
Comma list: 729/728, 1029/1024
Mapping: {{mapping| 1 1 3 0 | 0 3 -1 19 }}

===== 2.3.7.13.17 subgroup
Subgroup: 2.3.7.13.17
Comma list: 273/272, 729/728, 833/832
Mapping: {{mapping| 1 1 3 0 0 | 0 3 -1 19 21 }}

===== 2.3.7.13.17.19 subgroup
Subgroup: 2.3.7.13.17.19
Comma list: 273/272, 343/342, 513/512, 729/728
Mapping: {{mapping| 1 1 3 0 0 6 | 0 3 -1 19 21 -9 }}

===== 2.3.7.13.17.19.23 subgroup
Subgroup: 2.3.7.13.17.19.23
Comma list: 273/272, 343/342, 392/391, 513/512, 729/728
Mapping: {{mapping| 1 1 3 0 0 6 9 | 0 3 -1 19 21 -9 -23 }}

===== 2.3.7.13.17.19.23.29 subgroup
Subgroup: 2.3.7.13.17.19.23.29
Comma list: 273/272, 343/342, 378/377, 392/391, 513/512, 609/608
Mapping: {{mapping| 1 1 3 0 0 6 9 7 | 0 3 -1 19 21 -9 -23 -11 }}

==== Baladic (2.3.7.13)
Subgroup: 2.3.7.13
Comma list: 169/168, 1029/1024
Mapping: {{mapping| 2 2 6 7 | 0 3 -1 1 }}

===== 2.3.7.13.17 subgroup
Subgroup: 2.3.7.13.17
Comma list: 169/168, 273/272, 289/288
Mapping: {{mapping| 2 2 6 7 7 | 0 3 -1 1 3 }}

==== Gigapyth (2.3.7.85)
Subgroup: 2.3.7.85
Comma list: 1029/1024, 7225/7203
Mapping: {{mapping| 1 -2 4 7 | 0 6 -2 -1 }}

=== References


= Gamelismic family

=== Gamelismic
Subgroup: 2.3.5.7
Comma list: 1029/1024
Mapping: {{mapping|legend=1| 1 1 0 3 | 0 3 0 -1 | 0 0 1 0 }}
Mapping to lattice: [{{val| 0 3 0 -1 }}, {{val| 0 0 1 0 }}]

=== Portent
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440
Mapping: {{mapping|legend=1| 1 1 0 3 5 | 0 3 0 -1 4 | 0 0 1 0 -1 }}
Mapping to lattice: [{{val| 0 3 1 -1 3 }}, {{val| 0 0 1 0 -1 }}]

==== Portending
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384
Mapping: {{mapping| 1 1 0 3 5 6 | 0 3 0 -1 4 12 | 0 0 1 0 -1 -2 }}

==== Portentous
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 625/624
Mapping: {{mapping| 1 1 0 3 5 -5 | 0 3 0 -1 4 -3 | 0 0 1 0 -1 4 }}

==== Ominous
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 -10 | 0 0 1 0 -1 2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 351/350, 385/384, 441/440
Mapping: {{mapping| 1 1 0 3 5 1 1 | 0 3 0 -1 4 -10 -8 | 0 0 1 0 -1 2 2 }}
Mapping to lattice: [{{val| 0 1 1 0 0 -1 0 }}, {{val| 0 -1 -1 0 -1 2 1 }}]

==== Momentous
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384
Mapping: {{mapping| 1 1 0 3 5 7 | 0 3 0 -4 1 -5 | 0 0 1 0 -1 -1 }}

==== Foreboding
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 275/273
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 2 | 0 0 1 0 -1 1 }}

==== Portannic
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 10985/10976
Mapping: {{mapping| 1 1 2 3 3 4 | 0 3 0 -1 4 -1 | 0 0 3 0 -3 -1 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 385/384, 441/440, 8624/8619
Mapping: {{mapping| 1 1 2 3 3 4 4 | 0 3 0 -1 4 -1 1 | 0 0 3 0 -3 -1 -1 }}

=== Gamel
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1029/1024
Mapping: {{mapping|legend=1| 1 1 0 3 -1 | 0 3 0 -1 11 | 0 0 1 0 1 }}


= Gammic family

=== Gammic
Subgroup: 2.3.5
Comma list: {{monzo| -29 -11 20 }}
Mapping: {{mapping|legend=1| 1 1 2 | 0 20 11 }}

==== 2.3.5.17 subgroup
Subgroup: 2.3.5.17
Comma list: 15625/15606, 24576/24565
Mapping: {{mapping|legend=1| 1 1 2 4 | 0 20 11 3 }}

=== Septimal gammic
Subgroup: 2.3.5.7
Comma list: 4375/4374, 6591796875/6576668672
Mapping: {{mapping|legend=1| 1 1 2 0 | 0 20 11 96 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 4375/4356, 100352/99825
Mapping: {{mapping| 1 1 2 0 2 | 0 20 11 96 50 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 625/624, 2200/2197
Mapping: {{mapping| 1 1 2 0 2 3 | 0 20 11 96 50 24 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 375/374, 595/594, 2200/2197
Mapping: {{mapping| 1 1 2 0 2 3 4 | 0 20 11 96 50 24 3 }}

=== Gammy
Subgroup: 2.3.5.7
Comma list: 225/224, 94143178827/91913281250
Mapping: {{mapping| 1 1 2 1 | 0 20 11 62 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 215622/214375
Mapping: {{mapping| 1 1 2 1 2 | 0 20 11 62 50 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 351/350, 1188/1183
Mapping: {{mapping| 1 1 2 1 2 3 | 0 20 11 62 50 24 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 243/242, 351/350, 375/374, 1188/1183
Mapping: {{mapping| 1 1 2 1 2 3 4 | 0 20 11 62 50 24 3 }}

=== Neptune

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 2401/2400, 48828125/48771072
Mapping: {{mapping|legend=1| 1 21 13 13 | 0 -40 -22 -21 }}

===== 2.3.5.7.17 subgroup
Subgroup: 2.3.5.7.17
Comma list: 1225/1224, 2401/2400, 24576/24565
Mapping: {{mapping|legend=1| 1 21 13 13 7 | 0 -40 -22 -21 -6 }}

===== 2.3.5.7.17.31 subgroup
Subgroup: 2.3.5.7.17.31
Comma list: 868/867, 961/960, 1225/1224, 2401/2400
Mapping: {{mapping|legend=1| 1 21 13 13 7 20 | 0 -40 -22 -21 -6 -31 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 78408/78125
Mapping: {{mapping| 1 21 13 13 2 | 0 -40 -22 -21 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624, 1188/1183, 1375/1372
Mapping: {{mapping| 1 21 13 13 2 27 | 0 -40 -22 -21 3 -48 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 385/384, 561/560, 625/624, 715/714, 1188/1183
Mapping: {{mapping| 1 21 13 13 2 27 7 | 0 -40 -22 -21 3 -48 -6 }}

==== Salacia
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 9765625/9732096
Mapping: {{mapping| 1 21 13 13 52 | 0 -40 -22 -21 -100 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 441/440, 625/624, 2200/2197
Mapping: {{mapping| 1 21 13 13 52 27 | 0 -40 -22 -21 -100 -48 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 375/374, 441/440, 625/624, 2200/2197
Mapping: {{mapping| 1 21 13 13 52 27 7 | 0 -40 -22 -21 -100 -48 -6 }}

==== Poseidon
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 9453125/9437184
Mapping: {{mapping| 2 2 4 5 8 | 0 40 22 21 -37 }}


= Gariboh family

=== Gariboh
Subgroup: 2.3.5.7
Comma list: [[3125/3087]]
Mapping: {{mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }}

=== Undecimal gariboh
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3125/3087
Mapping: {{mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 2 | 0 0 3 5 -7 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 275/273, 325/324, 540/539
Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 1 1 2 2 | 0 0 3 5 -7 -6 }}

=== Androboh
Subgroup: 2.3.5.7.11
Comma list: 100/99, 1375/1372
Mapping: {{mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 0 | 0 0 3 5 6 }}

=== Trismegiboh
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3125/3087
Mapping: {{mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 1 | 0 0 6 10 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 275/273, 847/845
Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 1 1 1 1 | 0 0 6 10 -1 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 120/119, 144/143, 170/169, 847/845
Mapping: {{mapping| 1 0 0 0 2 2 3 | 0 1 1 1 1 1 1 | 0 0 6 10 -1 1 -4 }}


= Gravity family

=== Gravity
Subgroup: 2.3.5
Comma list: 129140163/128000000
Mapping: {{mapping|legend=1| 1 -1 -5 | 0 6 17 }}

==== Overview to extensions

==== 2.3.5.11 subgroup (larry)
Subgroup: 2.3.5.11
Comma list: 243/242, 4000/3993

=== Marvo
Subgroup: 2.3.5.7
Comma list: 225/224, 78125000/78121827
Mapping: {{mapping|legend=1| 1 -1 -5 -17 | 0 6 17 46 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 4000/3993
Mapping: {{mapping| 1 -1 -5 -17 -3 | 0 6 17 46 15 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 351/350, 1625/1617
Mapping: {{mapping| 1 -1 -5 -17 -3 -23 | 0 6 17 46 15 62 }}

=== Zarvo
Subgroup: 2.3.5.7
Comma list: 4375/4374, 33075/32768
Mapping: {{mapping|legend=1| 1 -1 -5 14 | 0 6 17 -26 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384, 4000/3993
Mapping: {{mapping| 1 -1 -5 14 -3 | 0 6 17 -26 15 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 243/242, 325/324, 385/384
Mapping: {{mapping| 1 -1 -5 14 -3 8 | 0 6 17 -26 15 -10 }}

=== Gravid
Subgroup: 2.3.5.7
Comma list: 126/125, 1605632/1594323
Mapping: {{mapping|legend=1| 1 -1 -5 -14 | 0 6 17 39 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 896/891
Mapping: {{mapping| 1 -1 -5 -14 -3 | 0 6 17 39 15 }}

=== Harry
Subgroup: 2.3.5.7
Comma list: 2401/2400, 19683/19600
Mapping: {{mapping|legend=1| 2 4 7 7 | 0 -6 -17 -10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 4000/3993
Mapping: {{mapping| 2 4 7 7 9 | 0 -6 -17 -10 -15 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 364/363, 441/440
Mapping: {{mapping| 2 4 7 7 9 11 | 0 -6 -17 -10 -15 -26 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 243/242, 289/288, 351/350, 441/440
Mapping: {{mapping| 2 4 7 7 9 11 9 | 0 -6 -17 -10 -15 -26 -6 }}

=== References


= Greenwoodmic temperaments

=== Secund
Subgroup: 2.3.5.7
Comma list: 405/392, 525/512
Mapping: {{mapping|legend=1| 1 1 3 2 | 0 5 -6 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 385/384
Mapping: {{mapping| 1 1 3 2 3 | 0 5 -6 7 4 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 385/384
Mapping: {{mapping| 1 1 3 2 3 2 | 0 5 -6 7 4 15 }}

===== Secundly
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 65/64, 78/77, 99/98
Mapping: {{mapping| 1 1 3 2 3 3 | 0 5 -6 7 4 6 }}

=== Semishallowtone
Subgroup: 2.3.5.7
Comma list: 405/392, 35721/32768
Mapping: {{mapping|legend=1| 2 0 36 15 | 0 1 -10 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 35721/32768
Mapping: {{mapping| 2 0 36 15 32 | 0 1 -10 -3 -8 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 35721/32768
Mapping: {{mapping| 2 0 36 15 32 -2 | 0 1 -10 -3 -8 3 }}


= Hemifamity family

=== Hemifamity
Subgroup: 2.3.5.7
Comma list: [[5120/5103]]
Mapping: {{mapping|legend=1| 1 0 0 10 | 0 1 0 -6 | 0 0 1 1 }}
Mapping to lattice: [{{val| 0 1 2 -4 }}, {{val| 0 0 1 1 }}]

==== Overview to extensions

===== 11- and 13-limit extensions

===== Subgroup extensions

==== Counterpyth
Subgroup: 2.3.5.7.19
Comma list: 400/399, 1216/1215
Mapping: {{mapping| 1 0 0 10 -6 | 0 1 0 -6 5 | 0 0 1 1 1 }}

=== Pele
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891
Mapping: {{mapping|legend=1| 1 0 0 10 17 | 0 1 0 -6 -10 | 0 0 1 1 1 }}
Mapping to lattice: [{{val| 0 1 4 -2 -6 }}, {{val| 0 0 -1 -1 -1 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363
Mapping: {{mapping| 1 0 0 10 17 22 | 0 1 0 -6 -10 -13 | 0 0 1 1 1 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 364/363
Mapping: {{mapping| 1 0 0 10 17 22 8 | 0 1 0 -6 -10 -13 -1 | 0 0 1 1 1 1 -1 }}

=== Laka
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5120/5103
Mapping: {{mapping|legend=1| 1 0 0 10 -18 | 0 1 0 -6 15 | 0 0 1 1 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728
Mapping: {{mapping| 1 0 0 10 -18 -13 | 0 1 0 -6 15 12 | 0 0 1 1 -1 -1 }}

==== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 352/351, 400/399, 456/455, 495/494
Mapping: {{mapping| 1 0 0 10 -18 -13 -6 | 0 1 0 -6 15 12 5 | 0 0 1 1 -1 -1 1 }}

=== Akea
Subgroup: 2.3.5.7.11
Comma list: 385/384, 2200/2187
Mapping: {{mapping|legend=1| 1 0 0 10 -3 | 0 1 0 -6 7 | 0 0 1 1 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 385/384
Mapping: {{mapping| 1 0 0 10 -3 2 | 0 1 0 -6 7 4 | 0 0 1 1 -2 -2 }}
Mapping to lattice: [{{val| 0 1 3 -3 1 -2 }}, {{val| 0 0 -1 -1 2 2 }}]

=== Lono
Subgroup: 2.3.5.7.11
Comma list: 176/175, 5120/5103
Mapping: {{mapping|legend=1| 1 0 0 10 6 | 0 1 0 -6 -6 | 0 0 1 1 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 847/845
Mapping: {{mapping| 1 0 0 10 6 11 | 0 1 0 -6 -6 -9 | 0 0 1 1 3 3 }}

=== Kapo
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5120/5103
Mapping: {{mapping|legend=1| 1 0 0 10 7 | 0 1 1 -5 -2 | 0 0 2 2 -1 }}

=== Namaka
Subgroup: 2.3.5.7.11
Comma list: 3388/3375, 5120/5103
Mapping: {{mapping|legend=1| 1 0 0 10 -6 | 0 2 0 -12 9 | 0 0 1 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845
Mapping: {{mapping| 1 0 0 10 -6 -1 | 0 2 0 -12 9 3 | 0 0 1 1 1 1 }}

=== References


= Hemifamity temperaments

=== Septiquarter
Subgroup: 2.3.5.7
Comma list: 5120/5103, 420175/419904
Mapping: {{mapping|legend=1| 1 -4 -28 6 | 0 7 38 -4 }}

==== Semiseptiquarter
Subgroup: 2.3.5.7.11
Comma list: 5120/5103, 9801/9800, 14641/14580
Mapping: {{mapping| 2 -8 -56 12 -25 | 0 7 38 -4 20 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 14641/14580
Mapping: {{mapping| 2 -8 -56 12 -25 9 | 0 7 38 -4 20 -1 }}

=== Kwai
Subgroup: 2.3.5.7
Comma list: 5120/5103, 16875/16807
Mapping: {{mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 5120/5103
Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 1375/1372
Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088
Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845
Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}

===== Hemikwai
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 676/675, 1375/1372, 5120/5103
Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}

=== Ketchup
Subgroup: 2.3.5.7
Comma list: 5120/5103, 1071875/1062882
Mapping: {{mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1331/1323, 2200/2187
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 385/384, 1331/1323
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 325/324, 352/351, 385/384, 442/441
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}

==== 2.3.5.7.11.13.17.23 subgroup
Subgroup: 2.3.5.7.11.13.17.23
Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }}

=== Undecental
Subgroup: 2.3.5.7
Comma list: 5120/5103, 235298/234375
Mapping: {{mapping|legend=1| 1 0 61 71 | 0 1 -37 -43 }}

=== Leapday
Subgroup: 2.3.5.7
Comma list: 686/675, 5120/5103
Mapping: {{mapping|legend=1| 1 0 -31 -21 | 0 1 21 15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 686/675
Mapping: {{mapping| 1 0 -31 -21 -14 | 0 1 21 15 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 169/168, 352/351
Mapping: {{mapping| 1 0 -31 -21 -14 -9 | 0 1 21 15 11 8 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 121/120, 136/135, 154/153, 169/168
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 | 0 1 21 15 11 8 24 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 | 0 1 21 15 11 8 24 -3 }}

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 161/160, 169/168
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 -5 | 0 1 21 15 11 8 24 -3 6 }}

===== Leapling
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 | 0 1 21 15 11 8 24 26 }}

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 77/76, 91/90, 115/114, 121/120, 136/135, 153/152, 161/160
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 -5 | 0 1 21 15 11 8 24 26 6 }}

=== Mystery
Subgroup: 2.3.5.7
Comma list: 5120/5103, 50421/50000
Mapping: {{mapping|legend=1| 29 46 0 14 | 0 0 1 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 3388/3375
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 676/675
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}

=== Hemidromeda
Subgroup: 2.3.5.7
Comma list: 5120/5103, 52734375/52706752
Mapping: {{mapping|legend=1| 1 0 38 48 | 0 2 -45 -57 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1331/1323, 1375/1372, 5120/5103
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845, 1331/1323
Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 442/441, 561/560, 676/675, 715/714
Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 286/285, 352/351, 363/361, 442/441, 476/475, 561/560
Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 253/252, 286/285, 352/351, 363/361, 391/390, 442/441, 460/459
Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}

=== Countriton
Subgroup: 2.3.5.7
Comma list: 5120/5103, 7558272/7503125
Mapping: {{mapping|legend=1| 1 -3 -15 13 | 0 9 34 -20 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 5120/5103, 41503/41472
Mapping: {{mapping| 1 -3 -15 13 -21 | 0 9 34 -20 48 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 847/845, 2197/2187
Mapping: {{mapping| 1 -3 -15 13 -21 -7 | 0 9 34 -20 48 21 }}

=== Artoneutral
Subgroup: 2.3.5.7
Comma list: 5120/5103, 3828125/3779136
Mapping: {{mapping|legend=1| 1 -1 -4 12 | 0 9 22 -32 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 2200/2187, 4000/3993
Mapping: {{mapping| 1 -1 -4 12 -2 | 0 9 22 -32 19 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 385/384, 1575/1573
Mapping: {{mapping| 1 -1 -4 12 -2 6 | 0 9 22 -32 19 -8 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 | 0 9 22 -32 19 -8 56 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 | 0 9 22 -32 19 -8 56 67 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 -13 | 0 9 22 -32 19 -8 56 67 61 }}

=== Quanic
Subgroup: 2.3.5.7
Comma list: 5120/5103, 5832000/5764801
Mapping: {{mapping|legend=1| 1 1 -4 0 | 0 5 54 24 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1331/1323, 5120/5103
Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 1331/1323
Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 442/441, 540/539, 715/714, 847/845
Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714
Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}

=== Jorgensen
Subgroup: 2.3.5.7
Comma list: 5120/5103, 578509309952/576650390625
Mapping: {{mapping|legend=1| 70 111 0 34 | 0 0 1 1 }}

=== References


= Hemimage family

=== Hemimage
Subgroup: 2.3.5.7
Comma list: 10976/10935
Mapping: {{mapping|legend=1| 1 0 2 -1 | 0 1 2 3 | 0 0 -3 -1 }}

=== Uni
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891
Mapping: {{mapping|legend=1| 1 0 2 -1 6 | 0 1 2 3 -1 | 0 0 -3 -1 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 540/539
Mapping: {{mapping| 1 0 2 -1 6 11 | 0 1 2 3 -1 -4 | 0 0 -3 -1 -1 -1 }}

==== Tin
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 729/728
Mapping: {{mapping| 1 0 2 -1 6 -2 | 0 1 2 3 -1 3 | 0 0 -3 -1 -1 1 }}

=== Turan
Subgroup: 2.3.5.7.11
Comma list: 441/440, 10976/10935
Mapping: {{mapping|legend=1| 1 0 2 -1 -7 | 0 1 2 3 6 | 0 0 -3 -1 1 }}


= Hemimage temperaments

=== Chromat
Subgroup: 2.3.5.7
Comma list: 10976/10935, 235298/234375
Mapping: {{mapping|legend=1| 3 4 5 6 | 0 5 13 16 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4356, 10976/10935
Mapping: {{mapping| 3 4 5 6 6 | 0 5 13 16 29 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 625/624, 10976/10935
Mapping: {{mapping| 3 4 5 6 6 4 | 0 5 13 16 29 47 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 375/374, 441/440, 595/594, 3773/3757
Mapping: {{mapping| 3 4 5 6 6 4 10 | 0 5 13 16 29 47 15 }}

===== Catachrome
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 441/440, 1001/1000, 10976/10935
Mapping: {{mapping| 3 4 5 6 6 12 | 0 5 13 16 29 -6 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 375/374, 441/440, 4928/4913
Mapping: {{mapping| 3 4 5 6 6 12 10 | 0 5 13 16 29 -6 15 }}

===== Chromic
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 729/728, 1875/1859
Mapping: {{mapping| 3 4 5 6 6 9 | 0 5 13 16 29 14 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 196/195, 352/351, 375/374, 595/594
Mapping: {{mapping| 3 4 5 6 6 9 10 | 0 5 13 16 29 14 15 }}

==== Hemichromat
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 10976/10935, 102487/102400
Mapping: {{mapping| 3 4 5 6 10 | 0 10 26 32 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 10976/10935
Mapping: {{mapping| 3 4 5 6 10 8 | 0 10 26 32 5 41 }}

=== Bisupermajor
Subgroup: 2.3.5.7
Comma list: 10976/10935, 65625/65536
Mapping: {{mapping|legend=1| 2 1 6 1 | 0 8 -5 17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375, 9801/9800
Mapping: {{mapping| 2 1 6 1 8 | 0 8 -5 17 -4 }}

=== Bicommatic
Subgroup: 2.3.5.7
Comma list: 10976/10935, 50421/50000
Mapping: {{mapping|legend=1| 2 3 4 5 | 0 5 19 18 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375, 8019/8000
Mapping: {{mapping| 2 3 4 5 6 | 0 5 19 18 27 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 729/728, 1001/1000
Mapping: {{mapping| 2 3 4 5 6 7 | 0 5 19 18 27 12 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 196/195, 289/288, 352/351, 561/560
Mapping: {{mapping| 2 3 4 5 6 7 8 | 0 5 19 18 27 12 5 }}

=== Degrees
Subgroup: 2.3.5.7
Comma list: 10976/10935, 390625/388962
Mapping: {{mapping|legend=1| 20 0 -17 -39 | 0 1 2 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1331/1323, 1375/1372, 2200/2187
Mapping: {{mapping| 20 0 -17 -39 -26 | 0 1 2 3 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 1001/1000, 1331/1323
Mapping: {{mapping| 20 0 -17 -39 -26 74 | 0 1 2 3 3 0 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 325/324, 352/351, 561/560, 1001/1000
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 | 0 1 2 3 3 0 1 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 286/285, 289/288, 325/324, 352/351, 400/399, 476/475
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 | 0 1 2 3 3 0 1 0 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 253/252, 286/285, 289/288, 325/324, 352/351, 391/390, 400/399
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 | 0 1 2 3 3 0 1 0 2 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 253/252, 286/285, 289/288, 325/324, 352/351, 391/390, 400/399, 406/405
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 | 0 1 2 3 3 0 1 0 2 3 }}

==== 2.3.5.7.11.13.17.19.23.29.37 subgroup
Subgroup: 2.3.5.7.11.13.17.19.23.29.37
Comma list: 253/252, 286/285, 289/288, 325/324, 352/351, 391/390, 400/399, 406/405, 481/480
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 9 | 0 1 2 3 3 0 1 0 2 3 3 }}

==== 2.3.5.7.11.13.17.19.23.29.37.41 subgroup
Subgroup: 2.3.5.7.11.13.17.19.23.29.37.41
Comma list: 253/252, 286/285, 289/288, 325/324, 352/351, 391/390, 400/399, 451/450, 476/475, 481/480, 2871/2870
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 9 12 | 0 1 2 3 3 0 1 0 2 3 3 3 }}

=== Squarschmidt
Subgroup: 2.3.5.7
Comma list: 10976/10935, 29360128/29296875
Mapping: {{mapping|legend=1| 1 -8 1 -20 | 0 29 4 69 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 10976/10935
Mapping: {{mapping| 1 -8 1 -20 -21 | 0 29 4 69 74 }}

=== Leapmonth
Subgroup: 2.3.5.7
Comma list: 10976/10935, 51200/50421
Mapping: {{mapping|legend=1| 1 0 -58 -21 | 0 1 38 15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891, 1331/1323
Mapping: {{mapping| 1 0 -58 -21 -14 | 0 1 38 15 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 352/351, 364/363, 540/539
Mapping: {{mapping| 1 0 -58 -21 -14 -1 | 0 1 38 15 11 8 }}


= Hemimean clan

== 2.5.7 subgroup

=== Didacus
Subgroup: 2.5.7
Comma list: [[3136/3125]]
Mapping: {{mapping|legend=2| 1 0 -3 | 0 2 5 }}
Mapping: {{mapping|legend=3| 1 0 0 -3 | 0 0 2 5 }}

== Strong extensions
! rowspan="2" | Extension !! colspan="2" | 5-limit re-restriction !! rowspan="2" | Mapping of 3 !! rowspan="2" | Tuning range*

=== Hemiwürschmidt
Subgroup: 2.3.5.7
Comma list: 2401/2400, 3136/3125
Mapping: {{mapping|legend=1| 1 15 4 7 | 0 -16 -2 -5 }}

==== 2.3.5.7.23 subgroup
Subgroup: 2.3.5.7.23
Comma list: 576/575, 736/735, 1127/1125
Mapping: {{mapping|legend=1| 1 15 4 7 28 | 0 -16 -2 -5 -28 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 3136/3125
Mapping: {{mapping| 1 15 4 7 37 | 0 -16 -2 -5 -40 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 441/440, 3584/3575
Mapping: {{mapping| 1 15 4 7 37 -29 | 0 -16 -2 -5 -40 39 }}

===== Hemithir
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 196/195, 275/273
Mapping: {{mapping| 1 15 4 7 37 -3 | 0 -16 -2 -5 -40 8 }}

==== Hemiwur
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 1375/1372
Mapping: {{mapping| 1 15 4 7 11 | 0 -16 -2 -5 -9 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 196/195, 275/273
Mapping: {{mapping| 1 15 4 7 11 -3 | 0 -16 -2 -5 -9 8 }}

===== Hemiwar
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 1375/1372
Mapping: {{mapping| 1 15 4 7 11 23 | 0 -16 -2 -5 -9 -23 }}

==== Quadrawürschmidt
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 3136/3125
Mapping: {{mapping| 1 15 4 7 24 | 0 -32 -4 -10 -49 }}

==== Semihemiwür
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3136/3125, 9801/9800
Mapping: {{mapping| 2 14 6 9 -10 | 0 -16 -2 -5 25 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715, 3136/3125
Mapping: {{mapping| 2 14 6 9 -10 25 | 0 -16 -2 -5 25 -26 }}

====== Semihemiwürat
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 442/441, 561/560, 676/675, 1632/1625
Mapping: {{mapping| 2 14 6 9 -10 25 19 | 0 -16 -2 -5 25 -26 -16 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 289/288, 442/441, 456/455, 476/475, 561/560, 627/625
Mapping: {{mapping| 2 14 6 9 -10 25 19 20 | 0 -16 -2 -5 25 -26 -16 -17 }}

====== Semihemiwüram
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 676/675, 715/714, 1001/1000, 1225/1224
Mapping: {{mapping| 2 14 6 9 -10 25 -4 | 0 -16 -2 -5 25 -26 18 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 256/255, 286/285, 400/399, 476/475, 495/494, 1225/1224
Mapping: {{mapping| 2 14 6 9 -10 25 -4 -3 | 0 -16 -2 -5 25 -26 18 17 }}

=== Hemithirds
Subgroup: 2.3.5.7
Comma list: 1029/1024, 3136/3125
Mapping: {{mapping|legend=1| 1 4 2 2 | 0 -15 2 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 3136/3125
Mapping: {{mapping| 1 4 2 2 7 | 0 -15 2 5 -22 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 625/624
Mapping: {{mapping| 1 4 2 2 7 0 | 0 -15 2 5 -22 23 }}

=== Spell
Subgroup: 2.3.5.7
Comma list: 49/48, 3125/3072
Mapping: {{mapping|legend=1| 1 0 2 2 | 0 10 2 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 125/121
Mapping: {{mapping| 1 0 2 2 3 | 0 10 2 5 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 78/77, 125/121
Mapping: {{mapping| 1 0 2 2 3 4 | 0 10 2 5 3 -2 }}

===== Cantrip
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 91/90, 125/121
Mapping: {{mapping| 1 0 2 2 3 1 | 0 10 2 5 3 17 }}

== Weak extensions

=== Semisept
Subgroup: 2.3.5.7
Comma list: 1728/1715, 3136/3125
Mapping: {{mapping|legend=1| 1 12 6 12 | 0 -17 -6 -15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 1331/1323
Mapping: {{mapping| 1 12 6 12 20 | 0 -17 -6 -15 -27 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539, 1375/1372
Mapping: {{mapping| 1 12 6 12 20 -11 | 0 -17 -6 -15 -27 24 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 351/350, 640/637, 715/714
Mapping: {{mapping| 1 12 6 12 20 -11 -10 | 0 -17 -6 -15 -27 24 23 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323
Mapping: {{mapping| 1 12 6 12 20 -11 -10 -8 | 0 -17 -6 -15 -27 24 23 20 }}

====== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459
Mapping: {{mapping| 1 12 6 12 20 -11 -10 -8 18 | 0 -17 -6 -15 -27 24 23 20 -22 }}

===== Semishly
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 196/195, 275/273
Mapping: {{mapping| 1 12 6 12 20 8 | 0 -17 -6 -15 -27 -7 }}

=== Emka
Subgroup: 2.3.5.7
Comma list: 3136/3125, 84035/82944
Mapping: {{mapping|legend=1| 1 14 6 12 | 0 -27 -8 -20 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 2401/2376, 3136/3125
Mapping: {{mapping| 1 14 6 12 3 | 0 -27 -8 -20 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 364/363, 385/384, 625/624
Mapping: {{mapping| 1 14 6 12 3 6 | 0 -27 -8 -20 1 -5 }}

=== Decipentic
Subgroup: 2.3.5.7
Comma list: 3136/3125, 2097152/2083725
Mapping: {{mapping|legend=1| 1 6 0 -3 | 0 -19 10 25 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1344/1331, 3136/3125
Mapping: {{mapping| 1 6 0 -3 3 | 0 -19 10 25 2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 441/440, 832/825, 975/968
Mapping: {{mapping| 1 6 0 -3 3 3 | 0 -19 10 25 2 3 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 256/255, 273/272, 375/374
Mapping: {{mapping| 1 6 0 -3 3 3 2 | 0 -19 10 25 2 3 9 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 210/209, 221/220, 256/255, 273/272, 286/285
Mapping: {{mapping| 1 6 0 -3 3 3 2 1 | 0 -19 10 25 2 3 9 14 }}

==== Quasijerome
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 15488/15435, 16384/16335
Mapping: {{mapping| 1 6 0 -3 3 | 0 -38 20 50 47 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3136/3125, 15488/15435
Mapping: {{mapping| 1 6 0 -3 3 8 | 0 -38 20 50 47 -37 }}

=== Sengagen
Subgroup: 2.3.5.7
Comma list: 3136/3125, 420175/419904
Mapping: {{mapping|legend=1| 1 1 2 2 | 0 29 16 40 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1344/1331, 3136/3125
Mapping: {{mapping| 1 1 2 2 3 | 0 29 16 40 23 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 975/968, 1344/1331
Mapping: {{mapping| 1 1 2 2 3 4 | 0 29 16 40 23 -15 }}

===== Sengage
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 364/363, 625/624
Mapping: {{mapping| 1 1 2 2 3 3 | 0 29 16 40 23 35 }}

=== Mowglic
Subgroup: 2.3.5.7
Comma list: 3136/3125, 177147/175000
Mapping: {{mapping|legend=1| 1 0 0 -3 | 0 15 22 55 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3136/3125, 72171/71680
Mapping: {{mapping| 1 0 0 -3 8 | 0 15 22 55 -43 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 1701/1690, 3136/3125
Mapping: {{mapping| 1 0 0 -3 8 -2 | 0 15 22 55 -43 54 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 540/539, 833/832, 1701/1690, 3136/3125
Mapping: {{mapping| 1 0 0 -3 8 -2 10 | 0 15 22 55 -43 54 -56 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 351/350, 476/475, 495/494, 513/512, 540/539, 1701/1690
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 | 0 15 22 55 -43 54 -56 -45 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 | 0 15 22 55 -43 54 -56 -45 -14 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 261/260, 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 0 | 0 15 22 55 -43 54 -56 -45 -14 46 }}

==== 31-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 261/260, 276/275, 351/350, 435/434, 476/475, 495/494, 513/512, 529/528, 540/539
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 0 2 | 0 15 22 55 -43 54 -56 -45 -14 46 28 }}

=== Tremka

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 3136/3125, 2125764/2100875
Mapping: {{mapping|legend=1| 1 -4 -2 -8 | 0 31 24 60 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3136/3125, 35937/35840
Mapping: {{mapping| 1 -4 -2 -8 4 | 0 31 24 60 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845, 3136/3125
Mapping: {{mapping| 1 -4 -2 -8 4 1 | 0 31 24 60 -3 15 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 540/539, 561/560, 847/845, 1089/1088
Mapping: {{mapping| 1 -4 -2 -8 4 1 -6 | 0 31 24 60 -3 15 56 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 324/323, 351/350, 456/455, 476/455, 495/494, 540/539
Mapping: {{mapping| 1 -4 -2 -8 4 1 -6 -8 | 0 31 24 60 -3 15 56 68 }}

=== Undetrita
Subgroup: 2.3.5.7
Comma list: 3136/3125, 14348907/14336000
Mapping: {{mapping|legend=1| 1 0 -2 -8 | 0 11 30 75 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3136/3125, 8019/8000
Mapping: {{mapping| 1 0 -2 -8 0 | 0 11 30 75 24 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 729/728, 1001/1000, 3025/3024
Mapping: {{mapping| 1 0 -2 -8 0 5 | 0 11 30 75 24 -9 }}

===== Undetritoid
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 1573/1568, 2080/2079, 3136/3125
Mapping: {{mapping| 1 0 -2 -8 0 -11 | 0 11 30 75 24 102 }}

== Subgroup extensions

=== Undecimal didacus
Subgroup: 2.5.7.11
Comma list: [[176/175]], [[1375/1372]]

==== Tridecimal didacus
Subgroup: 2.5.7.11.13
Comma list: 176/175, 640/637, 1375/1372

===== Mediantone
Subgroup: 2.5.7.11.13.17.19
Comma list: [[176/175]], [[640/637]], [[221/220]], [[476/475]], [[1375/1372]]

===== Roulette
Subgroup: 2.5.7.11.13.17.19
Comma list: [[170/169]], [[176/175]], [[476/475]], [[640/637]], [[1375/1372]]

=== Rectified hebrew
Subgroup: 2.5.7.13
Comma list: 3136/3125, 4394/4375

=== Isra
Subgroup: 2.9.5.7
Comma list: 81/80, 126/125
Mapping: {{mapping|legend=2| 1 0 -4 -13 | 0 1 2 5 }}

==== Tutone
Subgroup: 2.9.5.7.11
Comma list: 81/80, 99/98, 126/125
Mapping: {{mapping|legend=2| 1 0 -4 -13 -25 | 0 1 2 5 9 }}
Mapping: {{mapping|legend=3| 1 3/2 2 2 2 | 0 1/2 2 5 9 }}

==== Leantone
Subgroup: 2.9.5.7.11
Comma list: 45/44, 56/55, 81/80
Mapping: {{mapping|legend=2| 1 0 -4 -13 -6 | 0 1 2 5 3 }}
Mapping: {{mapping|legend=3| 1 3/2 2 2 3 | 0 1/2 2 5 3 }}

==== Deutone
Subgroup: 2.9.5.7.13
Comma list: 65/64, 81/80, 91/90
Mapping: {{mapping|legend=2| 1 0 -4 -13 10 | 0 1 2 5 -2 }}
Mapping: {{mapping|legend=3| 1 3/2 2 2 0 4 | 0 1/2 2 5 0 -2 }}


= Hemimean family

=== Hemimean
Subgroup: 2.3.5.7
Comma list: 3136/3125
Mapping: {{mapping|legend=1| 1 0 0 -3 | 0 1 0 0 | 0 0 2 5 }}
Mapping to lattice: {{mapping| 0 0 2 5 | 0 1 0 0 }}

==== Hemimean orion
Subgroup: 2.3.5.7.17
Comma list: 1701/1700, 3136/3125

===== 2.3.5.7.17.19 subgroup
Subgroup: 2.3.5.7.17.19
Comma list: 476/475, 1216/1215, 1445/1444

==== Semiorion
Subgroup: 2.3.5.7.17
Comma list: 289/288, 3136/3125

===== 2.3.5.7.17.19 subgroup
Subgroup: 2.3.5.7.17.19
Comma list: 289/288, 361/360, 476/475
Mapping: {{mapping| 2 0 0 -6 5 3 | 0 1 0 0 1 1 | 0 0 2 5 0 1 }}

=== Belobog
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125
Mapping: {{mapping|legend=1| 1 0 0 -3 -9 | 0 1 0 0 2 | 0 0 2 5 8 }}
Mapping to lattice: {{mapping| 0 -2 2 5 4 | 0 -1 0 0 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1001/1000, 3136/3125
Mapping: {{mapping| 1 0 0 -3 -9 15 | 0 1 0 0 2 -2 | 0 0 2 5 8 -7 }}

==== Bellowblog
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 625/624
Mapping: {{mapping| 1 0 0 -3 -9 -4 | 0 1 0 0 2 -1 | 0 0 2 5 8 8 }}

=== Siebog
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3136/3125
Mapping: {{mapping|legend=1| 1 0 0 -3 8 | 0 1 0 0 3 | 0 0 2 5 -8 }}

=== Triglav
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3136/3125
Mapping: {{mapping|legend=1| 1 0 2 2 1 | 0 1 2 5 2 | 0 0 -4 -10 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 1001/1000, 3025/3024
Mapping: {{mapping| 1 0 2 2 1 6 | 0 1 2 5 2 -1 | 0 0 -4 -10 -1 -1 }}

=== Semihemimean
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 9801/9800
Mapping: {{mapping|legend=1| 2 0 0 -6 -3 | 0 1 0 0 -2 | 0 0 2 5 7 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 3136/3125, 4459/4455
Mapping: {{mapping| 2 0 0 -6 -3 15 | 0 1 0 0 -2 2 | 0 0 2 5 7 -6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 561/560, 1001/1000, 1632/1625
Mapping: {{mapping| 2 0 0 -6 -3 15 5 | 0 1 0 0 -2 2 1 | 0 0 2 5 7 -6 0 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 289/288, 361/360, 456/455, 476/475, 561/560
Mapping: {{mapping| 2 0 0 -6 -3 15 5 3 | 0 1 0 0 -2 2 1 1 | 0 0 2 5 7 -6 0 1 }}


= Miscellaneous 5-limit temperaments

=== Unidecmic
Subgroup: 2.3.5
Comma list: 31381059609/31250000000
Mapping: {{mapping|legend=1| 2 -1 -3 | 0 6 11 }}

=== Quasithird
Subgroup: 2.3.5
Comma list: {{monzo| 55 -64 20 }}
Mapping: {{mapping|legend=1| 4 0 -11 | 0 5 16 }}

=== Supersharp
Subgroup: 2.3.5
Comma list: 800/729
Mapping: {{mapping|legend=1| 2 0 -5 | 0 1 3 }}

=== Avila
Subgroup: 2.3.5
Comma list: 729/640
Mapping: {{mapping|legend=1| 1 0 -7 | 0 1 6 }}

=== Lafa
Subgroup: 2.3.5
Comma list: {{monzo| 77 -31 -12 }}
Mapping: {{mapping|legend=1| 1 -1 9 | 0 12 -31 }}

=== Lafayette
Subgroup: 2.3.5
Comma list: 3456/3125
Mapping: {{mapping|legend=1| 1 1 2 | 0 5 3 }}

=== Dodifo
Subgroup: 2.3.5
Comma list: {{monzo| -67 -9 35 }}
Mapping: {{mapping|legend=1| 1 12 5 | 0 -35 -9 }}

=== Doublewide
Subgroup: 2.3.5
Comma list: 390625/373248
Mapping: {{mapping|legend=1| 2 1 3 | 0 4 3 }}

=== Shibboleth
Subgroup: 2.3.5
Comma list: 1953125/1889568
Mapping: {{mapping|legend=1| 1 4 5 | 0 -9 -10 }}

=== Semidimfourth
Subgroup: 2.3.5
Comma list: {{monzo| 7 41 -31 }}
Mapping: {{mapping|legend=1| 1 21 28 | 0 -31 -41 }}

=== Mynic
Subgroup: 2.3.5
Comma list: 10077696/9765625
Mapping: {{mapping|legend=1| 1 9 9 | 0 -10 -9 }}

=== Progress
Subgroup: 2.3.5
Comma list: 32768/30375
Mapping: {{mapping|legend=1| 1 0 5 | 0 3 -5 }}

=== Abigail
Subgroup: 2.3.5
Comma list: {{monzo| 25 -48 22 }}
Mapping: {{mapping|legend=1| 2 7 13 | 0 -11 -24 }}

=== Supermajor
Subgroup: 2.3.5
Comma list: {{monzo| -13 -46 37 }}
Mapping: {{mapping|legend=1| 1 15 19 | 0 -37 -46 }}

=== Gamera
Subgroup: 2.3.5
Comma list: {{monzo| 10 -40 23 }}
Mapping: {{mapping|legend=1| 1 6 10 | 0 -23 -40 }}

=== Tritriple
Subgroup: 2.3.5
Comma list: {{monzo| 31 20 -27 }}
Mapping: {{mapping|legend=1| 1 -11 -7 | 0 27 20 }}

=== Kangaroo
Subgroup: 2.3.5
Comma list: 64000/59049
Mapping: {{mapping|legend=1| 1 0 -3 | 0 3 10 }}

=== Tertiaseptal
Subgroup: 2.3.5
Comma list: {{monzo| -59 5 22 }}
Mapping: {{mapping|legend=1| 1 3 2 | 0 -22 5 }}

=== Untriton
Subgroup: 2.3.5
Comma list: {{monzo| -51 19 9 }}
Mapping: {{mapping|legend=1| 1 6 -7 | 0 -9 19 }}

=== Nessafof
Subgroup: 2.3.5
Comma list: {{monzo| 25 15 -21 }}
Mapping: {{mapping|legend=1| 3 2 5 | 0 7 5 }}

=== Lemba
Subgroup: 2.3.5
Comma list: 140625/131072
Mapping: {{mapping|legend=1| 2 2 5 | 0 3 -1 }}

=== Delorean
Subgroup: 2.3.5
Comma list: 17496/15625
Mapping: {{mapping|legend=1| 1 3 4 | 0 -6 -7 }}

=== Majvam
Subgroup: 2.3.5
Comma list: 2404631929946112/2384185791015625
Mapping: {{mapping|legend=1| 1 10 5 | 0 -22 -7 }}

=== Beatles
Subgroup: 2.3.5
Comma list: 524288/492075
Mapping: {{mapping|legend=1| 1 1 5 | 0 2 -9 }}

=== Magus
Subgroup: 2.3.5
Comma list: 50331648/48828125
Mapping: {{mapping|legend=1| 1 -2 2 | 0 11 1 }}

=== Tritonic
Subgroup: 2.3.5
Comma list: 553584375/536870912
Mapping: {{mapping|legend=1| 1 4 -3 | 0 -5 11 }}

=== Wizard
Subgroup: 2.3.5
Comma list: 2197265625/2147483648
Mapping: {{mapping|legend=1| 2 1 5 | 0 6 -1 }}

=== Merman
Subgroup: 2.3.5
Comma list: {{monzo| -40 15 7 }}
Mapping: {{mapping|legend=1| 1 5 -5 | 0 -7 15 }}

=== Nusecond
Subgroup: 2.3.5
Comma list: 51018336/48828125
Mapping: {{mapping|legend=1| 1 3 4 | 0 -11 -13 }}

=== Comic
Subgroup: 2.3.5
Comma list: 5120000/4782969
Mapping: {{mapping|legend=1| 2 1 -3 | 0 2 7 }}

=== Sfourth
Subgroup: 2.3.5
Comma list: {{monzo| -5 31 -19 }}
Mapping: {{mapping|legend=1| 1 2 3 | 0 -19 -31 }}

=== Thuja
Subgroup: 2.3.5
Comma list: 254803968/244140625
Mapping: {{mapping|legend=1| 1 -4 0 | 0 12 5 }}

=== Leapday
Subgroup: 2.3.5
Comma list: 10737418240/10460353203
Mapping: {{mapping|legend=1| 1 0 -31 | 0 1 21 }}

=== Vines
Subgroup: 2.3.5
Comma list: 156728328192/152587890625
Mapping: {{mapping|legend=1| 2 7 8 | 0 -8 -7 }}

=== Emka
Subgroup: 2.3.5
Comma list: {{monzo| -50 -8 27 }}
Mapping: {{mapping|legend=1| 1 14 6 | 0 -27 -8 }}

=== Misneb
Subgroup: 2.3.5
Comma list: {{monzo| -57 14 15 }}
Mapping: {{mapping|legend=1| 1 3 1 | 0 -15 14 }}

=== Semisept
Subgroup: 2.3.5
Comma list: 782757789696/762939453125
Mapping: {{mapping|legend=1| 1 12 6 | 0 -17 -6 }}

=== Septimin
Subgroup: 2.3.5
Comma list: 35595703125/34359738368
Mapping: {{mapping|legend=1| 1 4 1 | 0 -11 6 }}

=== Slurpee
Subgroup: 2.3.5
Comma list: 177147/156250
Mapping: {{mapping|legend=1| 1 2 3 | 0 -7 -11 }}

=== Pentadecal
Subgroup: 2.3.5
Comma list: 30517578125/29386561536
Mapping: {{mapping|legend=1| 15 0 11 | 0 1 1 }}

=== Anthoine
Subgroup: 2.3.5
Comma list: 286102294921875/281474976710656
Mapping: {{mapping|legend=1| 1 8 2 | 0 -20 1 }}

=== Sentinel
Subgroup: 2.3.5
Comma list: 8968066875/8589934592
Mapping: {{mapping|legend=1| 1 3 -3 | 0 -4 15 }}

=== Kumonga
Subgroup: 2.3.5
Comma list: 1289945088/1220703125
Mapping: {{mapping|legend=1| 1 4 4 | 0 -13 -9 }}

=== Mirkat
Subgroup: 2.3.5
Comma list: {{monzo| 20 -39 18 }}
Mapping: {{mapping|legend=1| 3 2 1 | 0 6 13 }}

=== Semidimi
Subgroup: 2.3.5
Comma list: {{monzo| -12 -73 55 }}
Mapping: {{mapping|legend=1| 1 36 48 | 0 -55 -73 }}

=== Slender
Subgroup: 2.3.5
Comma list: {{monzo| -46 10 13 }}
Mapping: {{mapping|legend=1| 1 2 2 | 0 -13 10 }}

=== Quasitemp
Subgroup: 2.3.5
Comma list: 6103515625/5804752896
Mapping: {{mapping|legend=1| 1 5 5 | 0 -14 -11 }}

=== Cypress
Subgroup: 2.3.5
Comma list: 258280326/244140625
Mapping: {{mapping|legend=1| 1 7 10 | 0 -12 -17 }}

=== Chromo
Subgroup: 2.3.5
Comma list: 1220703125/1146617856
Mapping: {{mapping|legend=1| 1 1 2 | 0 13 7 }}

=== Tertiosec
Subgroup: 2.3.5
Comma list: {{monzo| -89 21 24 }}
Mapping: {{mapping|legend=1| 3 7 5 | 0 -8 7 }}

=== Fervor
Subgroup: 2.3.5
Comma list: 67108864/61509375
Mapping: {{mapping|legend=1| 1 4 -2 | 0 -5 9 }}

=== Bohpier
Subgroup: 2.3.5
Comma list: 1220703125/1162261467
Mapping: {{mapping|legend=1| 1 0 0 | 0 13 19 }}

=== Elvis
Subgroup: 2.3.5
Comma list: 36905625/33554432
Mapping: {{mapping|legend=1| 2 1 10 | 0 2 -5 }}

=== Enneadecacot
Subgroup: 2.3.5
Comma list: {{monzo| 79 -22 -19 }}
Mapping: {{mapping|legend=1| 1 1 3 | 0 19 -22 }}

=== Vinegar
Subgroup: 2.3.5
Comma list: 16000000/14348907
Mapping: {{mapping|legend=1| 3 0 -5 | 0 2 5 }}

=== Oolong
Subgroup: 2.3.5
Comma list: 793437161472/762939453125
Mapping: {{mapping|legend=1| 1 6 7 | 0 -17 -18 }}

=== Oncle
Subgroup: 2.3.5
Comma list: 145282683375/137438953472
Mapping: {{mapping|legend=1| 1 1 6 | 0 3 -19 }}

=== Quasiorwell
Subgroup: 2.3.5
Comma list: {{monzo| -93 3 38 }}
Mapping: {{mapping|legend=1| 1 31 0 | 0 -38 3 }}

=== Diesic
Subgroup: 2.3.5
Comma list: 10460353203/9765625000
Mapping: {{mapping|legend=1| 1 2 3 | 0 -13 -21 }}

=== Quartemka
Subgroup: 2.3.5
Comma list: {{monzo| 2 -32 21 }}
Mapping: {{mapping|legend=1| 1 4 6 | 0 -21 -32 }}

=== Genocchi
Subgroup: 2.3.5
Comma list: 2359296/1953125
Mapping: {{mapping|legend=1| 1 0 2 | 0 9 2 }}

=== Casablanca
Subgroup: 2.3.5
Comma list: {{monzo| 22 14 -19 }}
Mapping: {{mapping|legend=1| 1 -7 -14 | 0 19 14 }}

=== Archaeotherium
Subgroup: 2.3.5
Comma list: 597871125/536870912
Mapping: {{mapping|legend=1| 1 1 5 | 0 3 -14 }}

=== Octacoid
Subgroup: 2.3.5
Comma list: 8589934592/7688671875
Mapping: {{mapping|legend=1| 1 1 3 | 0 8 -9 }}

=== Quasimoha
Subgroup: 2.3.5
Comma list: {{monzo| -41 23 2 }}
Mapping: {{mapping|legend=1| 1 1 9 | 0 2 -23 }}

=== Phillips
Subgroup: 2.3.5
Comma list: 9685512225/8589934592
Mapping: {{mapping|legend=1| 2 0 33 | 0 1 -9 }}

=== Satin
Subgroup: 2.3.5
Comma list: {{monzo| 104 -70 3 }}
Mapping: {{mapping|legend=1| 1 2 12 | 0 -3 -70 }}

=== Lockerbie
Subgroup: 2.3.5
Comma list: {{monzo| 91 51 -74 }}
Mapping: {{mapping|legend=1| 1 -25 -16 | 0 74 51 }}

=== Rarity
Subgroup: 2.3.5
Comma list: {{monzo| -57 17 13 }}
Mapping: {{mapping|legend=1| 1 11 -10 | 0 -13 17 }}

=== Jorgensen
Subgroup: 2.3.5
Comma list: {{monzo| 111 -70 }}
Mapping: {{mapping|legend=1| 70 111 0 | 0 0 1 }}

=== References


= Horwell family

=== Horwell
Subgroup: 2.3.5.7
Comma list: 65625/65536
Mapping: {{mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }}
Mapping to lattice: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]

=== Zelda
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375
Mapping: {{mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }}

=== Horwellic
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 65625/65536
Mapping: {{mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }}


= Horwell temperaments

=== Mutt
Subgroup: 2.3.5
Comma list: {{monzo| -44 -3 21 }}
Mapping: {{mapping|legend=1| 3 5 7 | 0 -7 -1 }}

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 65625/65536, 250047/250000
Mapping: {{mapping|legend=1| 3 5 7 8 | 0 -7 -1 12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4356, 16384/16335
Mapping: {{mapping| 3 5 7 8 10 | 0 -7 -1 12 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 625/624, 2200/2197
Mapping: {{mapping| 3 5 7 8 10 11 | 0 -7 -1 12 11 3 }}

=== Fifthplus
Subgroup: 2.3.5.7
Comma list: 65625/65536, 420175/419904
Mapping: {{mapping|legend=1| 1 11 -3 20 | 0 -23 13 -42 }}

=== Emkay
Subgroup: 2.3.5.7
Comma list: 65625/65536, 244140625/243045684
Mapping: {{mapping|legend=1| 1 14 6 -28 | 0 -27 -8 67 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 65625/65536
Mapping: {{mapping| 1 14 6 -28 3 | 0 -27 -8 67 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197
Mapping: {{mapping| 1 14 6 -28 3 6 | 0 -27 -8 67 1 -5 }}

==== See also

=== Kastro
Subgroup: 2.3.5.7
Comma list: 65625/65536, 117649/116640
Mapping: {{mapping|legend=1| 1 5 1 6 | 0 -31 12 -29 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375, 12005/11979
Mapping: {{mapping| 1 5 1 6 5 | 0 -31 12 -29 -14 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 364/363, 385/384, 3388/3375
Mapping: {{mapping| 1 5 1 6 5 7 | 0 -31 12 -29 -14 -30 }}

=== Oquatonic
Subgroup: 2.3.5.7
Comma list: 65625/65536, 390625/388962
Mapping: {{mapping|legend=1| 28 0 65 123 | 0 1 0 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 6250/6237, 65625/65536
Mapping: {{mapping| 28 0 65 123 230 | 0 1 0 -1 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1375/1372, 2080/2079, 2200/2197
Mapping: {{mapping| 28 0 65 123 230 148 | 0 1 0 -1 -3 -1 }}

=== Bezique
Subgroup: 2.3.5.7
Comma list: 65625/65536, 847288609443/843308032000
Mapping: {{mapping|legend=1| 32 0 125 -113 | 0 1 -1 4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 46656/46585, 65625/65536
Mapping: {{mapping| 32 0 125 -113 60 | 0 1 -1 4 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 1575/1573, 4225/4224, 6656/6655
Mapping: {{mapping| 32 0 125 -113 60 17 | 0 1 -1 4 1 2 }}

=== Notes


= Immunity family

=== Immunity
Subgroup: 2.3.5
Comma list: 1638400/1594323
Mapping: {{mapping|legend=1| 1 0 -8 | 0 2 13 }}

==== 2.3.5.13 subgroup
Subgroup: 2.3.5.13
Comma list: 676/675, 3200/3159

==== Overview to extensions

=== Septimal immunity
Subgroup: 2.3.5.7
Comma list: 49/48, 2240/2187
Mapping: {{mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 896/891
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 91/90, 896/891
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}

==== Impunity
Subgroup: 2.3.5.7.11
Comma list: 49/48, 100/99, 1232/1215
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 91/90, 100/99, 352/351
Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}

=== Immunized
Subgroup: 2.3.5.7
Comma list: 64/63, 8748/8575
Mapping: {{mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 99/98, 1944/1925
Mapping: {{mapping| 1 0 -8 6 13 | 0 2 13 -4 -12 }}

=== Immune
Subgroup: 2.3.5.7
Comma list: 225/224, 781250/750141
Mapping: {{mapping|legend=1| 1 2 5 9 | 0 -2 -13 -30 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 1331/1323
Mapping: {{mapping| 1 2 5 9 8 | 0 -2 -13 -30 -22 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 169/168, 225/224, 275/273
Mapping: {{mapping| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }}


= Jubilismic clan

=== Jubilic
Subgroup: 2.5.7
Comma list: 50/49
Mapping: {{mapping|legend=2| 2 0 1 | 0 1 1 }}
Mapping: {{mapping|legend=3| 2 0 0 1 | 0 0 1 1 }}

==== Overview to extensions

=== Lemba
Subgroup: 2.3.5.7
Comma list: 50/49, 525/512
Mapping: {{mapping|legend=1| 2 2 5 6 | 0 3 -1 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 385/384
Mapping: {{mapping| 2 2 5 6 5 | 0 3 -1 -1 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 50/49, 65/64, 78/77
Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}

=== Astrology
Subgroup: 2.3.5.7
Comma list: 50/49, 3125/3072
Mapping: {{mapping|legend=1| 2 0 4 5 | 0 5 1 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 121/120, 176/175
Mapping: {{mapping| 2 0 4 5 5 | 0 5 1 1 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 65/64, 78/77, 121/120
Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}

===== Horoscope
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 66/65, 105/104, 121/120
Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}

=== Walid
Subgroup: 2.3.5.7
Comma list: 16/15, 50/49
Mapping: {{mapping|legend=1| 2 0 8 9 | 0 1 -1 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 50/49
Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}

=== Doublewide
Subgroup: 2.3.5.7
Comma list: 50/49, 875/864
Mapping: {{mapping|legend=1| 2 1 3 4 | 0 4 3 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98, 385/384
Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}

==== Fleetwood
Subgroup: 2.3.5.7.11
Comma list: 50/49, 55/54, 176/175
Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 55/54, 65/63, 176/175
Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}

==== Cavalier
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 875/864
Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 50/49, 78/77, 325/324
Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}

=== Elvis
Subgroup: 2.3.5.7
Comma list: 50/49, 8505/8192
Mapping: {{mapping|legend=1| 2 1 10 11 | 0 2 -5 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 1344/1331
Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 50/49, 78/77, 1053/1024
Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}

=== Comic
Subgroup: 2.3.5.7
Comma list: 50/49, 2240/2187
Mapping: {{mapping|legend=1| 2 1 -3 -2 | 0 2 7 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98, 2662/2625
Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 65/63, 99/98, 968/945
Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}

=== Bipyth
Subgroup: 2.3.5.7
Comma list: 50/49, 20480/19683
Mapping: {{mapping|legend=1| 2 0 -24 -23 | 0 1 9 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 121/120, 896/891
Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}

=== Sedecic
Subgroup: 2.3.5.7
Comma list: 50/49, 546875/524288
Mapping: {{mapping|legend=1| 16 0 37 45 | 0 1 0 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 385/384, 1331/1323
Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}

=== Subgroup extensions

==== Antikythera (2.9.5.7)
Subgroup: 2.9.5.7
Comma list: 50/49, 64/63
Mapping: {{mapping|legend=2| 2 0 11 12 | 0 1 -1 -1 }}
Mapping: {{mapping|legend=3| 2 0 11 12 | 0 1/2 -1 -1 }}

=== References


= Jubilismic family

=== Jubilismic
Subgroup: 2.3.5.7
Comma list: 50/49
Mapping: {{mapping|legend=1| 2 0 0 1 | 0 1 0 0 | 0 0 1 1 }}

=== Undecimal jubilismic
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98
Mapping: {{mapping|legend=1| 2 0 0 1 4 | 0 1 0 0 -2 | 0 0 1 1 2 }}

=== Festival
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49
Mapping: {{mapping|legend=1| 2 0 0 1 -4 | 0 1 0 0 2 | 0 0 1 1 1 }}

=== Fiesta
Subgroup: 2.3.5.7.11
Comma list: 50/49, 56/55
Mapping: {{mapping|legend=1| 2 0 0 1 7 | 0 1 0 0 0 | 0 0 1 1 0 }}

=== Jamboree
Subgroup: 2.3.5.7.11
Comma list: 50/49, 55/54
Mapping: {{mapping|legend=1| 2 0 0 1 2 | 0 1 0 0 3 | 0 0 1 1 -1 }}


= Kalismic temperaments

=== Lycoris
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 1771561/1771470
Mapping: {{mapping|legend=1| 2 0 -2 1 0 | 0 1 1 3 2 | 0 0 6 -5 1 }}

==== Higanbana
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 10648/10647, 1399680/1399489
Mapping: {{mapping| 2 1 -1 2 2 4 | 0 2 2 6 4 1 | 0 0 6 -5 1 4 }}

=== Van gogh
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 199297406/199290375
Mapping: {{mapping|legend=1| 2 0 8 0 11 | 0 1 1 2 1 | 0 0 -9 -1 -10 }}

=== Sif
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 2097152/2096325
Mapping: {{mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 4096/4095, 6656/6655, 9801/9800
Mapping: {{mapping| 2 0 1 7 11 16 | 0 1 0 1 -1 -3 | 0 0 4 -5 -1 1 }}

=== Loki
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800
Mapping: {{mapping|legend=1| 2 0 0 -21 -18 | 0 1 0 4 2 | 0 0 1 3 4 }}

=== Pessoal
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 131072/130977
Mapping: {{mapping|legend=1| 2 0 1 10 14 | 0 1 0 -1 -3 | 0 0 3 -1 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 4096/4095
Mapping: {{mapping| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}

=== Linus
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 391314/390625
Mapping: {{mapping|legend=1| 10 0 0 -11 4 | 0 1 0 1 -1 | 0 0 1 1 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 4225/4224, 4459/4455
Mapping: {{mapping| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }}


= Keemic family

=== Keemic
Subgroup: 2.3.5.7
Comma list: 875/864
Mapping: {{mapping|legend=1| 1 0 0 5 | 0 1 0 3 | 0 0 1 -3 }}
Mapping to lattice: [{{val| 0 0 -1 3 }}, {{val| 0 1 1 0 }}]

=== Undecimal keemic
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384
Mapping: {{mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }}

=== Supernatural
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/243
Mapping: {{mapping|legend=1| 1 0 2 -1 0 | 0 5 1 12 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 245/243
Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }}


= Keemic temperaments

=== Quasitemp
Subgroup: 2.3.5.7
Comma list: 875/864, 2401/2400
Mapping: {{mapping|legend=1| 1 -9 -6 -4 | 0 14 11 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1375/1372
Mapping: {{mapping| 1 -9 -6 -4 8 | 0 14 11 9 -6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 275/273, 385/384
Mapping: {{mapping| 1 -9 -6 -4 8 9 | 0 14 11 9 -6 -7 }}

==== Quato
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 625/616
Mapping: {{mapping| 1 -9 -6 -4 -23 | 0 14 11 9 35 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 243/242, 275/273, 325/324
Mapping: {{mapping| 1 -9 -6 -4 -23 -22 | 0 14 11 9 35 34 }}

=== Chromo
Subgroup: 2.3.5.7
Comma list: 875/864, 2430/2401
Mapping: {{mapping|legend=1| 1 1 2 2 | 0 13 7 18 }}

=== Barbad
Subgroup: 2.3.5.7
Comma list: 875/864, 16875/16807
Mapping: {{mapping|legend=1| 1 -10 -5 -10 | 0 19 12 21 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/242, 540/539, 625/616
Mapping: {{mapping| 1 -10 -5 -10 -13 | 0 19 12 21 27 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 245/242, 275/273
Mapping: {{mapping| 1 -10 -5 -10 -13 -3 | 0 19 12 21 27 11 }}

=== Hyperkleismic
Subgroup: 2.3.5.7
Comma list: 875/864, 51200/50421
Mapping: {{mapping|legend=1| 1 -3 -2 2 | 0 17 16 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 2420/2401
Mapping: {{mapping| 1 -3 -2 2 4 | 0 17 16 3 -2}}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 169/168, 275/273, 385/384
Mapping: {{mapping| 1 -3 -2 2 4 1 | 0 17 16 3 -2 10 }}

=== Sevond
Subgroup: 2.3.5.7
Comma list: 875/864, 327680/321489
Mapping: {{mapping|legend=1| 7 0 -6 53 | 0 1 2 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 6655/6561
Mapping: {{mapping| 7 0 -6 53 2 | 0 1 2 -3 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 169/168, 352/351, 385/384
Mapping: {{mapping| 7 0 -6 53 2 37 | 0 1 2 -3 2 -1 }}


= Keenanismic family

=== Keenanismic
Subgroup: 2.3.5.7.11
Comma list: 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }}

=== Martwin
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }}

=== Ancient
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624
Mapping: {{mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }}

=== Zaxa
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }}


= Kleismic family

=== Kleismic a.k.a. hanson
Subgroup: 2.3.5
Comma list: 15625/15552
Mapping: {{mapping|legend=1| 1 0 1 | 0 6 5 }}

==== Overview to extensions

=== Catakleismic

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 225/224, 4375/4374
Mapping: {{mapping|legend=1| 1 0 1 -3 | 0 6 5 22 }}

===== 2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: 169/168, 225/224, 325/324
Mapping: {{mapping| 1 0 1 -3 0 | 0 6 5 22 14 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 4375/4374
Mapping: {{mapping| 1 0 1 -3 9 | 0 6 5 22 -21 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 325/324, 385/384
Mapping: {{mapping| 1 0 1 -3 9 0 | 0 6 5 22 -21 14 }}

==== Cataclysmic
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 2200/2187
Mapping: {{mapping| 1 0 1 -3 -5 | 0 6 5 22 32 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 169/168, 176/175, 275/273
Mapping: {{mapping| 1 0 1 -3 -5 0 | 0 6 5 22 32 14 }}

==== Catalytic
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 4375/4374
Mapping: {{mapping| 1 0 1 -3 -10 | 0 6 5 22 51 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 325/324, 1716/1715
Mapping: {{mapping| 1 0 1 -3 -10 0 | 0 6 5 22 51 14 }}

==== Cataleptic
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 864/847
Mapping: {{mapping| 1 0 1 -3 4 | 0 6 5 22 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 100/99, 144/143, 676/675
Mapping: {{mapping| 1 0 1 -3 4 0 | 0 6 5 22 -2 14 }}

==== Bikleismic
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 4375/4356
Mapping: {{mapping| 2 0 2 -6 -1 | 0 6 5 22 15 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 243/242, 325/324
Mapping: {{mapping| 2 0 2 -6 -1 0 | 0 6 5 22 15 14 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 225/224, 243/242, 325/324
Mapping: {{mapping| 2 0 2 -6 -1 0 5 | 0 6 5 22 15 14 6 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 153/152, 169/168, 221/220, 225/224, 243/242, 325/324
Mapping: {{mapping| 2 0 2 -6 -1 0 5 -1 | 0 6 5 22 15 14 6 18 }}

=== Keemun
Subgroup: 2.3.5.7
Comma list: 49/48, 126/125
Mapping: {{mapping|legend=1| 1 0 1 2 | 0 6 5 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 100/99
Mapping: {{mapping| 1 0 1 2 4 | 0 6 5 3 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 65/64, 100/99
Mapping: {{mapping| 1 0 1 2 4 5 | 0 6 5 3 -2 -5 }}

===== Kema
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 91/90, 100/99
Mapping: {{mapping| 1 0 1 2 4 0 | 0 6 5 3 -2 14 }}

===== Kumbaya
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 49/48, 56/55, 66/65
Mapping: {{mapping| 1 0 1 2 4 4 | 0 6 5 3 -2 -1 }}

==== Qeema
Subgroup: 2.3.5.7.11
Comma list: 45/44, 49/48, 126/125
Mapping: {{mapping| 1 0 1 2 -1 | 0 6 5 3 17 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 49/48, 78/77, 126/125
Mapping: {{mapping| 1 0 1 2 -1 0 | 0 6 5 3 17 14 }}

==== Darjeeling
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 77/75
Mapping: {{mapping| 1 0 1 2 0 | 0 6 5 3 13 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 66/65, 77/75
Mapping: {{mapping| 1 0 1 2 0 0 | 0 6 5 3 13 14 }}

=== Catalan
Subgroup: 2.3.5.7
Comma list: 64/63, 15625/15552
Mapping: {{mapping|legend=1| 1 0 1 6 | 0 6 5 -12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 1331/1323
Mapping: {{mapping| 1 0 1 6 4 | 0 6 5 -12 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 144/143, 275/273
Mapping: {{mapping| 1 0 1 6 4 0 | 0 6 5 -12 -2 14 }}

=== Countercata
Subgroup: 2.3.5.7
Comma list: 5120/5103, 15625/15552
Mapping: {{mapping|legend=1| 1 0 1 11 | 0 6 5 -31 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 2200/2187, 3388/3375
Mapping: {{mapping| 1 0 1 11 -5 | 0 6 5 -31 32 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 385/384, 625/624
Mapping: {{mapping| 1 0 1 11 -5 0 | 0 6 5 -31 32 14 }}

=== Metakleismic
Subgroup: 2.3.5.7
Comma list: 15625/15552, 179200/177147
Mapping: {{mapping|legend=1| 1 0 1 -12 | 0 6 5 56 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 2200/2187, 14700/14641
Mapping: {{mapping| 1 0 1 -12 -5 | 0 6 5 56 32 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 625/624
Mapping: {{mapping| 1 0 1 -12 -5 0 | 0 6 5 56 32 14 }}

=== Hemikleismic
Subgroup: 2.3.5.7
Comma list: 4000/3969, 6144/6125
Mapping: {{mapping|legend=1| 1 0 1 4 | 0 12 10 -9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 4000/3969
Mapping: {{mapping| 1 0 1 4 2 | 0 12 10 -9 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 275/273, 325/324
Mapping: {{mapping| 1 0 1 4 2 0 | 0 12 10 -9 11 28 }}

=== Clyde
Subgroup: 2.3.5.7
Comma list: 245/243, 3136/3125
Mapping: {{mapping|legend=1| 1 -6 -4 -13 | 0 12 10 25 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 3136/3125
Mapping: {{mapping| 1 -6 -4 -13 18 | 0 12 10 25 -23 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 385/384, 625/624
Mapping: {{mapping| 1 -6 -4 -13 18 -14 | 0 12 10 25 -23 28 }}

=== Tritikleismic
Subgroup: 2.3.5.7
Comma list: 1029/1024, 15625/15552
Mapping: {{mapping|legend=1| 3 0 3 10 | 0 6 5 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 4000/3993
Mapping: {{mapping| 3 0 3 10 8 | 0 6 5 -2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 625/624
Mapping: {{mapping| 3 0 3 10 8 0 | 0 6 5 -2 3 14 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 375/374, 385/384
Mapping: {{mapping| 3 0 3 10 8 0 -2 | 0 6 5 -2 3 14 18 }}

=== Marfifths
Subgroup: 2.3.5.7
Comma list: 10976/10935, 15625/15552
Mapping: {{mapping|legend=1| 1 -6 -4 -17 | 0 18 15 47 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 6250/6237, 10976/10935
Mapping: {{mapping| 1 -6 -4 -17 22 | 0 18 15 47 -44 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 625/624, 10976/10935
Mapping: {{mapping| 1 -6 -4 -17 22 -14 | 0 18 15 47 -44 42 }}

==== Diatessic
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 2200/2187, 5632/5625
Mapping: {{mapping| 1 -6 -4 -17 -37 | 0 18 15 47 96 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 625/624, 1375/1372
Mapping: {{mapping| 1 -6 -4 -17 -37 -14 | 0 18 15 47 96 42 }}

==== Marf
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891, 15625/15552
Mapping: {{mapping| 1 -6 -4 -17 14 | 0 18 15 47 -25 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 540/539, 625/624, 896/891
Mapping: {{mapping| 1 -6 -4 -17 14 -14 | 0 18 15 47 -25 42 }}

=== Kleiboh
Subgroup: 2.3.5.7
Comma list: 1728/1715, 3125/3087
Mapping: {{mapping|legend=1| 1 -12 -9 -7 | 0 18 15 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 3125/3087
Mapping: {{mapping| 1 -12 -9 -7 -29 | 0 18 15 13 43 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 275/273, 325/324, 540/539
Mapping: {{mapping| 1 -12 -9 -7 -29 -28 | 0 18 15 13 43 42 }}

=== Quadritikleismic
Subgroup: 2.3.5.7
Comma list: 2401/2400, 15625/15552
Mapping: {{mapping|legend=1| 4 0 4 7 | 0 6 5 4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 6250/6237
Mapping: {{mapping| 4 0 4 7 17 | 0 6 5 4 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 625/624, 1375/1372
Mapping: {{mapping| 4 0 4 7 17 0 | 0 6 5 4 -3 14 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 325/324, 385/384, 442/441, 625/624
Mapping: {{mapping| 4 0 4 7 17 0 10 | 0 6 5 4 -3 14 6 }}

=== Marthirds
Subgroup: 2.3.5.7
Comma list: 15625/15552, 2460375/2458624
Mapping: {{mapping|legend=1| 1 -6 -4 -19 | 0 24 20 69 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 15625/15552, 19712/19683
Mapping: {{mapping| 1 -6 -4 -19 -43 | 0 24 20 69 147 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 625/624, 1375/1372, 19712/19683
Mapping: {{mapping| 1 -6 -4 -19 -43 -14 | 0 24 20 69 147 56 }}

=== Sqrtphi
Subgroup: 2.3.5.7
Comma list: 15625/15552, 16875/16807
Mapping: {{mapping|legend=1| 1 -18 -14 -22 | 0 30 25 38 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 4375/4356
Mapping: {{mapping| 1 -18 -14 -22 -22 | 0 30 25 38 39 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 625/624, 1375/1372
Mapping: {{mapping| 1 -18 -14 -22 -22 -42 | 0 30 25 38 39 70 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 364/363, 375/374, 540/539, 595/594
Mapping: {{mapping| 1 -18 -14 -22 -22 -42 -39 | 0 30 25 38 39 70 66 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594
Mapping: {{mapping| 1 -18 -14 -22 -22 -42 -39 16 | 0 30 25 38 39 70 66 -18 }}

=== Quartkeenlig
Subgroup: 2.3.5.7
Comma list: 15625/15552, 117649/116640
Mapping: {{mapping|legend=1| 1 0 1 1 | 0 36 30 41 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 6250/6237, 67228/66825
Mapping: {{mapping| 1 0 1 1 5 | 0 36 30 41 -35 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 625/624, 16807/16731
Mapping: {{mapping| 1 0 1 1 5 0 | 0 36 30 41 -35 84 }}

=== Novemkleismic
Subgroup: 2.3.5.7
Comma list: 15625/15552, 40353607/40310784
Mapping: {{mapping|legend=1| 9 0 9 11 | 0 6 5 6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4000/3993, 15625/15552
Mapping: {{mapping| 9 0 9 11 24 | 0 6 5 6 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 625/624, 1375/1372, 4000/3993
Mapping: {{mapping| 9 0 9 11 24 0 | 0 6 5 6 3 14 }}

=== Subgroup extensions

==== Kleismic (2.3.5.13) a.k.a. cata
Subgroup: 2.3.5.13
Comma list: 325/324, 625/624
Mapping: {{mapping| 1 0 1 0 | 0 6 5 14 }}

===== 2.3.5.13.37 subgroup
Subgroup: 2.3.5.13.37.41
Comma list: 325/324, 481/480, 625/624
Mapping: {{mapping| 1 0 1 0 6 | 0 6 5 14 -3 }}

===== 2.3.5.13.37.41 subgroup
Subgroup: 2.3.5.13.37.41
Comma list: 325/324, 481/480, 625/624, 1025/1024
Mapping: {{mapping| 1 0 1 0 6 8 | 0 6 5 14 -3 -10 }}


= Kleismic rank-3 family

=== Rank-3 kleismic
Subgroup: 2.3.5.7
Comma list: 15625/15552
Mapping: {{mapping|legend=1| 1 0 1 0 | 0 6 5 0 | 0 0 0 1 }}

==== 2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: 325/324, 625/624
Mapping: {{mapping| 1 0 1 0 0 | 0 6 5 0 14 | 0 0 0 1 0 }}

=== Enlil
Subgroup: 2.3.5.7.11
Comma list: 385/384, 6250/6237
Mapping: {{mapping|legend=1| 1 0 1 0 6 | 0 6 5 0 1 | 0 0 0 1 -1 }}

==== 13-limit (sumatra)
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 625/624
Mapping: {{mapping| 1 0 1 0 6 0 | 0 6 5 0 1 14 | 0 0 0 1 -1 0 }}

=== Isimud
Subgroup: 2.3.5.7.11
Comma list: 4125/4096, 8019/8000
Mapping: {{mapping|legend=1| 1 0 1 0 9 | 0 6 5 0 -21 | 0 0 0 1 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 625/624, 1287/1280
Mapping: {{mapping| 1 0 1 0 9 0 | 0 6 5 0 -21 14 | 0 0 0 1 0 0 }}

=== Enki
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4356
Mapping: {{mapping|legend=1| 1 0 1 0 1 | 0 6 5 0 4 | 0 0 0 2 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 625/624
Mapping: {{mapping| 1 0 1 0 1 0 | 0 6 5 0 4 14 | 0 0 0 2 1 0 }}

=== Catakleismoid
Subgroup: 2.3.5.7.11
Comma list: 225/224, 4375/4374
Mapping: {{mapping|legend=1| 1 0 1 -3 0 | 0 6 5 22 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 325/324
Mapping: {{mapping| 1 0 1 -3 0 0 | 0 6 5 22 0 14 | 0 0 0 0 1 0 }}


= Landscape family

=== Landscape
Subgroup: 2.3.5.7
Comma list: 250047/250000
Mapping: {{mapping|legend=1| 3 0 0 4 | 0 1 0 -2 | 0 0 1 2 }}

==== Overview to extensions

=== Landy
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4356
Mapping: {{mapping|legend=1| 3 0 0 4 -1 | 0 1 0 -2 -2 | 0 0 1 2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 625/624
Mapping: {{mapping| 3 0 0 4 -1 -12 | 0 1 0 -2 -2 -1 | 0 0 1 2 3 4 }}

=== Odin
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 151263/151250
Mapping: {{mapping|legend=1| 6 0 0 8 17 | 0 1 0 -2 -4 | 0 0 1 2 3 }}

=== Tyr
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 102487/102400
Mapping: {{mapping|legend=1| 3 0 0 4 8 | 0 2 0 -4 1 | 0 0 1 2 0 }}

==== Borneo
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024
Mapping: {{mapping| 3 0 0 4 8 -3 | 0 2 0 -4 1 3 | 0 0 1 2 0 1 }}

=== House
Subgroup: 2.3.5.7.11
Comma list: 250047/250000, 117440512/117406179
Mapping: {{mapping|legend=1| 3 0 -13 -22 10 | 0 1 4 6 0 | 0 0 5 10 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 6656/6655, 105644/105625, 123201/123200
Mapping: {{mapping| 3 0 -13 -22 10 -10 | 0 1 4 6 0 4 | 0 0 5 10 -2 11 }}


= Lehmerismic temperaments

=== Skadi
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 703125/702464
Mapping: {{mapping|legend=1| 1 0 -1 -6 0 | 0 1 1 3 2 | 0 0 6 14 1 }}

=== Ganesha
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625
Mapping: {{mapping|legend=1| 1 0 0 -22 -9 | 0 1 0 1 2 | 0 0 1 10 4 }}

=== Hanuman
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993
Mapping: {{mapping|legend=1| 1 2 0 -8 1 | 0 -3 0 11 1 | 0 0 1 4 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079
Mapping: {{mapping| 1 2 0 -8 1 -6 | 0 -3 0 11 1 3 | 0 0 1 4 1 4 }}

=== Lux
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 131072/130977
Mapping: {{mapping|legend=1| 1 0 -5 4 9 | 0 1 4 -1 -3 | 0 0 5 2 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024, 4096/4095
Mapping: {{mapping| 1 0 -5 4 9 13 | 0 1 4 -1 -3 -5 | 0 0 5 2 -4 -7 }}

=== Galaxy
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 20614528/20588575
Mapping: {{mapping|legend=1| 1 0 -4 10 11 | 0 1 3 -3 -3 | 0 0 9 -14 -16 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 3025/3024, 4225/4224
Mapping: {{mapping| 1 0 -4 10 11 13 | 0 1 3 -3 -3 -4 | 0 0 9 -14 -16 -17 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 936/935, 1225/1224, 4225/4224
Mapping: {{mapping| 1 0 -4 10 11 13 9 | 0 1 3 -3 -3 -4 -2 | 0 0 9 -14 -16 -17 -10 }}


= Luna family

=== Luna
Subgroup: 2.3.5
Comma list: 274877906944/274658203125
Mapping: {{mapping|legend=1| 1 4 2 | 0 -15 2 }}

=== Lunatic
Subgroup: 2.3.5.7
Comma list: 4375/4374, 274877906944/274658203125
Mapping: {{mapping|legend=1| 1 4 2 21 | 0 -15 2 -113 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 12005/11979, 172032/171875
Mapping: {{mapping| 1 4 2 21 14 | 0 -15 2 -113 -140 }}

=== Hemiluna
Subgroup: 2.3.5.7
Comma list: 48828125/48771072, 67108864/66976875
Mapping: {{mapping|legend=1| 1 4 2 -5 | 0 -30 4 97 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 14641/14580, 131072/130977
Mapping: {{mapping| 1 4 2 -5 7 | 0 -30 4 97 -44 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580
Mapping: {{mapping| 1 4 2 -5 7 7 | 0 -30 4 97 -44 -41 }}

=== Semiluna
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 95703125/95551488
Mapping: {{mapping|legend=1| 2 8 4 23 | 0 -15 2 -54 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 14641/14580
Mapping: {{mapping| 2 8 4 23 14 | 0 -15 2 -54 -22 }}


= Magic family

=== Magic
Subgroup: 2.3.5
Comma list: 3125/3072
Mapping: {{mapping|legend=1| 1 0 2 | 0 5 1 }}

==== Overview to extensions

=== Septimal magic
Subgroup: 2.3.5.7
Comma list: 225/224, 245/243
Mapping: {{mapping|legend=1| 1 0 2 -1 | 0 5 1 12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 245/243
Mapping: {{mapping| 1 0 2 -1 6 | 0 5 1 12 -8 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 196/195
Mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 1 12 -8 18 }}

====== Magical
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 120/119, 144/143, 154/153
Mapping: {{mapping| 1 0 2 -1 6 -2 6 | 0 5 1 12 -8 18 -6 }}

======= Magicus
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 120/119, 133/132, 144/143, 154/153
Mapping: {{mapping| 1 0 2 -1 6 -2 6 9 | 0 5 1 12 -8 18 -6 -15 }}

======= Magica
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 120/119, 144/143, 154/153, 171/169
Mapping: {{mapping| 1 0 2 -1 6 -2 6 -4 | 0 5 1 12 -8 18 -6 26 }}

====== Magia
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 144/143, 170/169, 196/195
Mapping: {{mapping| 1 0 2 -1 6 -2 -7 | 0 5 1 12 -8 18 35 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 144/143, 170/169, 171/169, 196/195
Mapping: {{mapping| 1 0 2 -1 6 -2 -7 -4 | 0 5 1 12 -8 18 35 26 }}

====== Evening
Subgroup: 2.3.5.7.11.13.29.31
Comma list: 100/99, 105/104, 144/143, 145/144, 155/154, 196/195
Mapping: {{mapping| 1 0 2 -1 6 -2 2 4 | 0 5 1 12 -8 18 9 3 }}

===== Sorcery
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 0 2 -1 6 4 | 0 5 1 12 -8 -1 }}

===== Necromancy
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 225/224, 245/243, 275/273
Mapping: {{mapping| 1 0 2 -1 6 11 | 0 5 1 12 -8 -23 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 120/119, 154/153, 225/224, 273/272
Mapping: {{mapping| 1 0 2 -1 6 11 6 | 0 5 1 12 -8 -23 -6 }}

===== Soothsaying
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 225/224, 245/243, 1352/1331
Mapping: {{mapping| 2 0 4 -2 12 15 | 0 5 1 12 -8 -12 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 221/220, 225/224, 245/243, 273/272
Mapping: {{mapping| 2 0 4 -2 12 15 5 | 0 5 1 12 -8 -12 5 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 133/132, 221/220, 225/224, 245/243, 273/272
Mapping: {{mapping| 2 0 4 -2 12 15 5 18 | 0 5 1 12 -8 -12 5 -15 }}

==== Telepathy
Subgroup: 2.3.5.7.11
Comma list: 55/54, 99/98, 176/175
Mapping: {{mapping| 1 0 2 -1 -1 | 0 5 1 12 14 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 65/64, 91/90, 99/98
Mapping: {{mapping| 1 0 2 -1 -1 4 | 0 5 1 12 14 -1 }}

===== Intuition
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 66/65, 99/98, 105/104
Mapping: {{mapping| 1 0 2 -1 -1 -2 | 0 5 1 12 14 18 }}

==== Horcrux
Subgroup: 2.3.5.7.11
Comma list: 45/44, 56/55, 245/243
Mapping: {{mapping| 1 0 2 -1 0 | 0 5 1 12 11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 56/55, 78/77, 245/243
Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 11 18 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 45/44, 56/55, 78/77, 85/84, 245/243
Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 16 }}

====== Horcruxic
Subgroup: 2.3.5.7.11.13.17
Comma list: 35/34, 45/44, 52/51, 56/55, 245/243
Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 13 }}

===== Glamour
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 56/55, 65/64, 245/243
Mapping: {{mapping| 1 0 2 -1 0 4 | 0 5 1 12 11 -1 }}

==== Witchcraft
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/243, 441/440
Mapping: {{mapping| 1 0 2 -1 -7 | 0 5 1 12 33 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 245/243, 275/273
Mapping: {{mapping| 1 0 2 -1 -7 -2 | 0 5 1 12 33 18 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 154/153, 170/169, 196/195, 245/243
Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 | 0 5 1 12 33 18 35 }}

==== Divination
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 245/243
Mapping: {{mapping| 2 0 4 -2 5 | 0 5 1 12 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 121/120, 196/195, 245/243
Mapping: {{mapping| 2 0 4 -2 5 -4 | 0 5 1 12 3 18 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 121/120, 154/153, 196/195, 245/243
Mapping: {{mapping| 2 0 4 -2 5 -4 5 | 0 5 1 12 3 18 5 }}

==== Hocus
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 245/242
Mapping: {{mapping| 1 -5 1 -13 -13 | 0 10 2 24 25 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 243/242, 245/242
Mapping: {{mapping| 1 -5 1 -13 -13 -20 | 0 10 2 24 25 36 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 154/153, 196/195, 243/242, 245/242
Mapping: {{mapping| 1 -5 1 -13 -13 -20 -15 | 0 10 2 24 25 36 29 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 154/153, 196/195, 243/242, 245/242
Mapping: {{mapping| 1 -5 1 -13 -13 -20 -3 | 0 10 2 24 25 36 29 11 }}

=== Muggles
Subgroup: 2.3.5.7
Comma list: 126/125, 525/512
Mapping: {{mapping|legend=1| 1 0 2 5 | 0 5 1 -7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 126/125, 385/384
Mapping: {{mapping| 1 0 2 5 0 | 0 5 1 -7 11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 65/64, 78/77, 126/125
Mapping: {{mapping| 1 0 2 5 0 4 | 0 5 1 -7 11 -1 }}

==== Muggloid
Subgroup: 2.3.5.7.11
Comma list: 33/32, 126/125, 176/175
Mapping: {{mapping| 1 0 2 5 5 | 0 5 1 -7 -5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 33/32, 65/64, 105/104, 126/125
Mapping: {{mapping| 1 0 2 5 5 4 | 0 5 1 -7 -5 -1 }}

=== Brightstone
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/3024
Mapping: {{mapping|legend=1| 1 0 2 6 | 0 5 1 -10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 625/616
Mapping: {{mapping| 1 0 2 6 -1 | 0 5 1 -10 14 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 55/54, 64/63, 625/616
Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 14 -4 }}

=== Darkstone
Subgroup: 2.3.5.7
Comma list: 36/35, 1875/1792
Mapping: {{mapping|legend=1| 1 0 2 0 | 0 5 1 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 363/343
Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44, 363/343
Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}

=== Hocum
Subgroup: 2.3.5.7
Comma list: 3125/3072, 4000/3969
Mapping: {{mapping|legend=1| 1 -5 1 14 | 0 10 2 -17 }}

=== Trismegistus
Subgroup: 2.3.5.7
Comma list: 1029/1024, 3125/3072
Mapping: {{mapping|legend=1| 1 -5 1 5 | 0 15 3 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 625/616
Mapping: {{mapping| 1 -5 1 5 -4 | 0 15 3 -5 17 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 275/273, 625/616
Mapping: {{mapping| 1 -5 1 5 -4 -2 | 0 15 3 -5 17 13 }}

==== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 105/104, 144/143, 441/440, 210/209, 625/616
Mapping: {{mapping| 1 -5 1 5 -4 -2 6 | 0 15 3 -5 17 13 -4 }}

=== Quadrimage
Subgroup: 2.3.5.7
Comma list: 2401/2400, 3125/3072
Mapping: {{mapping|legend=1| 1 -15 -1 -3 | 0 20 4 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/242, 385/384, 625/616
Mapping: {{mapping| 1 -15 -1 -3 -4 | 0 20 4 7 9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 245/242, 625/616
Mapping: {{mapping| 1 -15 -1 -3 -22 | 0 20 4 7 9 31 }}

=== Quinmage
Subgroup: 2.3.5.7
Comma list: 3125/3072, 16875/16807
Mapping: {{mapping|legend=1| 1 -10 0 -6 | 0 25 5 19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 625/616, 2401/2376
Mapping: {{mapping| 1 -10 0 -6 3 | 0 25 5 19 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 364/363, 385/384, 625/616
Mapping: {{mapping| 1 -10 0 -6 3 0 | 0 25 5 19 1 8 }}

=== Warlock
Subgroup: 2.3.5.7
Comma list: 3125/3072, 16807/16384
Mapping: {{mapping|legend=1| 5 0 10 14 | 0 5 1 0 }}


= Maja family

=== Maja
Subgroup: 2.3.5
Comma list: 762939453125/753145430616
Mapping: {{mapping|legend=1| 1 8 11 | 0 -17 -23 }}

=== Septimal maja
Subgroup: 2.3.5.7
Comma list: 2430/2401, 3125/3087
Mapping: {{mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 3125/3087
Mapping: {{mapping| 1 8 11 13 11 | 0 -17 -23 -27 -20 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 169/168, 275/273
Mapping: {{mapping| 1 8 11 13 11 12 | 0 -17 -23 -27 -20 -22 }}

=== Majo
Subgroup: 2.3.5.7
Comma list: 6144/6125, 1250000/1240029
Mapping: {{mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2200/2187, 3388/3375, 6144/6125
Mapping: {{mapping| 1 8 11 -7 31 | 0 -17 -23 26 -73 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 1001/1000, 2704/2695
Mapping: {{mapping| 1 8 11 -7 31 12 | 0 -17 -23 26 -73 -22 }}

=== Notes


= Maquila family

=== Maquila
Subgroup: 2.3.5
Comma list: {{monzo| 49 -6 -17 }}
Mapping: {{mapping|legend=1| 1 -6 5 | 0 17 -6 }}

=== Septimal maquila
Subgroup: 2.3.5.7
Comma list: 225/224, 30233088/28824005
Mapping: {{mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 73728/73205
Mapping: {{mapping| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 144/143, 176/175, 847/845
Mapping: {{mapping| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}

=== Maquiloid
Subgroup: 2.3.5.7
Comma list: 686/675, 65625/65536
Mapping: {{mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/242, 385/384, 686/675
Mapping: {{mapping| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 169/168, 245/242, 385/384
Mapping: {{mapping| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}

=== Hemimaquila
Subgroup: 2.3.5.7
Comma list: 6144/6125, 184528125/184473632
Mapping: {{mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625, 12005/11979
Mapping: {{mapping| 1 -6 5 -5 -1 | 0 34 -12 35 20 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675, 3584/3575
Mapping: {{mapping| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}


= Marvel family

=== Marvel
Subgroup: 2.3.5.7
Comma list: 225/224
Mapping: {{mapping|legend=1| 1 0 0 -5 | 0 1 0 2 | 0 0 1 2 }}

==== Overview to extensions

=== Undecimal marvel
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384
Mapping: {{mapping|legend=1| 1 0 0 -5 12 | 0 1 0 2 -1 | 0 0 1 2 -3 }}
Mapping to lattice: [{{val| 0 -1 0 -2 1 }}, {{val| 0 -1 1 0 -2 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 385/384
Mapping: {{mapping| 1 0 0 -5 12 -4 | 0 1 0 2 -1 -1 | 0 0 1 2 -3 4 }}

==== Hecate

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384
Mapping: {{mapping| 1 0 0 -5 12 2 | 0 1 0 2 -1 4 | 0 0 1 2 -3 -2 }}

====== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 225/224, 325/324, 385/384, 400/399
Mapping: {{mapping| 1 0 0 -5 12 2 9 | 0 1 0 2 -1 4 -3 | 0 0 1 2 -3 -2 0 }}

===== Apotropaia
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 325/324, 385/384, 595/594
Mapping: {{mapping| 1 0 0 -5 12 2 18 | 0 1 0 2 -1 4 0 | 0 0 1 2 -3 -2 -6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 225/224, 325/324, 385/384, 400/399, 595/594
Mapping: {{mapping| 1 0 0 -5 12 2 18 9 | 0 1 0 2 -1 4 0 -3 | 0 0 1 2 -3 -2 -6 0 }}

===== Enodia
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 325/324, 375/374, 385/384
Mapping: {{mapping| 1 0 0 -5 12 2 -13 | 0 1 0 2 -1 4 2 | 0 0 1 2 -3 -2 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399
Mapping: {{mapping| 1 0 0 -5 12 2 -13 9 | 0 1 0 2 -1 4 2 -3 | 0 0 1 2 -3 -2 6 0 }}

==== Marvell
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 385/384, 1573/1568
Mapping: {{mapping| 1 0 0 -5 12 -29 | 0 1 0 2 -1 6 | 0 0 1 2 -3 10 }}

==== Isis
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 385/384
Mapping: {{mapping| 1 0 0 -5 12 17 | 0 1 0 2 -1 -4 | 0 0 1 2 -3 -3 }}

==== Deecee
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 364/363, 385/384
Mapping: {{mapping| 1 0 0 -5 12 27 | 0 1 0 2 -1 -3 | 0 0 1 2 -3 -8 }}

==== Tripod
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195
Mapping: {{mapping| 1 0 0 -5 12 -8 | 0 1 0 2 -1 3 | 0 0 1 2 -3 3 }}

==== Marvelcat
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 385/384
Mapping: {{mapping| 1 0 0 -5 12 -1 | 0 2 0 4 -2 3 | 0 0 1 2 -3 1 }}

=== Prodigy
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440
Mapping: {{mapping|legend=1| 1 0 0 -5 -13 | 0 1 0 2 6 | 0 0 1 2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 352/351
Mapping: {{mapping| 1 0 0 -5 -13 -8 | 0 1 0 2 6 3 | 0 0 1 2 3 3 }}

==== Prodigious
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 364/363, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 -23 | 0 1 0 2 6 11 | 0 0 1 2 3 4 }}

==== Prodigal
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 -4 | 0 1 0 2 6 -1 | 0 0 1 2 3 4 }}

==== Protannic
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 441/440, 1001/1000
Mapping: {{mapping| 1 0 0 -5 -13 21 | 0 1 0 2 6 -8 | 0 0 1 2 3 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 375/374, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 21 12 | 0 1 0 2 6 -8 -5 | 0 0 1 2 3 -2 0 }}

=== Minerva
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175
Mapping: {{mapping|legend=1| 1 0 0 -5 -9 | 0 1 0 2 2 | 0 0 1 2 4 }}

==== Athene
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 275/273
Mapping: {{mapping| 1 0 0 -5 -9 -4 | 0 1 0 2 2 -1 | 0 0 1 2 4 4 }}

=== Apollo
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224
Mapping: {{mapping|legend=1| 1 0 0 -5 2 | 0 1 0 2 -2 | 0 0 1 2 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 225/224, 275/273
Mapping: {{mapping| 1 0 0 -5 2 7 | 0 1 0 2 -2 -5 | 0 0 1 2 2 2 }}

==== Phoebus
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 196/195
Mapping: {{mapping| 1 0 0 -5 2 1 | 0 1 0 2 -2 3 | 0 0 1 2 2 3 }}

==== Musagetes
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 225/224
Mapping: {{mapping| 1 0 0 -5 2 2 | 0 1 0 2 -2 4 | 0 0 1 2 2 -2 }}

=== Potassium
Subgroup: 2.3.5.7.11
Comma list: 45/44, 56/55
Mapping: {{mapping|legend=1| 1 0 0 -5 -2 | 0 1 0 2 2 | 0 0 1 2 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 56/55, 78/77
Mapping: {{mapping| 1 0 0 -5 -2 -8 | 0 1 0 2 2 3 | 0 0 1 2 1 3 }}

=== Malcolm
Subgroup: 2.3.5.7.11
Comma list: 225/224, 2200/2187
Mapping: {{mapping|legend=1| 1 0 0 -5 -3 | 0 1 0 2 7 | 0 0 1 2 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 325/324
Mapping: {{mapping| 1 0 0 -5 -3 2 | 0 1 0 2 7 4 | 0 0 1 2 -2 -2 }}

=== Fantastic
Subgroup: 2.3.5.7.11
Comma list: 225/224, 4375/4356
Mapping: {{mapping|legend=1| 2 0 0 -10 -7 | 0 1 0 2 0 | 0 0 1 2 3 }}

=== Hestia
Subgroup: 2.3.5.7.11
Comma list: 225/224, 125000/124509
Mapping: {{mapping|legend=1| 1 0 0 -5 9 | 0 2 0 4 -7 | 0 0 1 2 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 1001/1000
Mapping: {{mapping| 1 0 0 -5 9 -1 | 0 2 0 4 -7 3 | 0 0 1 2 0 1 }}

=== Morfil
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1331/1323
Mapping: {{mapping|legend=1| 1 0 -2 -9 -6 | 0 1 2 6 5 | 0 0 3 6 4 }}

=== Subgroup extensions

==== Char
Subgroup: 2.3.5.7.17
Comma list: 120/119, 225/224
Mapping: {{mapping| 1 0 0 -5 8 | 0 1 0 2 -1 | 0 0 1 2 -1 }}

==== Devimarvel
Subgroup: 2.3.5.7.19
Comma list: 225/224, 400/399
Mapping: {{mapping| 1 0 0 -5 9 | 0 1 0 2 -3 | 0 0 1 2 0 }}

=== References


= Marvel temperaments

=== Wizard
Subgroup: 2.3.5.7
Comma list: 225/224, 118098/117649
Mapping: {{mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 4000/3993
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}

===== Lizard
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 364/363, 385/384
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}

===== Gizzard
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 1573/1568
Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}

==== Mage
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 1331/1296
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}

=== Tritonic
Subgroup: 2.3.5.7
Comma list: 225/224, 50421/50000
Mapping: {{mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 441/440
Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 121/120, 196/195, 275/273
Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}

===== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}

==== Tritoni
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 27783/27500
Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}

=== Septimin
Subgroup: 2.3.5.7
Comma list: 225/224, 84035/82944
Mapping: {{mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/242, 385/384
Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 245/242
Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}

=== Merman
Subgroup: 2.3.5.7
Comma list: 225/224, 2500000/2470629
Mapping: {{mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 1344/1331
Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 225/224, 364/363, 441/440
Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}

==== Mermaid
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 532400/531441
Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 10648/10647
Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}

=== Slender
Subgroup: 2.3.5.7
Comma list: 225/224, 589824/588245
Mapping: {{mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 1331/1323
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 385/384, 1331/1323
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}

=== Triton
Subgroup: 2.3.5.7
Comma list: 225/224, 1029/1000
Mapping: {{mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 56/55, 1029/1000
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}

=== Marvolo
Subgroup: 2.3.5.7
Comma list: 225/224, 156250000/155649627
Mapping: {{mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 4000/3993
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 364/363, 441/440
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}

=== Enneaportent
Subgroup: 2.3.5.7
Comma list: 225/224, 40353607/40310784
Mapping: {{mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 12005/11979
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 364/363, 1716/1715
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}

=== Gracecordial
Subgroup: 2.3.5.7
Comma list: 225/224, 781250000/771895089
Mapping: {{mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 236328125/234365481
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 831875/830466
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}

===== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}

===== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}

===== 31-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}

==== Gracecord
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 109375/107811
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 364/363, 441/440, 6125/6084
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}

=== Alphorn
Subgroup: 2.3.5.7
Comma list: 225/224, 5764801/5668704
Mapping: {{mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 12250/11979
Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}

=== Misneb
Subgroup: 2.3.5.7
Comma list: 225/224, 4194304/4117715
Mapping: {{mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 1310720/1294139
Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 640/637, 847/845
Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}

==== Musneb
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 66550/64827
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}

=== Untriton
Subgroup: 2.3.5.7
Comma list: 225/224, 125000000/121060821
Mapping: {{mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 22000/21609
Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 1040/1029
Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}

=== Naiadical
Subgroup: 2.3.5.7
Comma list: 225/224, 823543/800000
Mapping: {{mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/242, 1617/1600
Mapping: {{mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 245/242, 1001/1000
Mapping: {{mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
Mapping: {{mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}

=== Quintannic
Subgroup: 2.3.5.7
Comma list: 225/224, 9805926501/9765625000
Mapping: {{mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 43923/43750
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 441/440, 1001/1000, 1188/1183
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}

=== Gwazy
Subgroup: 2.3.5.7
Comma list: 225/224, 5971968/5764801
Mapping: {{mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 65536/65219
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}

=== Tertiosec
Subgroup: 2.3.5.7
Comma list: 225/224, 14495514624/13841287201
Mapping: {{mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 3840/3773, 12005/11979
Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}

=== References


= Meantone family

=== Meantone
Subgroup: 2.3.5
Comma list: 81/80
Mapping: {{mapping|legend=1| 1 0 -4 | 0 1 4 }}

==== Overview to extensions

===== Strong extensions

===== Splitting the meantone fifth into two (243/242)

===== Splitting the meantone fifth into three (1029/1024)

===== 31edo as splitting the fifth into two, three and nine

=== Septimal meantone
Subgroup: 2.3.5.7
Comma list: 81/80, 126/125
Mapping: {{mapping|legend=1| 1 0 -4 -13 | 0 1 4 10 }}

==== Undecimal meantone (huygens)
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98, 126/125
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}

===== Grosstone
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 99/98, 126/125, 144/143
Mapping: {{mapping| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 99/98, 120/119, 126/125, 144/143
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 96/95, 99/98, 120/119, 126/125, 144/143
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}

===== Fokkertone
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 81/80, 99/98, 105/104
Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 66/65, 81/80, 96/95, 99/98, 105/104, 120/119
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}

===== Meridetone
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 81/80, 99/98, 126/125
Mapping: {{mapping| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 78/77, 81/80, 99/98, 120/119, 126/125
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 78/77, 81/80, 96/95, 99/98, 120/119, 126/125
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}

===== Hemimeantone
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 99/98, 126/125, 169/168
Mapping: {{mapping| 1 0 -4 -13 -25 -5 | 0 2 8 20 36 11 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 99/98, 126/125, 169/168, 221/220
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 99/98, 126/125, 153/152, 169/168, 221/220
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}

===== Semimeantone
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 99/98, 126/125, 847/845
Mapping: {{mapping| 2 0 -8 -26 -50 -59 | 0 1 4 10 18 21 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 99/98, 126/125, 221/220, 289/288
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 99/98, 126/125, 153/152, 209/208, 221/220
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}

==== Meanpop
Subgroup: 2.3.5.7.11
Comma list: 81/80, 126/125, 385/384
Mapping: {{mapping| 1 0 -4 -13 24 | 0 1 4 10 -13 }}

===== Tridecimal meanpop
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 105/104, 126/125, 144/143
Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}

====== Meanpoppic
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 105/104, 126/125, 144/143, 273/272
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 105/104, 126/125, 144/143, 153/152, 273/272
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}

====== Meanpoid
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 105/104, 120/119, 126/125, 144/143
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 77/76, 81/80, 96/95, 105/104, 120/119, 126/125
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}

===== Semimeanpop
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 126/125, 385/384, 847/845
Mapping: {{mapping| 2 0 -8 -26 48 39 | 0 1 4 10 -13 -10 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 126/125, 221/220, 273/272, 289/288
Mapping: {{mapping| 2 0 -8 -26 48 39 5 | 0 1 4 10 -13 -10 1 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 126/125, 153/152, 209/208, 221/220, 273/272
Mapping: {{mapping| 2 0 -8 -26 48 39 5 -1 | 0 1 4 10 -13 -10 1 3 }}

==== Meanenneadecal
Subgroup: 2.3.5.7.11
Comma list: 45/44, 56/55, 81/80
Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 56/55, 78/77, 81/80
Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 45/44, 56/55, 78/77, 81/80, 120/119
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 45/44, 56/55, 78/77, 81/80, 96/95, 120/119
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}

===== Vincenzo
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 56/55, 65/64, 81/80
Mapping: {{mapping| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 45/44, 52/51, 56/55, 65/64, 81/80
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 81/80
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}

==== Bimeantone
Subgroup: 2.3.5.7.11
Comma list: 81/80, 126/125, 245/242
Mapping: {{mapping| 2 0 -8 -26 -31 | 0 1 4 10 12 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 105/104, 126/125, 245/242
Mapping: {{mapping| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 105/104, 126/125, 189/187, 221/220
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 105/104, 126/125, 153/152, 189/187, 221/220
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}

==== Trimean
Subgroup: 2.3.5.7.11
Comma list: 81/80, 126/125, 1344/1331
Mapping: {{mapping| 1 2 4 7 5 | 0 -3 -12 -30 -11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 126/125, 144/143, 364/363
Mapping: {{mapping| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 126/125, 144/143, 189/187, 221/220
Mapping: {{mapping| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}

==== Migration

=== Flattone
Subgroup: 2.3.5.7
Comma list: 81/80, 525/512
Mapping: {{mapping|legend=1| 1 0 -4 17 | 0 1 4 -9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 81/80, 385/384
Mapping: {{mapping| 1 0 -4 17 -6 | 0 1 4 -9 6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 65/64, 78/77, 81/80
Mapping: {{mapping| 1 0 -4 17 -6 10 | 0 1 4 -9 6 -4 }}

==== Ptolemy

=== Dominant
Subgroup: 2.3.5.7
Comma list: 36/35, 64/63
Mapping: {{mapping|legend=1| 1 0 -4 6 | 0 1 4 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 56/55, 64/63
Mapping: {{mapping| 1 0 -4 6 13 | 0 1 4 -2 -6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 56/55, 64/63, 66/65
Mapping: {{mapping| 1 0 -4 6 13 18 | 0 1 4 -2 -6 -9 }}

===== Dominion
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 36/35, 56/55, 64/63
Mapping: {{mapping| 1 0 -4 6 13 -9 | 0 1 4 -2 -6 8 }}

==== Domination
Subgroup: 2.3.5.7.11
Comma list: 36/35, 64/63, 77/75
Mapping: {{mapping| 1 0 -4 6 -14 | 0 1 4 -2 11 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 36/35, 64/63, 66/65
Mapping: {{mapping| 1 0 -4 6 -14 -9 | 0 1 4 -2 11 8 }}

==== Domineering
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 64/63
Mapping: {{mapping| 1 0 -4 6 -6 | 0 1 4 -2 6 }}

==== Arnold
Subgroup: 2.3.5.7.11
Comma list: 22/21, 33/32, 36/35
Mapping: {{mapping| 1 0 -4 6 5 | 0 1 4 -2 -1 }}

==== Neutrominant

=== Flattertone
Subgroup: 2.3.5.7
Comma list: 81/80, 1875/1792
Mapping: {{mapping|legend=1| 1 0 -4 -24 | 0 1 4 17 }}

===== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 81/80, 1375/1344
Mapping: {{mapping| 1 0 -4 -24 -6 | 0 1 4 17 6 }}

=== Sharptone
Subgroup: 2.3.5.7
Comma list: 21/20, 28/27
Mapping: {{mapping|legend=1| 1 0 -4 -2 | 0 1 4 3 }}

==== Meanertone
Subgroup: 2.3.5.7.11
Comma list: 21/20, 28/27, 33/32
Mapping: {{mapping| 1 0 -4 -2 5 | 0 1 4 3 -1 }}

=== Mildtone
Subgroup: 2.3.5.7
Comma list: 81/80, 16128/15625
Mapping: {{mapping|legend=1| 1 0 -4 -32 | 0 1 4 22 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 176/175, 7058/6875
Mapping: {{mapping|legend=1| 1 0 -4 -32 | 0 1 4 22 30}}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 176/175, 196/195, 832/825
Mapping: {{mapping|legend=1| 1 0 -4 -32 -44 | 0 1 4 22 30}}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 176/175, 189/197, 196/195, 832/825
Mapping: {{mapping|legend=1| 1 0 -4 -32 -44 12| 0 1 4 22 30 -5}}

==== 19-limit
Subgroup: 2.3.5.7.11.13.19
Comma list: 81/80, 96/95, 176/175, 189/187, 196/195, 832/825
Mapping: {{mapping|legend=1| 1 0 -4 -32 -44 12 9| 0 1 4 22 30 -5 -3}}

=== Supermean
Subgroup: 2.3.5.7
Comma list: 81/80, 672/625
Mapping: {{mapping|legend=1| 1 0 -4 -21 | 0 1 4 15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 81/80, 132/125
Mapping: {{mapping| 1 0 -4 -21 -14 | 0 1 4 15 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 56/55, 66/65, 81/80
Mapping: {{mapping| 1 0 -4 -21 -14 -9 | 0 1 4 15 11 8 }}

=== Mohajira
Subgroup: 2.3.5.7
Comma list: 81/80, 6144/6125
Mapping: {{mapping|legend=1| 1 1 0 6 | 0 2 8 -11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 121/120, 176/175
Mapping: {{mapping| 1 1 0 6 2 | 0 2 8 -11 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 81/80, 105/104, 121/120
Mapping: {{mapping| 1 1 0 6 2 4 | 0 2 8 -11 5 -1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 66/65, 81/80, 105/104, 121/120, 154/153
Mapping: {{mapping| 1 1 0 6 2 4 7 | 0 2 8 -11 5 -1 -10 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152
Mapping: {{mapping| 1 1 0 6 2 4 7 6 | 0 2 8 -11 5 -1 -10 -6 }}

=== Mohamaq
Subgroup: 2.3.5.7
Comma list: 81/80, 392/375
Mapping: {{mapping|legend=1| 1 1 0 -1 | 0 2 8 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 77/75, 243/242
Mapping: {{mapping| 1 1 0 -1 2 | 0 2 8 13 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 66/65, 77/75, 243/242
Mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 8 13 5 -1 }}

=== Liese
Subgroup: 2.3.5.7
Comma list: 81/80, 686/675
Mapping: {{mapping|legend=1| 1 0 -4 -3 | 0 3 12 11 }}

==== Liesel
Subgroup: 2.3.5.7.11
Comma list: 56/55, 81/80, 540/539
Mapping: {{mapping| 1 0 -4 -3 4 | 0 3 12 11 -1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 81/80, 91/90
Mapping: {{mapping| 1 0 -4 -3 4 0 | 0 3 12 11 -1 7 }}

==== Elisa
Subgroup: 2.3.5.7.11
Comma list: 77/75, 81/80, 99/98
Mapping: {{mapping| 1 0 -4 -3 -5 | 0 3 12 11 16 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 77/75, 81/80, 99/98
Mapping: {{mapping| 1 0 -4 -3 -5 0 | 0 3 12 11 16 7 }}

==== Lisa
Subgroup: 2.3.5.7.11
Comma list: 45/44, 81/80, 343/330
Mapping: {{mapping| 1 0 -4 -3 -6 | 0 3 12 11 18 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 81/80, 91/88, 147/143
Mapping: {{mapping| 1 0 -4 -3 -6 0 | 0 3 12 11 18 7 }}

=== Superpine
Subgroup: 2.3.5.7
Comma list: 81/80, 1119744/1071875
Mapping: {{mapping|legend=1| 1 2 4 1 | 0 -3 -12 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 176/175, 864/847
Mapping: {{mapping| 1 2 4 1 5 | 0 -3 -12 13 -11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 81/80, 144/143, 176/175
Mapping: {{mapping| 1 2 4 1 5 3 | 0 -3 -12 13 -11 5 }}

=== Lithium
Subgroup: 2.3.5.7
Comma list: 81/80, 3125/3087
Mapping: {{mapping|legend=1| 3 0 -12 -20 | 0 1 4 6 }}

=== Squares
Subgroup: 2.3.5.7
Comma list: 81/80, 2401/2400
Mapping: {{mapping|legend=1| 1 -1 -8 -3 | 0 4 16 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98, 121/120
Mapping: {{mapping| 1 -1 -8 -3 -3 | 0 4 16 9 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 81/80, 99/98, 121/120
Mapping: {{mapping| 1 -1 -8 -3 -3 5 | 0 4 16 9 10 -2 }}

===== Squad
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 81/80, 91/90, 99/98
Mapping: {{mapping| 1 -1 -8 -3 -3 -6 | 0 4 16 9 10 15 }}

===== Agora
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 99/98, 105/104, 121/120
Mapping: {{mapping| 1 -1 -8 -3 -3 -15 | 0 4 16 9 10 29 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 99/98, 105/104, 120/119, 121/119
Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 | 0 4 16 9 10 29 11 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119
Mapping: {{mapping| 1 -1 -8 -3 -3 -15 -3 -8 | 0 4 16 9 10 29 11 19 }}

==== Cuboctahedra
Subgroup: 2.3.5.7.11
Comma list: 81/80, 385/384, 1375/1372
Mapping: {{mapping| 1 -1 -8 -3 17 | 0 4 16 9 -21 }}

=== Jerome
Subgroup: 2.3.5.7
Comma list: 81/80, 17280/16807
Mapping: {{mapping|legend=1| 1 1 0 2 | 0 5 20 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98, 864/847
Mapping: {{mapping| 1 1 0 2 3 | 0 5 20 7 4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 81/80, 99/98, 144/143
Mapping: {{mapping| 1 1 0 2 3 3 | 0 5 20 7 4 6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 78/77, 81/80, 99/98, 144/143, 189/187
Mapping: {{mapping| 1 1 0 2 3 3 2 | 0 5 20 7 4 6 18 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 78/77, 81/80, 99/98, 120/119, 135/133, 144/143
Mapping: {{mapping| 1 1 0 2 3 3 2 1 | 0 5 20 7 4 6 18 28 }}

=== Meantritone
Subgroup: 2.3.5.7
Comma list: 81/80, 16875/16807
Mapping: {{mapping|legend=1| 1 -1 -8 -7 | 0 5 20 19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98, 2541/2500
Mapping: {{mapping| 1 -1 -8 -7 -11 | 0 5 20 19 28 }}

=== Injera
Subgroup: 2.3.5.7
Comma list: 50/49, 81/80
Mapping: {{mapping|legend=1| 2 0 -8 -7 | 0 1 4 4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 81/80
Mapping: {{mapping| 2 0 -8 -7 -12 | 0 1 4 4 6 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 50/49, 78/77, 81/80
Mapping: {{mapping| 2 0 -8 -7 -12 -21 | 0 1 4 4 6 9 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 45/44, 50/49, 78/77, 81/80, 85/84
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 | 0 1 4 4 6 9 1 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 45/44, 50/49, 57/56, 78/77, 81/80, 85/84
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 -1 | 0 1 4 4 6 9 1 3 }}

===== Enjera
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 40/39, 45/44, 50/49
Mapping: {{mapping| 2 0 -8 -7 -12 -2 | 0 1 4 4 6 3 }}

==== Injerous
Subgroup: 2.3.5.7.11
Comma list: 33/32, 50/49, 55/54
Mapping: {{mapping| 2 0 -8 -7 10 | 0 1 4 4 -1 }}

==== Lahoh
Subgroup: 2.3.5.7.11
Comma list: 50/49, 56/55, 81/77
Mapping: {{mapping| 2 0 -8 -7 7 | 0 1 4 4 0 }}

==== Teff
Subgroup: 2.3.5.7.11
Comma list: 50/49, 81/80, 864/847
Mapping: {{mapping| 2 1 -4 -3 8 | 0 2 8 8 -1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 78/77, 81/80, 144/143
Mapping: {{mapping| 2 1 -4 -3 8 2 | 0 2 8 8 -1 5 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 78/77, 81/80, 85/84, 144/143
Mapping: {{mapping| 2 1 -4 -3 8 2 6 | 0 2 8 8 -1 5 2 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143
Mapping: {{mapping| 2 1 -4 -3 8 2 6 2 | 0 2 8 8 -1 5 2 6 }}

=== Pombe
Subgroup: 2.3.5.7
Comma list: 81/80, 300125/294912
Mapping: {{mapping|legend=1| 2 1 -4 11 | 0 2 8 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 245/242, 385/384
Mapping: {{mapping| 2 1 -4 11 8 | 0 2 8 -5 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 105/104, 144/143, 245/242
Mapping: {{mapping| 2 1 -4 11 8 2 | 0 2 8 -5 -1 5 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 81/80, 105/104, 144/143, 245/242, 273/272
Mapping: {{mapping| 2 1 -4 11 8 2 6 | 0 2 8 -5 -1 5 2 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 81/80, 105/104, 133/132, 144/143, 171/170, 210/209
Mapping: {{mapping| 2 1 -4 11 8 2 6 2 | 0 2 8 -5 -1 5 2 6 }}

=== Orphic
Subgroup: 2.3.5.7
Comma list: 81/80, 5898240/5764801
Mapping: {{mapping|legend=1| 2 1 -4 4 | 0 4 16 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98, 73728/73205
Mapping: {{mapping| 2 1 -4 4 8 | 0 4 16 3 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 99/98, 144/143, 2200/2197
Mapping: {{mapping| 2 1 -4 4 8 2 | 0 4 16 3 -2 10 }}

=== Cloudtone
Subgroup: 2.3.5.7
Comma list: 81/80, 16807/16384
Mapping: {{mapping|legend=1| 5 0 -20 14 | 0 1 4 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 385/384, 2401/2376
Mapping: {{mapping| 5 0 -20 14 41 | 0 1 4 0 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 105/104, 144/143, 2401/2376
Mapping: {{mapping| 5 0 -20 14 41 -21 | 0 1 4 0 -3 5 }}

=== Subgroup extensions

==== Stützel (2.3.5.19)
Subgroup: 2.3.5.19
Comma list: 81/80, 96/95
Mapping: {{mapping|legend=2| 1 0 -4 9 | 0 1 4 -3 }}
Mapping: {{mapping|legend=3| 1 0 -4 0 0 0 0 9 | 0 1 4 0 0 0 0 -3 }}

==== Hypnotone
Subgroup: 2.3.5.11
Comma list: 45/44, 81/80
Mapping: {{mapping|legend=2| 1 0 -4 -6 | 0 1 4 6 }}
Mapping: {{mapping|legend=3| 1 0 -4 0 -6 | 0 1 4 0 6 }}

===== 2.3.5.11.13 subgroup
Subgroup: 2.3.5.11.13
Comma list: 45/44, 65/64, 81/80
Mapping: {{mapping| 1 0 -4 -6 10 | 0 1 4 6 -4 }}

==== Dequarter
Subgroup: 2.3.5.11
Comma list: 33/32, 55/54
Mapping: {{mapping|legend=2| 1 0 -4 5 | 0 1 4 -1 }}
Mapping: {{mapping|legend=3| 1 0 -4 0 5 | 0 1 4 0 -1 }}

===== Dreamtone
Subgroup: 2.3.5.11.13
Comma list: 33/32, 55/54, 975/968
Mapping: {{mapping| 1 0 -4 5 21 | 0 1 4 -1 -11 }}

=== References


= Minortonic family

=== Minortone
Subgroup: 2.3.5
Comma list: {{monzo| -16 35 -17 }}
Mapping: {{mapping|legend=1| 1 -1 -3 | 0 17 35 }}

=== Mitonic
Subgroup: 2.3.5.7
Comma list: 4375/4374, 2100875/2097152
Mapping: {{mapping|legend=1| 1 -1 -3 6 | 0 17 35 -21 }}

==== Mineral
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4374, 16384/16335
Mapping: {{mapping| 1 -1 -3 6 10 | 0 17 35 -21 -43 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 3584/3575, 4375/4374
Mapping: {{mapping| 1 -1 -3 6 10 11 | 0 17 35 -21 -43 -48 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 1156/1155, 3584/3575
Mapping: {{mapping| 1 -1 -3 6 10 11 5 | 0 17 35 -21 -43 -48 -6 }}

==== Ore
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1331/1323, 4375/4374
Mapping: {{mapping| 1 -1 -3 6 3 | 0 17 35 -21 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384, 1331/1323, 3267/3250
Mapping: {{mapping| 1 -1 -3 6 3 11 | 0 17 35 -21 3 -48 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 385/384, 561/560, 715/714, 1452/1445
Mapping: {{mapping| 1 -1 -3 6 3 11 5 | 0 17 35 -21 3 -48 -6 }}

===== Goldmine
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 385/384, 1331/1323
Mapping: {{mapping| 1 -1 -3 6 3 4 | 0 17 35 -21 3 -2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 273/272, 325/324, 385/384, 1331/1323
Mapping: {{mapping| 1 -1 -3 6 3 4 5 | 0 17 35 -21 3 -2 -6 }}

==== Seminar
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 2100875/2097152
Mapping: {{mapping| 2 -2 -6 12 13 | 0 17 35 -21 -20 }}

=== Domain
Subgroup: 2.3.5.7
Comma list: 250047/250000, 645700815/645657712
Mapping: {{mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}

==== Hemidomain
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 250047/250000, 14348907/14348180
Mapping: {{mapping| 6 11 17 20 24 | 0 -17 -35 -36 -37 }}


= Mint family

=== Mint
Subgroup: 2.3.5.7
Comma list: 36/35
Mapping: {{mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }}

=== Nickel
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44
Mapping: {{mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44
Mapping: {{mapping| 1 0 0 2 -2 -1 | 0 1 0 2 2 3 | 0 0 1 -1 1 0 }}


= Mint temperaments

=== Penta
Subgroup: 2.3.5.7
Comma list: 28/25, 36/35
Mapping: {{mapping|legend=1| 1 1 2 2 | 0 3 2 4 }}

=== Progression
Subgroup: 2.3.5.7
Comma list: 36/35, 392/375
Mapping: {{mapping|legend=1| 1 1 2 2 | 0 5 3 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 56/55, 77/75
Mapping: {{mapping| 1 1 2 2 3 | 0 5 3 7 4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 36/35, 56/55, 66/65
Mapping: {{mapping| 1 1 2 2 3 3 | 0 5 3 7 4 6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 26/25, 36/35, 51/50, 56/55, 66/65
Mapping: {{mapping| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65
Mapping: {{mapping| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }}

=== Subklei
Subgroup: 2.3.5.7
Comma list: 36/35, 1029/1000
Mapping: {{mapping|legend=1| 1 -3 -3 -1 | 0 6 7 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 77/75, 352/343
Mapping: {{mapping| 1 -3 -3 -1 -8 | 0 6 7 5 15 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 36/35, 66/65, 352/343
Mapping: {{mapping| 1 3 4 4 7 7 | 0 6 7 5 15 14 }}

==== Subkla
Subgroup: 2.3.5.7.11
Comma list: 36/35, 56/55, 1029/1000
Mapping: {{mapping| 1 -3 -3 -1 5 | 0 6 7 5 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 56/55, 66/65, 640/637
Mapping: {{mapping| 1 -3 -3 -1 5 6 | 0 6 7 5 -2 -3 }}

=== Naian
Subgroup: 2.3.5.7
Comma list: 36/35, 9604/9375
Mapping: {{mapping|legend=1| 1 -4 -2 -4 | 0 9 7 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 56/55, 2541/2500
Mapping: {{mapping| 1 -4 -2 -4 1 | 0 9 7 11 4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 56/55, 66/65, 507/500
Mapping: {{mapping| 1 -4 -2 -4 1 0 | 0 9 7 11 4 6 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 36/35, 51/50, 56/55, 66/65, 170/169
Mapping: {{mapping| 1 -4 -2 -4 1 0 1 | 0 9 7 11 4 6 5 }}

=== Slurpee
Subgroup: 2.3.5.7
Comma list: 36/35, 51200/50421
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -7 -11 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 121/120, 352/343
Mapping: {{mapping| 1 2 3 3 4 | 0 -7 -11 -3 -9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 66/65, 143/140, 352/343
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }}

=== Shallowtone
Subgroup: 2.3.5.7
Comma list: 36/35, 295245/262144
Mapping: {{mapping|legend=1| 1 0 18 -16 | 0 1 -10 12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 72171/65536
Mapping: {{mapping| 1 0 18 -16 16 | 0 1 -10 12 -8 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44, 16731/16384
Mapping: {{mapping| 1 0 18 -16 16 -1 | 0 1 -10 12 -8 3 }}

=== References


= Mirkwai clan

=== Canopus
Subgroup: 3.5.7
Comma list: 16875/16807
Mapping: {{mapping|legend=2| 1 -2 -1 | 0 5 4 }}

==== Overview to extensions

=== Mirkat
Subgroup: 2.3.5.7
Comma list: 16875/16807, 19683/19600
Mapping: {{mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 8019/8000
Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 1375/1372
Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 442/441, 540/539, 561/560, 715/714
Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}

=== Eris
Subgroup: 2.3.5.7
Comma list: 16875/16807, 65625/65536
Mapping: {{mapping|legend=1| 1 -19 8 -5 | 0 29 -8 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 65625/65536
Mapping: {{mapping| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372, 4096/4095
Mapping: {{mapping| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}

=== Subsemifourth
Subgroup: 2.3.5.7
Comma list: 16875/16807, 26873856/26796875
Mapping: {{mapping|legend=1| 1 -8 -4 -8 | 0 47 31 53 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 234375/234256
Mapping: {{mapping| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 847/845, 1375/1372, 1575/1573
Mapping: {{mapping| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}

=== Septendesemi
Subgroup: 2.3.5.7
Comma list: 16875/16807, 1959552/1953125
Mapping: {{mapping|legend=1| 1 -2 -1 -2 | 0 41 38 55 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 43923/43750
Mapping: {{mapping| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 1375/1372, 4225/4224
Mapping: {{mapping| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224
Mapping: {{mapping| 1 -2 -1 -2 -1 3 4 | 0 41 38 55 51 8 1 }}

=== Gaster
Subgroup: 2.3.5.7
Comma list: 16875/16807, 14348907/14336000
Mapping: {{mapping|legend=1| 1 -8 -34 -32 | 0 19 72 69 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 14348907/14336000
Mapping: {{mapping| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372, 2200/2197
Mapping: {{mapping| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}

==== 31-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}

==== 37-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}

==== 41-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}

=== Hemiseptisix
Subgroup: 2.3.5.7
Comma list: 16875/16807, 95703125/95551488
Mapping: {{mapping|legend=1| 1 -19 -7 -17 | 0 53 24 51 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 2734375/2725888
Mapping: {{mapping| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372, 2200/2197
Mapping: {{mapping| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197
Mapping: {{mapping| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}

=== Browser
Subgroup: 2.3.5.7
Comma list: 16875/16807, 78732/78125
Mapping: {{mapping|legend=1| 1 -29 -37 -47 | 0 35 45 57 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 78732/78125
Mapping: {{mapping| 1 -29 -37 -47 -28 | 0 35 45 57 36 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845, 1375/1372
Mapping: {{mapping| 1 -29 -37 -47 -28 -33 | 0 35 45 57 36 42 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 540/539, 561/560, 715/714, 847/845
Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 | 0 35 45 57 36 42 31 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714
Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 -91 | 0 35 45 57 36 42 31 109 }}

=== Grazer
Subgroup: 2.3.5.7
Comma list: 16875/16807, 1071875/1062882
Mapping: {{mapping|legend=1| 1 -3 -4 -5 | 0 37 51 63 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 218750/216513
Mapping: {{mapping| 1 -3 -4 -5 -1 | 0 37 51 63 36 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 540/539, 2200/2197
Mapping: {{mapping| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989
Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663
Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}


= Mirkwai family

=== Mirkwai
Subgroup: 2.3.5.7
Comma list: 16875/16807 (mirkwai)
Mapping: [{{val| 1 0 0 0 }}, {{val| 0 1 3 3 }}, {{val| 0 0 -5 -4 }}]

=== Indra
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372
Mapping: [{{val| 1 0 0 0 2 }}, {{val| 0 1 3 3 0 }}, {{val| 0 0 -5 -4 3 }}]
Mapping to lattice: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}]

==== Shibi
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372
Mapping: [{{val| 1 0 0 0 2 -3 }}, {{val| 0 1 3 3 0 3 }}, {{val| 0 0 -5 -4 4 }}]

==== Yajna
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372
Mapping: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 3 3 0 11 }}, {{val| 0 0 -5 -4 3 -20 }}]

==== Vibhu
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 1375/1372
Mapping: [{{val| 1 0 0 0 2 1 }}, {{val| 0 1 3 3 0 6 }}, {{val| 0 0 -5 -4 3 -14 }}]

==== Vish
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 540/539
Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 3 3 0 -2 }}, {{val| 0 0 -5 -4 3 10 }}]


= Misty family

=== Misty
Subgroup: 2.3.5
Comma list: 67108864/66430125
Mapping: {{mapping|legend=1| 3 0 26 | 0 1 -4 }}

==== Overview to extensions

=== Septimal misty

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 3136/3125, 5120/5103
Mapping: {{mapping|legend=1| 3 0 26 56 | 0 1 -4 -10 }}

===== 2.3.5.7.17-subgroup
Subgroup: 2.3.5.7.17
Comma list: 256/255, 1701/1700, 2025/2023
Mapping: {{mapping| 3 0 26 56 -2 | 0 1 -4 -10 3 }}

===== 2.3.5.7.17.19 subgroup
Subgroup: 2.3.5.7.17.19
Comma list: 256/255, 324/323, 400/399, 476/475
Mapping: {{mapping| 3 0 26 56 -2 8 | 0 1 -4 -10 3 1 }}

==== Murky
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 3136/3125
Mapping: {{mapping| 3 0 26 56 77 | 0 1 -4 -10 -14 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 625/624
Mapping: {{mapping| 3 0 26 56 77 92 | 0 1 -4 -10 -14 -17 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594
Mapping: {{mapping| 3 0 26 56 77 92 -2 | 0 1 -4 -10 -14 -17 3 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Mapping: {{mapping| 3 0 26 56 77 92 -2 8 | 0 1 -4 -10 -14 -17 3 1 }}

==== Hazy
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1375/1372, 5120/5103
Mapping: {{mapping| 3 0 26 56 96 | 0 1 -4 -10 -18 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 847/845, 1375/1372
Mapping: {{mapping| 3 0 26 56 96 111 | 0 1 -4 -10 -18 -21 }}

==== Smoky
Subgroup: 2.3.5.7.11
Comma list: 385/384, 2200/2187, 3136/3125
Mapping: {{mapping| 3 0 26 56 -61 | 0 1 -4 -10 15 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 385/384, 3136/3125
Mapping: {{mapping| 3 0 26 56 -61 -46 | 0 1 -4 -10 15 12 }}

==== Ashy
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3136/3125, 5120/5103
Mapping: {{mapping| 3 0 26 56 -80 | 0 1 -4 -10 19 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 3136/3125
Mapping: {{mapping| 3 0 26 56 -80 -65 | 0 1 -4 -10 19 16 }}

==== Semimist
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 5120/5103, 9801/9800
Mapping: {{mapping| 6 0 52 112 173 | 0 1 -4 -10 -16 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 3136/3125
Mapping: {{mapping| 6 0 52 112 173 203 | 0 1 -4 -10 -16 -19 }}

==== Hemimist
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3136/3125, 5120/5103
Mapping: {{mapping| 3 0 26 56 8 | 0 2 -8 -20 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845, 3025/3024
Mapping: {{mapping| 3 0 26 56 8 23 | 0 2 -8 -20 1 -5 }}

=== Fog
Subgroup: 2.3.5.7
Comma list: 225/224, 156250/151263
Mapping: {{mapping|legend=1| 3 0 26 37 | 0 1 -4 -6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 2420/2401
Mapping: {{mapping| 3 0 26 37 58 | 0 1 -4 -6 -10 }}


= Octagar family

=== Octagar
Subgroup: 2.3.5.7
Comma list: [[4000/3969]]
Mapping: {{mapping|legend=1| 1 0 1 4 | 0 1 0 -2 | 0 0 2 3 }}
Mapping to lattice: [{{val| 0 -1 -2 -1 }}, {{val| 0 -1 0 2 }}]

=== Nakika
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242
Mapping: {{mapping|legend=1| 1 0 1 4 4 | 0 1 0 -2 -2 | 0 0 2 3 4 }}
Mapping to lattice: [{{val| 0 1 2 1 2 }}, {{val| 0 -1 0 2 2 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 245/242
Mapping: {{mapping| 1 0 1 4 4 2 | 0 1 0 -2 -2 -1 | 0 0 2 3 4 5 }}

=== Octasand
Subgroup: 2.3.5.7.11
Comma list: 540/539, 2200/2187
Mapping: {{mapping|legend=1| 1 0 1 4 -5 | 0 1 0 -2 7 | 0 0 2 3 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 540/539
Mapping: {{mapping| 1 0 1 4 -5 0 | 0 1 0 -2 7 4 | 0 0 2 3 -4 -4 }}


= Octagar temperaments

=== Pluto
Subgroup: 2.3.5.7
Comma list: 4000/3969, 10976/10935
Mapping: {{mapping|legend=1| 1 -2 -11 -10 | 0 7 26 25 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891, 1375/1372
Mapping: {{mapping| 1 -2 -11 -10 5 | 0 7 26 25 -3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 540/539
Mapping: {{mapping| 1 -2 -11 -10 5 16 | 0 7 26 25 -3 -24 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 325/324, 352/351, 364/363, 540/539
Mapping: {{mapping| 1 -2 -11 -10 5 16 21 | 0 7 26 25 -3 -24 -33 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594
Mapping: {{mapping| 1 -2 -11 -10 5 16 21 -6 | 0 7 26 25 -3 -24 -33 20 }}

===== Orcus
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 275/273, 896/891
Mapping: {{mapping| 1 -2 -11 -10 5 -5 | 0 7 26 25 -3 17 }}

==== Plutino
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 10976/10935
Mapping: {{mapping| 1 -2 -11 -10 -16 | 0 7 26 25 38 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 245/242, 729/728
Mapping: {{mapping| 1 5 15 15 22 12 | 0 7 26 25 38 17 }}

=== Slithy
Subgroup: 2.3.5.7
Comma list: 4000/3969, 420175/419904
Mapping: {{mapping|legend=1| 1 -16 -31 -12 | 0 19 36 16 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 2200/2187, 4375/4356
Mapping: {{mapping| 1 -16 -31 -12 -53 | 0 19 36 16 61 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 540/539, 1575/1573
Mapping: {{mapping| 1 -16 -31 -12 -53 0 | 0 19 36 16 61 4 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 352/351, 375/374, 540/539, 595/594
Mapping: {{mapping| 1 -16 -31 -12 -53 0 -57 | 0 19 36 16 61 4 66 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 190/189, 325/324, 352/351, 361/360, 375/374, 595/594
Mapping: {{mapping| 1 -16 -31 -12 -53 0 -57 -30 | 0 19 36 16 61 4 66 37 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 190/189, 300/299, 323/322, 325/324, 352/351, 361/360, 484/483
Mapping: {{mapping| 1 -16 -31 -12 -53 0 -57 -30 -76 | 0 19 36 16 61 4 66 37 87 }}

=== Tridecatonic
Subgroup: 2.3.5.7
Comma list: 4000/3969, 8748/8575
Mapping: {{mapping|legend=1| 13 0 -11 16 | 0 1 2 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 1944/1925, 2560/2541
Mapping: {{mapping| 13 0 -11 16 45 | 0 1 2 1 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 144/143, 275/273, 1040/1029
Mapping: {{mapping| 13 0 -11 16 45 7 | 0 1 2 1 0 2 }}

=== Slendi
Subgroup: 2.3.5.7
Comma list: 4000/3969, 84035/82944
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -17 -28 -8 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 46656/46585
Mapping: {{mapping| 1 2 3 3 4 | 0 -17 -28 -8 -22 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 245/242, 343/338
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -17 -28 -8 -22 -12 }}

=== Dhaivatic
Subgroup: 2.3.5.7
Comma list: 4000/3969, 2100875/2097152
Mapping: {{mapping|legend=1| 1 -4 -3 6 | 0 21 20 -12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1331/1323, 4000/3969
Mapping: {{mapping| 1 -4 -3 6 0 | 0 21 20 -12 13 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 275/273, 325/324, 385/384, 1331/1323
Mapping: {{mapping| 1 -4 -3 6 0 -8 | 0 21 20 -12 13 44 }}

=== References


= Orgonia

=== Orgonismic
Subgroup: 2.3.5.7.11
Comma list: 65536/65219
Mapping: {{mapping| 1 0 0 2 4 | 0 1 0 0 0 | 0 0 1 0 0 | 0 0 0 3 -2 }}

=== Subgroup temperaments

==== Orgone
Subgroup: 2.7.11
Comma list: [[65536/65219]]
Mapping: {{mapping|legend=2| 1 2 4 | 0 3 -2 }}
Mapping: {{mapping|legend=3| 1 0 0 2 4 | 0 0 0 3 -2 }}

===== Oregon
Subgroup: 2.9.15.7.11
Comma list: 55/54, 64/63, 100/99
Mapping: {{mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}
Mapping: {{mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}

====== Orca
Subgroup: 2.9.15.7.11.17
Comma list: 55/54, 64/63, 100/99, 85/84

====== Ork
Subgroup: 2.9.15.7.11.17
Comma list: 99/98, 121/120, 136/135, 256/255


= Orwellismic family

=== Orwellismic
Subgroup: 2.3.5.7
Comma list: 1728/1715
Mapping: {{mapping|legend=1| 1 0 0 2 | 0 1 0 1 | 0 0 3 -1 }}
Mapping to lattice: {{mapping| 0 0 -3 1 | 0 1 0 1 }}

=== Guanyin
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539
Mapping: {{mapping|legend=1| 1 0 0 2 -2 | 0 1 0 1 1 | 0 0 3 -1 5 }}
Mapping to lattice: {{mapping| 0 0 -3 1 -5 | 0 1 0 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539
Mapping: {{mapping| 1 0 0 2 -2 3 | 0 1 0 1 1 -2 | 0 0 3 -1 5 5 }}

==== Avalokita
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 196/195
Mapping: {{mapping| 1 0 0 2 -2 6 | 0 1 0 1 1 1 | 0 0 3 -1 5 -5 }}

=== Orwellian
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384
Mapping: {{mapping|legend=1| 1 0 0 2 5 | 0 1 0 1 0 | 0 0 3 -1 -2 }}


= Orwellismic temperaments

=== Sentinel
Subgroup: 2.3.5.7
Comma list: 1728/1715, 3645/3584
Mapping: {{mapping|legend=1| 1 -1 12 -3 | 0 4 -15 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 243/242, 385/384
Mapping: {{mapping| 1 -1 12 -3 -3 | 0 4 -15 9 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 105/104, 144/143, 243/242
Mapping: {{mapping| 1 -1 12 -3 -3 5 | 0 4 -15 9 10 -2 }}

=== Secant
Subgroup: 2.3.5.7
Comma list: 1728/1715, 177147/175000
Mapping: {{mapping|legend=1| 2 1 0 5 | 0 7 15 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1344/1331, 1728/1715
Mapping: {{mapping| 2 1 0 5 6 | 0 7 15 2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 351/350, 364/363, 441/440
Mapping: {{mapping| 2 1 0 5 6 4 | 0 7 15 2 3 11 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 144/143, 170/169, 221/220, 351/350, 441/440
Mapping: {{mapping| 2 1 0 5 6 4 6 | 0 7 15 2 3 11 7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399
Mapping: {{mapping| 2 1 0 5 6 4 6 2 | 0 7 15 2 3 11 7 21 }}

=== Diesic
Subgroup: 2.3.5.7
Comma list: 1728/1715, 5103/5000
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 891/875
Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 121/120, 343/338, 441/440
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}

=== Infraorwell
Subgroup: 2.3.5.7
Comma list: 1728/1715, 28672/28125
Mapping: {{mapping|legend=1| 1 -2 3 -1 | 0 16 -3 17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 1344/1331
Mapping: {{mapping| 1 -2 3 -1 1 | 0 16 -3 17 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 196/195, 364/363
Mapping: {{mapping| 1 -2 3 -1 1 -1 | 0 16 -3 17 11 21 }}

=== Pentaorwell
Subgroup: 2.3.5.7
Comma list: 1728/1715, 179200/177147
Mapping: {{mapping|legend=1| 5 0 -36 22 | 0 1 6 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 1728/1715, 2200/2187
Mapping: {{mapping| 5 0 -36 22 57 | 0 1 6 -1 -5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 1728/1715
Mapping: {{mapping| 5 0 -36 22 57 82 | 0 1 6 -1 -5 -8 }}

=== Triskaidekic
Subgroup: 2.3.5.7
Comma list: 1728/1715, 1875/1792
Mapping: {{mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 125/121, 385/384
Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 99/98, 125/121, 1200/1183
Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }}

=== Phillips
Subgroup: 2.3.5.7
Comma list: 1728/1715, 6561/6272
Mapping: {{mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 729/704
Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}


= Mavila family

=== Mavila
Subgroup: 2.3.5
Comma list: 135/128
Mapping: {{mapping|legend=1| 1 0 7 | 0 1 -3 }}

==== Overview to extensions

===== 7-limit extensions

===== Subgroup extensions

==== 2.3.5.11 subgroup
Subgroup: 2.3.5.11
Comma list: 33/32, 45/44

=== Armodue
Subgroup: 2.3.5.7
Comma list: 36/35, 135/128
Mapping: {{mapping|legend=1| 1 0 7 -5 | 0 1 -3 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 36/35, 45/44
Mapping: {{mapping| 1 0 7 -5 5 | 0 1 -3 5 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 33/32, 36/35, 45/44
Mapping: {{mapping| 1 0 7 -5 5 -1 | 0 1 -3 5 -1 3 }}

===== Armodog
Subgroup: 2.3.5.7.11.13.19
Comma list: 27/26, 33/32, 36/35, 39/38, 45/44
Mapping: {{mapping| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}

=== Mavling
Subgroup: 2.3.5.7
Comma list: 126/125, 135/128
Mapping: {{mapping|legend=1| 1 0 7 20 | 0 1 -3 -11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 126/125
Mapping: {{mapping| 1 0 7 20 5 | 0 1 -3 -11 -1 }}

=== Pelogic
Subgroup: 2.3.5.7
Comma list: 21/20, 135/128
Mapping: {{mapping|legend=1| 1 0 7 9 | 0 1 -3 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 21/20, 33/32, 45/44
Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}

=== Hornbostel
Subgroup: 2.3.5.7
Comma list: 135/128, 729/700
Mapping: {{mapping|legend=1| 1 0 7 -16 | 0 1 -3 12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 729/700
Mapping: {{mapping| 1 0 7 -16 5 | 0 1 -3 12 -1 }}

=== Bipelog
Subgroup: 2.3.5.7
Comma list: 50/49, 135/128
Mapping: {{mapping|legend=1| 2 0 14 15 | 0 1 -3 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 50/49
Mapping: {{mapping| 2 0 14 15 10 | 0 1 -3 -3 -1 }}

=== Mohavila
Subgroup: 2.3.5.7
Comma list: 135/128, 1323/1250
Mapping: {{mapping|legend=1| 1 1 4 7 | 0 2 -6 -15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 1323/1250
Mapping: {{mapping| 1 1 4 7 4 | 0 2 -6 -15 -2 }}

=== References


= Quintile family

=== Quintile
Subgroup: 2.3.5
Comma list: 847288609443/838860800000
Mapping: {{mapping|legend=1| 5 0 -28 | 0 1 5 }}

=== Pentacloud
Subgroup: 2.3.5.7
Comma list: 245/243, 16807/16384
Mapping: {{mapping|legend=1| 5 0 -28 14 | 0 1 5 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 3087/3025
Mapping: {{mapping| 5 0 -28 14 49 | 0 1 5 0 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 245/243, 3087/3025
Mapping: {{mapping| 5 0 -28 14 49 -29 | 0 1 5 0 -4 6 }}

=== Hemiquintile
Subgroup: 2.3.5.7
Comma list: 19683/19600, 589824/588245
Mapping: {{mapping|legend=1| 5 0 -28 18 | 0 2 10 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 8019/8000, 180224/180075
Mapping: {{mapping| 5 0 -28 18 -54 | 0 2 10 -1 18 }}

===== Hemiquintilis
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 124215/123904
Mapping: {{mapping| 5 0 -28 18 -54 34 | 0 2 10 -1 18 13 }}

===== Hemiquint
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000
Mapping: {{mapping| 5 0 -28 18 -54 34 | 0 2 10 -1 18 -13 }}

=== Decile
Subgroup: 2.3.5.7
Comma list: 235298/234375, 321489/320000
Mapping: {{mapping|legend=1| 10 0 -56 -67 | 0 1 5 6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 234375/234256
Mapping: {{mapping| 10 0 -56 -67 -108 | 0 1 5 6 9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 729/728, 1001/1000, 4225/4224
Mapping: {{mapping| 10 0 -56 -67 -108 37 | 0 1 5 6 9 0 }}

=== Notes


= Porcupine family

=== Porcupine
Subgroup: 2.3.5
Comma list: 250/243
Mapping: {{mapping|legend=1| 1 2 3 | 0 -3 -5 }}

==== Overview to extensions

===== 7-limit extensions

===== Subgroup extensions

==== 2.3.5.11 subgroup (porkypine)
Subgroup: 2.3.5.11
Comma list: 55/54, 100/99
Mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}

===== Undecimation
Subgroup: 2.3.5.11.13
Comma list: 55/54, 100/99, 512/507
Mapping: {{mapping| 1 -1 -2 0 5 | 0 6 10 8 -3 }}

=== Septimal porcupine
Subgroup: 2.3.5.7
Comma list: 64/63, 250/243
Mapping: {{mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 100/99
Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }}

===== Porcupinefowl
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 55/54, 64/63, 66/65
Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}

===== Porcupinefish
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 91/90, 100/99
Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}

===== Pourcup
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 100/99, 196/195
Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}

===== Porkpie
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 65/63, 100/99
Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}

=== Opossum
Subgroup: 2.3.5.7
Comma list: 28/27, 126/125
Mapping: {{mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 55/54, 77/75
Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 55/54, 66/65
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}

=== Porky
Subgroup: 2.3.5.7
Comma list: 225/224, 250/243
Mapping: {{mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99, 225/224
Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 65/64, 91/90, 100/99
Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}

=== Coendou
Subgroup: 2.3.5.7
Comma list: 250/243, 525/512
Mapping: {{mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99, 525/512
Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 65/64, 100/99, 105/104
Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}

=== Hystrix
Subgroup: 2.3.5.7
Comma list: 36/35, 160/147
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -3 -5 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 22/21, 36/35, 80/77
Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}

=== Hedgehog
Subgroup: 2.3.5.7
Comma list: 50/49, 245/243
Mapping: {{mapping|legend=1| 2 1 1 2 | 0 3 5 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 55/54, 99/98
Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 55/54, 65/63, 99/98
Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}

===== Urchin
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 50/49, 55/54, 66/65
Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}

==== Hedgepig
Subgroup: 2.3.5.7.11
Comma list: 50/49, 245/243, 385/384
Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}

=== Nautilus
Subgroup: 2.3.5.7
Comma list: 49/48, 250/243
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -6 -10 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 245/242
Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 91/90, 100/99
Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}

===== Belauensis
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 49/48, 55/54, 66/65
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}

=== Ammonite
Subgroup: 2.3.5.7
Comma list: 250/243, 686/675
Mapping: {{mapping|legend=1| 1 -4 -7 -9 | 0 9 15 19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99, 686/675
Mapping: {{mapping| 1 -4 -7 -9 -4 | 0 9 15 19 12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 91/90, 100/99, 169/168
Mapping: {{mapping| 1 -4 -7 -9 -4 -5 | 0 9 15 19 12 14 }}

=== Ceratitid
Subgroup: 2.3.5.7
Comma list: 250/243, 1728/1715
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -9 -15 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99, 352/343
Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 65/63, 100/99, 352/343
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }}


= Porcupine rank-3 family

=== Rank-3 porcupine
Subgroup: 2.3.5.7
Comma list: [[250/243]]
Mapping: {{mapping|legend=1| 1 2 3 0 | 0 -3 -5 0 | 0 0 0 1 }}

=== Sonic
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99
Mapping: {{mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }}

=== Tikal
Subgroup: 2.3.5.7.11
Comma list: 56/55, 250/243
Mapping: {{mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }}


= Porwell family

=== Porwell
Subgroup: 2.3.5.7
Comma list: [[6144/6125]]
Mapping: {{mapping|legend=1| 1 0 1 4 | 0 1 1 -1 | 0 0 -2 3 }}

=== Zeus

=== Jupiter
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625
Mapping: {{mapping|legend=1| 1 0 1 4 -5 | 0 1 1 -1 6 | 0 0 -2 3 -8 }}

=== Hera
Subgroup: 2.3.5.7.11
Comma list: 6144/6125, 8019/8000
Mapping: {{mapping|legend=1| 1 0 1 4 9 | 0 1 1 -1 -3 | 0 0 -2 3 -6 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 2080/2079, 4096/4095
Mapping: {{mapping| 1 0 1 4 9 7 | 0 1 1 -1 -3 -2 | 0 0 -2 3 -6 -1 }}

=== Semiporwell
Subgroup: 2.3.5.7.11
Comma list: 6144/6125, 9801/9800
Mapping: {{mapping|legend=1| 2 0 0 11 14 | 0 1 1 -1 -2 | 0 0 2 -3 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3584/3575
Mapping: {{mapping| 2 0 0 11 14 15 | 0 1 1 -1 -2 -1 | 0 0 2 -3 -1 -6 }}


= Porwell temperaments

=== Hendecatonic
Subgroup: 2.3.5.7
Comma list: 6144/6125, 10976/10935
Mapping: {{mapping|legend=1| 11 0 43 -4 | 0 1 -1 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 10976/10935
Mapping: {{mapping| 11 0 43 -4 38 | 0 1 -1 2 0 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 351/350, 4459/4455
Mapping: {{mapping| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023
Mapping: {{mapping| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}

==== Cohendecatonic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891, 4375/4356
Mapping: {{mapping| 11 0 43 -4 73 | 0 1 -1 2 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 540/539, 625/624
Mapping: {{mapping| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 364/363, 375/374, 540/539
Mapping: {{mapping| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}

==== Icosidillic
Subgroup: 2.3.5.7.11
Comma list: 3388/3375, 6144/6125, 9801/9800
Mapping: {{mapping| 22 0 86 -8 111 | 0 1 -1 2 -1 }}

=== Nessafof
Subgroup: 2.3.5.7
Comma list: 6144/6125, 250047/250000
Mapping: {{mapping|legend=1| 3 2 5 10 | 0 7 5 -4 }}

==== Nessa
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1344/1331, 4375/4356
Mapping: {{mapping| 3 2 5 10 10 | 0 7 5 -4 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 364/363, 441/440, 625/624
Mapping: {{mapping| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}

==== Fof
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 250047/250000
Mapping: {{mapping| 3 2 5 10 8 | 0 7 5 -4 6 }}

=== Grendel
Subgroup: 2.3.5.7
Comma list: 6144/6125, 16875/16807
Mapping: {{mapping|legend=1| 1 -14 3 -6 | 0 23 -1 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 5632/5625
Mapping: {{mapping| 1 -14 3 -6 -25 | 0 23 -1 13 42 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 625/624, 1375/1372
Mapping: {{mapping| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274
Mapping: {{mapping| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714
Mapping: {{mapping| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}

=== Twothirdtonic
Subgroup: 2.3.5.7
Comma list: 686/675, 6144/6125
Mapping: {{mapping|legend=1| 1 -10 5 -7 | 0 13 -3 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 686/675
Mapping: {{mapping| 1 -10 5 -7 -1 | 0 13 -3 11 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 169/168, 176/175
Mapping: {{mapping| 1 -10 5 -7 -1 -7 | 0 13 -3 11 5 12 }}

=== Semaja
Subgroup: 2.3.5.7
Comma list: 3125/3087, 6144/6125
Mapping: {{mapping|legend=1| 1 -2 1 3 | 0 19 7 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 3125/3087
Mapping: {{mapping| 1 -2 1 3 1 | 0 19 7 -1 13 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 176/175, 275/273
Mapping: {{mapping| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }}

=== Aufo
Subgroup: 2.3.5.7
Comma list: 6144/6125, 177147/175616
Mapping: {{mapping|legend=1| 1 -3 12 -14 | 0 9 -19 33 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 177147/175616
Mapping: {{mapping| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 351/350, 58806/57967
Mapping: {{mapping| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}

==== Aufic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625, 72171/71680
Mapping: {{mapping| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845, 4096/4095
Mapping: {{mapping| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}

=== Absurdity
Subgroup: 2.3.5.7
Comma list: 6144/6125, 177147/175000
Mapping: {{mapping|legend=1| 7 0 -17 64 | 0 1 3 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 72171/71680
Mapping: {{mapping| 7 0 -17 64 124 | 0 1 3 -4 -9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 1188/1183, 3584/3575
Mapping: {{mapping| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625
Mapping: {{mapping| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 261/260, 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}

=== Polypyth
Subgroup: 2.3.5.7
Comma list: 6144/6125, 179200/177147
Mapping: {{mapping|legend=1| 1 0 -31 52 | 0 1 21 -31 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 2200/2187, 6144/6125
Mapping: {{mapping| 1 0 -31 52 59 | 0 1 21 -31 -35 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 1716/1715
Mapping: {{mapping| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715
Mapping: {{mapping| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}

=== Whoops
Subgroup: 2.3.5.7
Comma list: 6144/6125, 244140625/243045684
Mapping: {{mapping|legend=1| 1 -16 -11 14 | 0 33 25 -21 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 6144/6125
Mapping: {{mapping| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}

=== Dodifo
Subgroup: 2.3.5.7
Comma list: 6144/6125, 2500000/2470629
Mapping: {{mapping|legend=1| 1 -23 -4 0 | 0 35 9 4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 2560/2541, 4375/4356
Mapping: {{mapping| 1 -23 -4 0 14 | 0 35 9 4 -15 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 625/624, 640/637, 1375/1372
Mapping: {{mapping| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}

=== Icositritonic
Subgroup: 2.3.5.7
Comma list: 6144/6125, 9920232/9765625
Mapping: {{mapping|legend=1| 23 0 17 101 | 0 1 1 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 35937/35840
Mapping: {{mapping| 23 0 17 101 116 | 0 1 1 -1 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 847/845, 3584/3575
Mapping: {{mapping| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088
Mapping: {{mapping| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
Mapping: {{mapping| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
Mapping: {{mapping| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}

=== References


= Quartonic family

=== Quartonic
Subgroup: 2.3.5
Comma list: 390625000/387420489
Mapping: {{mapping|legend=1| 1 2 3 | 0 -11 -18 }}

==== Overview to extensions

=== Septimal quartonic
Subgroup: 2.3.5.7
Comma list: 1728/1715, 4000/3969
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -11 -18 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 2200/2187
Mapping: {{mapping| 1 2 3 3 5 | 0 -11 -18 -5 -41 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 176/175, 325/324, 540/539
Mapping: {{mapping| 1 2 3 3 5 4 | 0 -11 -18 -5 -41 -8 }}

==== Quarto
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 864/847
Mapping: {{mapping| 1 2 3 3 4 | 0 -11 -18 -5 -14 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 100/99, 144/143, 245/242
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -11 -18 -5 -14 -8 }}

==== Quartz
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 4000/3969
Mapping: {{mapping| 1 2 3 3 3 | 0 -11 -18 -5 12 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 169/168, 275/273, 385/384
Mapping: {{mapping| 1 2 3 3 3 4 | 0 -11 -18 -5 12 -8 }}

==== Biquartonic
Subgroup: 2.3.5.7.11
Comma list: 1728/1715, 2420/2401, 2560/2541
Mapping: {{mapping| 2 4 6 6 7 | 0 -11 -18 -5 -1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 364/363, 640/637
Mapping: {{mapping| 2 4 6 6 7 8 | 0 -11 -18 -5 -1 -8 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 289/288, 325/324, 544/539
Mapping: {{mapping| 2 4 6 6 7 8 9 | 0 -11 -18 -5 -1 -8 -11 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 221/220, 289/288, 325/324, 544/539, 400/399
Mapping: {{mapping| 2 4 6 6 7 8 9 10 | 0 -11 -18 -5 -1 -8 -11 -20 }}

==== Yarm
Subgroup: 2.3.5.7.11
Comma list: 1331/1323, 1728/1715, 4000/3969
Mapping: {{mapping| 1 2 3 3 4 | 0 -33 -54 -15 -43 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 640/637, 1331/1323
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -33 -54 -15 -43 -24 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 325/324, 561/560, 640/637, 850/847
Mapping: {{mapping| 1 2 3 3 4 4 4 | 0 -33 -54 -15 -43 -24 7 }}

=== Yarman I
Subgroup: 2.3.5.7
Comma list: 10976/10935, 244140625/243045684
Mapping: {{mapping|legend=1| 1 2 3 4 | 0 -33 -54 -95 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 10976/10935
Mapping: {{mapping| 1 2 3 4 4 | 0 -33 -54 -95 -43 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 1001/1000, 10976/10935
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -33 -54 -95 -43 -24 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 364/363, 595/594, 1001/1000, 10976/10935
Mapping: {{mapping| 1 2 3 4 4 4 4 | 0 -33 -54 -95 -43 -24 7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 325/324, 361/360, 364/363, 595/594, 969/968, 1001/1000
Mapping: {{mapping| 1 2 3 4 4 4 4 5 | 0 -33 -54 -95 -43 -24 7 -60 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 325/324, 361/360, 364/363, 460/459, 507/506, 529/528, 760/759
Mapping: {{mapping| 1 2 3 4 4 4 4 5 5 | 0 -33 -54 -95 -43 -24 7 -60 -38 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 325/324, 361/360, 364/363, 406/405, 460/459, 494/493, 507/506, 529/528
Mapping: {{mapping| 1 2 3 4 4 4 4 5 5 6 | 0 -33 -54 -95 -43 -24 7 -60 -38 -91 }}

=== Yarman II
Subgroup: 2.3.5.7
Comma list: 5359375/5308416, 390625000/387420489
Mapping: {{mapping|legend=1| 1 2 3 2 | 0 -33 -54 64 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 4000/3993, 78121827/77948684
Mapping: {{mapping| 1 2 3 2 4 | 0 -33 -54 64 -43 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 1575/1573, 85683/85184
Mapping: {{mapping| 1 2 3 2 4 4 | 0 -33 -54 64 -43 -24 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 385/384, 1575/1573, 4928/4913
Mapping: {{mapping| 1 2 3 2 4 4 4 | 0 -33 -54 64 -43 -24 7 }}

=== Tertiseptisix
Subgroup: 2.3.5.7
Comma list: 2401/2400, 390625000/387420489
Mapping: {{mapping|legend=1| 1 13 21 15 | 0 -44 -72 -47 }}

=== Triquart
Subgroup: 2.3.5.7
Comma list: 117649/116640, 250047/250000
Mapping: {{mapping|legend=1| 3 6 9 10 | 0 -11 -18 -14 }}

=== Quartiquart
Subgroup: 2.3.5.7
Comma list: 390625/388962, 4802000/4782969
Mapping: {{mapping|legend=1| 4 8 12 15 | 0 -11 -18 -25 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 6250/6237, 14641/14580
Mapping: {{mapping| 4 8 12 15 17 | 0 -11 -18 -25 -21 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 1001/1000, 1375/1372, 10648/10647
Mapping: {{mapping| 4 8 12 15 17 16 | 0 -11 -18 -25 -21 -8 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 325/324, 561/560, 1001/1000, 10648/10647
Mapping: {{mapping| 4 8 12 15 17 16 18 | 0 -11 -18 -25 -21 -8 -11 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 289/288, 325/324, 361/360, 561/560, 1001/1000, 1331/1330
Mapping: {{mapping| 4 8 12 15 17 16 18 20 | 0 -11 -18 -25 -21 -8 -11 20 }}

=== Quintiquart
Subgroup: 2.3.5.7
Comma list: 16875/16807, 390625000/387420489
Mapping: {{mapping|legend=1| 5 10 15 18 | 0 -11 -18 -21 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 390625000/387420489
Mapping: {{mapping| 5 10 15 18 19 | 0 -11 -18 -21 -9 }}


= Quince clan

=== Mercy
Subgroup: 2.5.7
Comma list: 823543/819200
Mapping: {{mapping|legend=2| 1 3 3 | 0 -7 -2 }}
Mapping: {{mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}

==== Overview to extensions

=== Countermiracle
Subgroup: 2.3.5.7
Comma list: 6144/6125, 50421/50000
Mapping: {{mapping|legend=1| 1 -21 -4 1 | 0 25 7 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375, 6144/6125
Mapping: {{mapping| 1 -21 -4 1 -39 | 0 25 7 2 47 }}

===== Countermiraculous
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 1001/1000, 6144/6125
Mapping: {{mapping| 1 -21 -4 1 -39 29 | 0 25 7 2 47 -28 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 1001/1000, 1225/1224
Mapping: {{mapping| 1 -21 -4 1 -39 29 33 | 0 25 7 2 47 -28 -32 }}

===== Counterbenediction
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 3146/3125, 3584/3575
Mapping: {{mapping| 1 -21 -4 1 -39 29 57 | 0 25 7 2 47 -59 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125
Mapping: {{mapping| 1 -21 -4 1 -39 29 57 61 | 0 25 7 2 47 -59 -63 }}

===== Countermanna
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 3388/3375, 6144/6125
Mapping: {{mapping| 1 -21 -4 1 -39 -102 | 0 25 7 2 47 117 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 1632/1625, 3388/3375
Mapping: {{mapping| 1 -21 -4 1 -39 -102 -98 | 0 25 7 2 47 117 113 }}

==== Counterrevelation
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 50421/50000
Mapping: {{mapping| 1 -21 -4 1 -11 | 0 25 7 2 16 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 196/195, 13750/13689
Mapping: {{mapping| 1 -21 -4 1 -11 29 | 0 25 7 2 16 -28 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 176/175, 196/195, 10647/10625
Mapping: {{mapping| 1 -21 -4 1 -11 29 33 | 0 25 7 2 16 -28 -32 }}

=== Subgroup extensions

==== Mercy (2.5.7.13)
Subgroup: 2.5.7.13
Comma list: 343/338, 640/637
Mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}

===== 2.5.7.13.17 subgroup
Subgroup: 2.5.7.13.17
Comma list: 170/169, 224/221, 343/338
Mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}

===== 2.5.7.13.17.19 subgroup
Subgroup: 2.5.7.13.17.19
Comma list: 170/169, 224/221, 343/338, 476/475
Mapping: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}


= Ragismic family

=== Ragismic
Subgroup: 2.3.5.7
Comma list: [[4375/4374]]
Mapping: {{mapping|legend=1| 1 0 0 1 | 0 1 0 7 | 0 0 1 -4 }}
Mapping to lattice: [{{val| 0 -1 -1 -3 }}, {{val| 0 -1 -2 1 }}]

=== Beyla
Subgroup: 2.3.5.7.11
Comma list: 385/384, 4375/4374
Mapping: {{mapping|legend=1| 1 0 0 1 6 | 0 1 0 7 -6 | 0 0 1 -4 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 385/384
Mapping: {{mapping| 1 0 0 1 6 2 | 0 1 0 7 -6 4 | 0 0 1 -4 3 -2 }}

=== Ulmo
Subgroup: 2.3.5.7.11
Comma list: 176/175, 2200/2187
Mapping: {{mapping|legend=1| 1 0 0 1 -3 | 0 1 0 7 7 | 0 0 1 -4 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 176/175, 325/324
Mapping: {{mapping| 1 0 0 1 -3 2 | 0 1 0 7 7 4 | 0 0 1 -4 -2 -2 }}

=== Thor
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374
Mapping: {{mapping|legend=1| 2 0 0 2 5 | 0 1 0 7 5 | 0 0 1 -4 -3 }}

==== Thunor
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3025/3024
Mapping: {{mapping| 2 0 0 2 5 -3 | 0 1 0 7 5 15 | 0 0 1 -4 -3 -8 }}
Mapping to lattice: [{{val| 0 -1 -2 -3 -2 -7 }}, {{val| 0 -1 -2 1 1 1 }}]

==== Rym
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 4096/4095, 4375/4374
Mapping: {{mapping| 2 0 0 2 5 22 | 0 1 0 7 5 -9 | 0 0 1 -4 -3 3 }}

==== Donar
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 4225/4224, 4375/4374
Mapping: {{mapping| 2 0 1 -2 2 7 | 0 1 0 7 5 3 | 0 0 2 -8 -6 -5 }}
Mapping to lattice: [{{val| 0 2 2 6 4 1 }}, {{val| 0 -1 -2 1 1 2 }}]

=== Heimdall
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 117649/117612
Mapping: {{mapping|legend=1| 1 0 0 1 2 | 0 2 0 14 37 | 0 0 1 -4 -12 }}

=== Bragi
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 2097152/2096325
Mapping: {{mapping|legend=1| 1 0 2 -7 8 | 0 1 0 7 -3 | 0 0 3 -12 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4375/4374, 10985/10976
Mapping: {{mapping| 1 0 2 -7 8 -6 | 0 1 0 7 -3 7 | 0 0 3 -12 2 -13 }}

=== Vidar
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 100663296/100656875
Mapping: {{mapping|legend=1| 1 0 -5 21 9 | 0 1 4 -9 -3 | 0 0 5 -20 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 4225/4224, 4375/4374, 6656/6655
Mapping: {{mapping| 1 0 -5 21 9 13 | 0 1 4 -9 -3 -5 | 0 0 5 -20 -4 -7 }}


= Catalog of rank-4 temperaments

=== Cake (45/44)
Subgroup: 2.3.5.7.11
Comma list: [[45/44]]
Mapping: {{mapping|legend=1| 1 0 0 0 -2 | 0 1 0 0 2 | 0 0 1 0 1 | 0 0 0 1 0 }}

=== Mothwellsmic (99/98)
Subgroup: 2.3.5.7.11
Comma list: [[99/98]]
Mapping: {{mapping|legend=1| 1 0 0 0 1 | 0 1 0 0 -2 | 0 0 1 0 0 | 0 0 0 1 2 }}

=== Ptolemismic (100/99)
Subgroup: 2.3.5.7.11
Comma list: [[100/99]]
Mapping: {{mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 0 }}

=== Biyatismic (121/120)
Subgroup: 2.3.5.7.11
Comma list: [[121/120]]
Mapping: {{mapping|legend=1| 1 0 1 0 2 | 0 1 1 0 1 | 0 0 -2 0 -1 | 0 0 0 1 0 }}

=== Valinorsmic (176/175)
Subgroup: 2.3.5.7.11
Comma list: [[176/175]]
Mapping: {{mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 0 | 0 0 1 0 2 | 0 0 0 1 1 }}

==== Tridecimal valinorsmic
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350
Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 0 0 0 -3 | 0 0 1 0 2 2 | 0 0 0 1 1 1 }}

=== Rastmic (243/242)
Subgroup: 2.3.5.7.11
Comma list: [[243/242]]
Mapping: {{mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0 }}

=== Frostmic (245/242)
Subgroup: 2.3.5.7.11
Comma list: [[245/242]]
Mapping: {{mapping|legend=1| 1 0 1 0 0 | 0 1 0 0 0 | 0 0 2 0 1 | 0 0 0 1 1 }}

=== Akua (352/351, 847/845)
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845
Mapping: {{mapping|legend=1| 1 0 0 10 0 5 | 0 1 0 -6 0 -3 | 0 0 1 1 0 0 | 0 0 0 0 1 1 }}

=== Keenanismic (385/384)
Subgroup: 2.3.5.7.11
Comma list: [[385/384]]
Mapping: {{mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }}

==== Martwin
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }}

==== Ancient
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624
Mapping: {{mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }}

==== Commas 351/350, 385/384
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 1 | 0 1 0 0 1 -3 | 0 0 1 0 -1 2 | 0 0 0 1 -1 1 }}

==== Zaxa
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }}

==== Commas 364/363, 385/384
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 3 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 -3 }}

==== Commas 385/384, 847/845
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 847/845
Mapping: {{mapping|legend=1| 1 0 0 0 7 7 | 0 1 0 0 1 1 | 0 0 1 1 -2 -2 | 0 0 0 2 -2 -1 }}

=== Werckismic (441/440)
Subgroup: 2.3.5.7.11
Comma list: [[441/440]]
Mapping: {{mapping|legend=1| 1 0 0 0 -3 | 0 1 0 0 2 | 0 0 1 0 -1 | 0 0 0 1 2 }}

==== Commas 364/363, 441/440
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440
Mapping: {{mapping|legend=1| 1 0 0 0 -3 -8 | 0 1 0 0 2 5 | 0 0 1 0 -1 -2 | 0 0 0 1 2 3 }}
Mapping to lattice: [{{val| 0 1 1 -1 -1 0 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 1 1 1 1 }}]

==== Commas 351/350, 441/440
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440
Mapping: {{mapping|legend=1| 1 0 0 0 -3 1 | 0 1 0 0 2 -3 | 0 0 1 0 -1 2 | 0 0 0 1 2 1 }}

==== Commas 196/195, 352/351
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351
Mapping: {{mapping|legend=1| 1 0 0 0 -3 2 | 0 1 0 0 2 -1 | 0 0 1 0 -1 -1 | 0 0 0 1 2 2 }}

==== Tannic
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1287/1280
Mapping: {{mapping|legend=1| 1 0 0 0 -3 11 | 0 1 0 0 2 -4 | 0 0 1 0 -1 2 | 0 0 0 1 2 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 441/440, 561/560
Mapping: {{mapping| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}

==== Commas 441/440, 847/845
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 847/845
Mapping: {{mapping|legend=1| 1 0 0 0 -3 -3 | 0 1 0 0 2 2 | 0 0 1 1 1 1 | 0 0 0 2 4 5 }}

=== Swetismic (540/539)
Subgroup: 2.3.5.7.11
Comma list: [[540/539]]
Mapping: {{mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 3 | 0 0 1 0 1 | 0 0 0 1 -2 }}

==== Commas 540/539, 729/728
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728
Mapping: {{mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 0 3 6 | 0 0 1 0 1 0 | 0 0 0 1 -2 -1 }}

==== Commas 540/539, 625/624
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624
Mapping: {{mapping|legend=1| 1 0 0 0 2 -4 | 0 1 0 0 3 -1 | 0 0 1 0 1 4 | 0 0 0 1 -2 0 }}

==== Commas 540/539, 676/675
Subgroup: 2.3.5.7.11
Comma list: 540/539, 676/675
Mapping: {{mapping|legend=1| 1 0 0 0 2 -1 | 0 2 0 0 6 3 | 0 0 1 0 1 1 | 0 0 0 1 -2 0 }}

==== Commas 540/539, 847/845
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 847/845
Mapping: {{mapping|legend=1| 1 0 0 0 2 2 | 0 1 0 0 3 3 | 0 0 1 1 -1 -1 | 0 0 0 2 -4 -3 }}

=== Pentacircle (896/891)
Subgroup: 2.3.5.7.11
Comma list: 896/891
Mapping: {{mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 -4 | 0 0 1 0 0 | 0 0 0 1 1 }}

==== Tridecimal pentacircle (gentle)
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363
Mapping: {{mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 -4 -7 | 0 0 1 0 0 0 | 0 0 0 1 1 1 }}

=== Topsy (847/845, 1001/1000)
Subgroup: 2.3.5.7.11.13
Comma list: 847/845, 1001/1000
Mapping: {{mapping|legend=1| 1 0 0 -2 3 2 | 0 1 0 0 0 0 | 0 0 1 1 1 1 | 0 0 0 4 -3 -1 }}

=== Lehmerismic (3025/3024)
Subgroup: 2.3.5.7.11
Comma list: [[3025/3024]]
Mapping: {{mapping|legend=1| 1 0 0 0 2 | 0 1 0 1 2 | 0 0 1 0 -1 | 0 0 0 2 1 }}

==== Commas 2080/2079, 3025/3024
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024
Mapping: {{mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 1 2 6 | 0 0 1 0 -1 -2 | 0 0 0 2 1 3 }}

=== Trimitone (8019/8000)
Subgroup: 2.3.5.7.11
Comma list: [[8019/8000]]
Mapping: {{mapping|legend=1| 1 0 0 0 6 | 0 1 0 0 -6 | 0 0 1 0 3 | 0 0 0 1 0 }}

==== Commas 729/728, 1001/1000
Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 1001/1000
Mapping: {{mapping|legend=1| 1 0 0 0 6 -3 | 0 1 0 0 -6 6 | 0 0 1 0 3 0 | 0 0 0 1 0 -1 }}

==== Commas 351/350, 2080/2079
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 2080/2079
Mapping: {{mapping|legend=1| 1 0 0 0 6 1 | 0 1 0 0 -6 -3 | 0 0 1 0 3 2 | 0 0 0 1 0 1 }}

=== Kalismic (9801/9800)
Subgroup: 2.3.5.7.11
Comma list: [[9801/9800]]
Mapping: {{mapping|legend=1| 2 0 0 0 3 | 0 1 0 0 -2 | 0 0 1 0 1 | 0 0 0 1 1 }}

==== Commas 1716/1715, 2080/2079
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079
Mapping: {{mapping|legend=1| 2 0 0 0 3 -7 | 0 1 0 0 -2 1 | 0 0 1 0 1 0 | 0 0 0 1 1 2 }}

=== Unisquary (12005/11979)
Subgroup: 2.3.5.7.11
Comma list: [[12005/11979]]
Mapping: {{mapping|legend=1| 1 0 0 -6 -8 | 0 1 0 2 2 | 0 0 1 2 3 | 0 0 0 3 4 }}

==== Hensquary
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 1716/1715
Mapping: {{mapping|legend=1| 1 0 0 -6 -8 -12 | 0 1 0 2 2 3 | 0 0 1 2 3 4 | 0 0 0 3 4 5 }}

==== Ekasquary
Subgroup: 2.3.5.7.11.13
Comma list: 1575/1573, 4459/4455
Mapping: {{mapping|legend=1| 1 0 0 -6 -8 10 | 0 1 0 2 2 0 | 0 0 1 2 3 -2 | 0 0 0 3 4 -5 }}

=== Semicanousmic (14641/14580)
Subgroup: 2.3.5.7.11
Comma list: [[14641/14580]]
Mapping: {{mapping|legend=1| 1 0 -2 0 0 | 0 1 2 0 2 | 0 0 4 0 1 | 0 0 0 1 0 }}

=== Semiporwellismic (16384/16335)
Subgroup: 2.3.5.7.11
Comma list: 16384/16335
Mapping: {{mapping|legend=1| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 | 0 0 0 1 0 }}

==== Tridecimal semiporwellismic
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3584/3575
Mapping: {{mapping|legend=1| 1 0 0 0 7 2 | 0 1 1 0 -2 0 | 0 0 2 0 -1 -3 | 0 0 0 1 0 1 }}

=== Symbiotic (19712/19683)
Subgroup: 2.3.5.7.11
Comma list: [[19712/19683]]
Mapping: {{mapping|legend=1| 1 0 0 0 -8 | 0 1 0 0 9 | 0 0 1 0 0 | 0 0 0 1 -1 }}

==== Tridecimal symbiotic
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 19712/19683
Mapping: {{mapping|legend=1| 1 0 0 0 -8 -13 | 0 1 0 0 9 12 | 0 0 1 0 0 -1 | 0 0 0 1 -1 0 }}

==== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 1216/1215, 1540/1539, 2080/2079
Mapping: {{mapping| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}

=== Argyric (41503/41472)
Subgroup: 2.3.5.7.11
Comma list: [[41503/41472]]
Mapping: {{mapping|legend=1| 1 0 0 1 3 | 0 1 0 0 2 | 0 0 1 0 0 | 0 0 0 2 -3 }}

=== Chrysic (43923/43904)
Subgroup: 2.3.5.7.11
Comma list: [[43923/43904]]
Mapping: {{mapping|legend=1| 1 0 0 3 4 | 0 1 0 3 2 | 0 0 1 0 0 | 0 0 0 -4 -3 }}

=== Olympic (131072/130977)
Subgroup: 2.3.5.7.11
Comma list: [[131072/130977]]
Mapping: {{mapping|legend=1| 1 0 0 0 17 | 0 1 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 -2 }}

==== Tridecimal olympic
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4096/4095
Mapping: {{mapping|legend=1| 1 0 0 0 17 12 | 0 1 0 0 -5 -2 | 0 0 1 0 0 -1 | 0 0 0 1 -2 -1 }}

=== Seascape (160083/160000)
Subgroup: 2.3.5.7.11
Comma list: [[160083/160000]]
Mapping: {{mapping|legend=1| 1 0 0 0 4 | 0 2 0 0 -3 | 0 0 1 0 2 | 0 0 0 1 -1 }}

=== Fifthchromismic (1610510/1594323)
Subgroup: 2.3.5.7.11
Comma list: [[1610510/1594323]]
Mapping: {{mapping|legend=1| 1 0 -6 0 1 | 0 1 3 0 2 | 0 0 5 0 -1 | 0 0 0 1 0 }}

==== Fifthchroma
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 951665/944784
Mapping: {{mapping|legend=1| 1 0 -6 0 1 6 | 0 1 3 0 2 -1 | 0 0 5 0 -1 -1 | 0 0 0 1 0 0 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 715/714, 155771/155520
Mapping: {{mapping| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 352/351, 715/714, 1463/1458, 2057/2052
Mapping: {{mapping| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }}

=== Quartismic (117440512/117406179)
Subgroup: 2.3.5.7.11
Comma list: 117440512/117406179
Mapping: {{mapping|legend=1| 1 0 0 1 5 | 0 1 0 1 -1 | 0 0 1 0 0 | 0 0 0 5 1 }}

==== Tridecimal quartismic
Subgroup: 2.3.5.7.11.13
Comma list: 6656/6655, 123201/123200
Mapping: {{mapping|legend=1| 1 0 0 1 5 6 | 0 1 0 1 -1 -3 | 0 0 1 0 0 1 | 0 0 0 5 1 3 }}


= Rastmic rank-3 clan

=== Spectacle
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242
Mapping: {{mapping|legend=1| 1 1 0 -3 2 | 0 2 0 4 5 | 0 0 1 2 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 351/350
Mapping: {{mapping| 1 1 0 -3 2 -5 | 0 2 0 4 5 -2 | 0 0 1 2 0 4 }}

=== Mirwomo
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384
Mapping: {{mapping|legend=1| 1 1 0 6 2 | 0 2 0 -3 5 | 0 0 1 -1 0 }}

=== Mandos
Subgroup: 2.3.5.7.11
Comma list: 176/175, 243/242
Mapping: {{mapping|legend=1| 1 1 0 6 2 | 0 2 0 5 5 | 0 0 1 -2 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 243/242
Mapping: {{mapping| 1 1 0 6 2 4 | 0 2 0 5 5 -1 | 0 0 1 -2 0 0 }}

=== Cuckoo
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242
Mapping: {{mapping|legend=1| 1 1 0 -3 2 | 0 2 0 -4 5 | 0 0 1 3 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 243/242
Mapping: {{mapping| 1 1 0 -3 2 -5 | 0 2 0 -4 5 -10 | 0 0 1 3 0 5 }}

=== Parahemif
Subgroup: 2.3.5.7.11
Comma list: 243/242, 896/891
Mapping: {{mapping|legend=1| 1 1 0 -1 2 | 0 2 0 13 5 | 0 0 1 0 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 243/242, 364/363
Mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 | 0 0 1 0 0 0 }}

=== Urania
Subgroup: 2.3.5.7.11
Comma list: 81/80, 121/120
Mapping: {{mapping|legend=1| 1 1 0 0 2 | 0 2 8 0 5 | 0 0 0 1 0 }}
Mapping to lattice: [{{val| 0 2 8 0 5 }}, {{val| 0 0 0 -1 0 }}]

=== Mirage
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 385/384
Mapping: {{mapping|legend=1| 1 1 3 3 2 0 | 0 6 -7 -2 15 0 | 0 0 0 0 0 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 243/242, 273/272, 385/384
Mapping: {{mapping| 1 1 3 3 2 0 0 | 0 6 -7 -2 15 0 4 | 0 0 0 0 0 1 1 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 210/209, 225/224, 243/242, 273/272, 343/342

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 210/209, 225/224, 243/242, 273/272, 300/299, 385/384

==== Prism
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 225/224, 243/242, 273/272, 324/323, 385/384

==== Prism 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 225/224, 243/242, 273/272, 300/299, 324/323, 385/384

==== No-19 23-limit
Subgroup: 2.3.5.7.11.13.17.23
Comma list: 225/224, 243/242, 273/272, 300/299, 385/384

=== References


= Schismatic family

=== Schismic, schismatic, a.k.a. helmholtz
Subgroup: 2.3.5
Comma list: 32805/32768
Mapping: {{mapping|legend=1| 1 0 15 | 0 1 -8 }}

==== Overview to extensions

=== Garibaldi
Subgroup: 2.3.5.7
Comma list: 225/224, 3125/3087
Mapping: {{mapping|legend=1| 1 0 15 25 | 0 1 -8 -14 }}

==== Cassandra
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 2200/2187
Mapping: {{mapping| 1 0 15 25 -33 | 0 1 -8 -14 23 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 325/324, 385/384
Mapping: {{mapping| 1 0 15 25 -33 -28 | 0 1 -8 -14 23 20 }}

====== Cassie
Subgroup: 2.3.5.7.11.13.17
Comma list: 120/119, 154/153, 225/224, 273/272, 325/324
Mapping: {{mapping| 1 0 15 25 -33 -28 -7 | 0 1 -8 -14 23 20 7 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 120/119, 154/153, 171/170, 190/189, 225/224, 273/272
Mapping: {{mapping| 1 0 15 25 -33 -28 -7 9 | 0 1 -8 -14 23 20 7 -3 }}

====== Cassandric
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 275/273, 325/324, 375/374, 385/384
Mapping: {{mapping| 1 0 15 25 -33 -28 77 | 0 1 -8 -14 23 20 -46 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 190/189, 209/208, 225/224, 275/273, 325/324, 375/374
Mapping: {{mapping| 1 0 15 25 -33 -28 77 9 | 0 1 -8 -14 23 20 -46 -3 }}

======= 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 190/189, 209/208, 225/224, 253/252, 275/273, 325/324, 375/374
Mapping: {{mapping| 1 0 15 25 -33 -28 77 9 60 | 0 1 -8 -14 23 20 -46 -3 -35 }}

====== Cassander
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 225/224, 275/273, 325/324, 385/384
Mapping: {{mapping| 1 0 15 25 -33 -28 -72 | 0 1 -8 -14 23 20 48 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 170/169, 190/189, 209/208, 225/224, 275/273, 325/324
Mapping: {{mapping| 1 0 15 25 -33 -28 -72 9 | 0 1 -8 -14 23 20 48 -3 }}

==== Andromeda
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 245/242
Mapping: {{mapping| 1 0 15 25 32 | 0 1 -8 -14 -18 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 196/195, 245/242
Mapping: {{mapping| 1 0 15 25 32 37 | 0 1 -8 -14 -18 -21 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 120/119, 189/187, 196/195
Mapping: {{mapping| 1 0 15 25 32 37 -7 | 0 1 -8 -14 -18 -21 7 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 120/119, 133/132, 189/187, 196/195
Mapping: {{mapping| 1 0 15 25 32 37 -7 9 | 0 1 -8 -14 -18 -21 7 -3 }}

====== Schisicosiennic
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 154/153, 170/169, 196/195
Mapping: {{mapping| 1 0 15 25 32 37 58 | 0 1 -8 -14 -18 -21 -34 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 133/132, 154/153, 170/169, 190/189
Mapping: {{mapping| 1 0 15 25 32 37 58 9 | 0 1 -8 -14 -18 -21 -34 -3 }}

====== Schisicosiennoid
Subgroup: 2.3.5.7.11.13.17
Comma list: 85/84, 100/99, 105/104, 119/117, 221/220
Mapping: {{mapping| 1 0 15 25 32 37 12 | 0 1 -8 -14 -18 -21 -5 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 85/84, 100/99, 105/104, 119/117, 133/132, 153/152
Mapping: {{mapping| 1 0 15 25 32 37 12 9 | 0 1 -8 -14 -18 -21 -5 -3 }}

==== Helenus
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 3125/3087
Mapping: {{mapping| 1 0 15 25 51 | 0 1 -8 -14 -30 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 275/273, 847/845
Mapping: {{mapping| 1 0 15 25 51 56 | 0 1 -8 -14 -30 -33 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 99/98, 120/119, 176/175, 275/273, 442/441
Mapping: {{mapping| 1 0 15 25 51 56 -7 | 0 1 -8 -14 -30 -33 7 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 99/98, 120/119, 176/175, 190/189, 209/208, 247/245
Mapping: {{mapping| 1 0 15 25 51 56 -7 9 | 0 1 -8 -14 -30 -33 7 -3 }}

==== Karadeniz
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 3125/3087
Mapping: {{mapping| 1 1 7 11 2 | 0 2 -16 -28 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 325/324, 640/637
Mapping: {{mapping| 1 1 7 11 2 -8 | 0 2 -16 -28 5 40 }}

==== Hemigari
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 3125/3087
Mapping: {{mapping| 1 0 15 25 9 | 0 2 -16 -28 -7 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 225/224, 275/273
Mapping: {{mapping| 1 0 15 25 9 14 | 0 2 -16 -28 -7 -13 }}

==== Sanjaab
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1331/1323, 3125/3087
Mapping: {{mapping| 1 2 -1 -3 0 | 0 -3 24 42 25 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 847/845, 1331/1323
Mapping: {{mapping| 1 2 -1 -3 0 -1 | 0 -3 24 42 25 34 }}

=== Pontiac
Subgroup: 2.3.5.7
Comma list: 4375/4374, 32805/32768
Mapping: {{mapping|legend=1| 1 0 15 -59 | 0 1 -8 39 }}

==== Helenoid
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375, 4375/4374
Mapping: {{mapping| 1 0 15 -59 51 | 0 1 -8 39 -30 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384, 625/624, 729/728
Mapping: {{mapping| 1 0 15 -59 51 56 | 0 1 -8 39 -30 -33 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 385/384, 561/560, 625/624, 729/728
Mapping: {{mapping| 1 0 15 -59 51 56 -91 | 0 1 -8 39 -30 -33 60 }}

===== Helena
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 385/384, 3146/3125
Mapping: {{mapping| 1 0 15 -59 51 -28 | 0 1 -8 39 -30 20 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 273/272, 325/324, 385/384, 3146/3125
Mapping: {{mapping| 1 0 15 -59 51 -28 -91 | 0 1 -8 39 -30 20 60 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 273/272, 286/285, 325/324, 385/384, 627/625
Mapping: {{mapping| 1 0 15 -59 51 -28 -91 9 | 0 1 -8 39 -30 20 60 -3 }}

==== Ponta
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4375/4374, 32805/32768
Mapping: {{mapping| 1 0 15 -59 135 | 0 1 -8 39 -83 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 729/728, 2200/2197
Mapping: {{mapping| 1 0 15 -59 135 56 | 0 1 -8 39 -83 -33 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 375/374, 540/539, 625/624, 729/728, 2200/2197
Mapping: {{mapping| 1 0 15 -59 135 56 -91 | 0 1 -8 39 -83 -33 60 }}

==== Pontic
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4374, 32805/32768
Mapping: {{mapping| 1 0 15 -59 -136 | 0 1 -8 39 88 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 625/624, 729/728, 3584/3575
Mapping: {{mapping| 1 0 15 -59 -136 56 | 0 1 -8 39 88 -33 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 441/440, 595/594, 625/624, 729/728, 2880/2873
Mapping: {{mapping| 1 0 15 -59 -136 56 -91 | 0 1 -8 39 88 -33 60 }}

===== Pontoid
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 4375/4374, 32805/32768
Mapping: {{mapping| 1 0 15 -59 -136 -215 | 0 1 -8 39 88 138 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 1156/1155, 32805/32768
Mapping: {{mapping| 1 0 15 -59 -136 -215 -91 | 0 1 -8 39 88 138 60 }}

==== Bipont
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 32805/32768
Mapping: {{mapping| 2 0 30 -118 -85 | 0 1 -8 39 29 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 729/728, 1575/1573, 4096/4095
Mapping: {{mapping| 2 0 30 -118 -85 112 | 0 1 -8 39 29 -33 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 729/728, 1089/1088, 1225/1224, 2880/2873
Mapping: {{mapping| 2 0 30 -118 -85 112 -182 | 0 1 -8 39 29 -33 60 }}

===== Counterbipont
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3025/3024, 32805/32768
Mapping: {{mapping| 2 0 30 -118 -85 -243 | 0 1 -8 39 29 79 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 936/935, 1089/1088, 1225/1224, 32805/32768
Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 | 0 1 -8 39 29 79 60 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 715/714, 936/935, 1089/1088, 1225/1224, 1540/1539, 4875/4864
Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 -169 | 0 1 -8 39 29 79 60 56 }}

===== Quadrapont
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 4225/4224, 4375/4374, 32805/32768
Mapping: {{mapping| 4 0 60 -236 -170 -131 | 0 1 -8 39 29 23 }}

=== Grackle
Subgroup: 2.3.5.7
Comma list: 126/125, 32805/32768
Mapping: {{mapping|legend=1| 1 0 15 44 | 0 1 -8 -26 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 32805/32768
Mapping: {{mapping| 1 0 15 44 70 | 0 1 -8 -26 -42 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 5445/5408
Mapping: {{mapping| 1 0 15 44 70 75 | 0 1 -8 -26 -42 -45 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 176/175, 196/195, 256/255, 2904/2873
Mapping: {{mapping| 1 0 15 44 70 75 -7 | 0 1 -8 -26 -42 -45 7 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 126/125, 171/170, 176/175, 196/195, 209/208, 324/323
Mapping: {{mapping| 1 0 15 44 70 75 -7 9 | 0 1 -8 -26 -42 -45 7 -3 }}

===== Grackloid
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 729/728, 1287/1280
Mapping: {{mapping| 1 0 15 44 70 -47 | 0 1 -8 -26 -42 32 }}

==== Grack
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 896/891
Mapping: {{mapping| 1 0 15 44 51 | 0 1 -8 -26 -30 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 245/242, 832/825
Mapping: {{mapping| 1 0 15 44 51 75 | 0 1 -8 -26 -30 -45 }}

===== Catahelenic
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 126/125, 245/242, 352/351
Mapping: {{mapping| 1 0 15 44 51 56 | 0 1 -8 -26 -30 -33 }}

=== Quasipyth
Subgroup: 2.3.5.7
Comma list: 32805/32768, 390625/387072
Mapping: {{mapping|legend=1| 1 0 15 109 | 0 1 -8 -67 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 19712/19683, 78125/77616
Mapping: {{mapping| 1 0 15 109 -117 | 0 1 -8 -67 76 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 2200/2197, 19712/19683
Mapping: {{mapping| 1 0 15 109 -117 -28 | 0 1 -8 -67 76 20 }}

=== Schism

=== Bischismic
Subgroup: 2.3.5.7
Comma list: 3136/3125, 32805/32768
Mapping: {{mapping|legend=1| 2 0 30 69 | 0 1 -8 -20 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 8019/8000
Mapping: {{mapping| 2 0 30 69 102 | 0 1 -8 -20 -30 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 729/728, 1001/1000, 3136/3125
Mapping: {{mapping| 2 0 30 69 102 -75 | 0 1 -8 -20 -30 26 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 441/440, 561/560, 729/728, 3136/3125
Mapping: {{mapping| 2 0 30 69 102 -75 5 | 0 1 -8 -20 -30 26 1 }}

===== Bischis
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440, 3136/3125
Mapping: {{mapping| 2 0 30 69 102 131 | 0 1 -8 -20 -30 -39 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 289/288, 351/350, 441/440, 3136/3125
Mapping: {{mapping| 2 0 30 69 102 131 5 | 0 1 -8 -20 -30 -39 1 }}

=== Kleischismic
Subgroup: 2.3.5.7
Comma list: 32805/32768, 1500625/1492992
Mapping: {{mapping|legend=1| 2 1 22 -15 | 0 2 -16 19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 9801/9800, 14641/14580
Mapping: {{mapping| 2 1 22 -15 8 | 0 2 -16 19 -1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384, 729/728, 1575/1573
Mapping: {{mapping| 2 1 22 -15 8 15 | 0 2 -16 19 -1 -7 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 289/288, 352/351, 385/384, 561/560
Mapping: {{mapping| 2 1 22 -15 8 15 6 | 0 2 -16 19 -1 -7 2 }}

===== Kleischis
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 1573/1568, 14641/14580
Mapping: {{mapping| 2 1 22 -15 8 -36 | 0 2 -16 19 -1 40 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 325/324, 385/384, 442/441, 14641/14580
Mapping: {{mapping| 2 1 22 -15 8 -36 6 | 0 2 -16 19 -1 40 2 }}

=== Salsa
Subgroup: 2.3.5.7
Comma list: 245/243, 32805/32768
Mapping: {{mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 245/242, 385/384
Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 243/242, 245/242
Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}

=== Hemischis
Subgroup: 2.3.5.7
Comma list: 6144/6125, 19683/19600
Mapping: {{mapping|legend=1| 1 0 15 -17 | 0 2 -16 25 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625, 8019/8000
Mapping: {{mapping| 1 0 15 -17 51 | 0 2 -16 25 -60 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 4096/4095
Mapping: {{mapping| 1 0 15 -17 51 14 | 0 2 -16 25 -60 -13 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 442/441, 561/560, 676/675, 4096/4095
Mapping: {{mapping| 1 0 15 -17 51 14 -49 | 0 2 -16 25 -60 -13 67 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 351/350, 442/441, 456/455, 561/560, 676/675, 4096/4095
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 | 0 2 -16 25 -60 -13 67 -6 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 351/350, 442/441, 456/455, 561/560, 676/675, 736/735, 4096/4095
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 -24 | 0 2 -16 25 -60 -13 67 -6 36 }}

=== Term
Subgroup: 2.3.5.7
Comma list: 32805/32768, 250047/250000
Mapping: {{mapping|legend=1| 3 0 45 94 | 0 1 -8 -18 }}

==== Terminal
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4356, 32805/32768
Mapping: {{mapping| 3 0 45 94 134 | 0 1 -8 -18 -26 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 625/624, 13720/13689
Mapping: {{mapping| 3 0 45 94 134 168 | 0 1 -8 -18 -26 -33 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 375/374, 441/440, 595/594, 8624/8619
Mapping: {{mapping| 3 0 45 94 134 168 -2 | 0 1 -8 -18 -26 -33 3 }}

==== Terminator
Subgroup: 2.3.5.7.11
Comma list: 540/539, 32805/32768, 137781/137500
Mapping: {{mapping| 3 0 45 94 -137 | 0 1 -8 -18 31 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 4096/4095, 31250/31213
Mapping: {{mapping| 3 0 45 94 -137 -103 | 0 1 -8 -18 31 24 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 540/539, 729/728, 936/935, 1156/1155, 4096/4095
Mapping: {{mapping| 3 0 45 94 -137 -103 -2 | 0 1 -8 -18 31 24 3 }}

==== Semiterm
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 32805/32768, 151263/151250
Mapping: {{mapping| 6 0 90 188 287 | 0 1 -8 -18 -28 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 32805/32768, 34398/34375
Mapping: {{mapping| 6 0 90 188 287 355 | 0 1 -8 -18 -28 -35 }}

==== Hemiterm
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 32805/32768, 102487/102400
Mapping: {{mapping| 3 0 45 94 8 | 0 2 -16 -36 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 19773/19712
Mapping: {{mapping| 3 0 45 94 8 42 | 0 2 -16 -36 1 -13 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 936/935, 1001/1000, 11271/11264
Mapping: {{mapping| 3 0 45 94 8 42 -2 | 0 2 -16 -36 1 -13 6 }}

=== Altinex
Subgroup: 2.3.5.7
Comma list: 32805/32768, 367653125/362797056
Mapping: {{mapping|legend=1| 3 0 45 -32 | 0 2 -16 17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 14700/14641, 19712/19683
Mapping: {{mapping| 3 0 45 -32 8 | 0 2 -16 17 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 385/384, 676/675, 19712/19683
Mapping: {{mapping| 3 0 45 -32 8 42 | 0 2 -16 17 1 -13 }}

=== Squirrel
Subgroup: 2.3.5.7
Comma list: 686/675, 32805/32768
Mapping: {{mapping|legend=1| 1 2 -1 1 | 0 -3 24 13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/242, 686/675, 896/891
Mapping: {{mapping| 1 2 -1 1 0 | 0 -3 24 13 25 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 169/168, 245/242, 896/891
Mapping: {{mapping| 1 2 -1 1 0 3 | 0 -3 24 13 25 5 }}

=== Tertiaschis
Subgroup: 2.3.5.7
Comma list: 32805/32768, 1071875/1062882
Mapping: {{mapping|legend=1| 1 2 -1 10 | 0 -3 24 -52 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 4000/3993, 19712/19683
Mapping: {{mapping| 1 2 -1 10 0 | 0 -3 24 -52 25 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 1575/1573, 10985/10976
Mapping: {{mapping| 1 2 -1 10 0 12 | 0 -3 24 -52 25 -60 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976
Mapping: {{mapping| 1 2 -1 10 0 12 -2 | 0 -3 24 -52 25 -60 44 }}

=== Countertertiaschis
Subgroup: 2.3.5.7
Comma list: 32805/32768, 244140625/243045684
Mapping: {{mapping|legend=1| 1 2 -1 -12 | 0 -3 24 107 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 32805/32768
Mapping: {{mapping| 1 2 -1 -12 0 | 0 -3 24 107 25 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 10985/10976
Mapping: {{mapping| 1 2 -1 -12 0 -10 | 0 -3 24 107 25 99 }}

=== Quadrant
Subgroup: 2.3.5.7
Comma list: 32805/32768, 390625/388962
Mapping: {{mapping|legend=1| 4 0 60 119 | 0 1 -8 -17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 6250/6237, 32805/32768
Mapping: {{mapping| 4 0 60 119 185 | 0 1 -8 -17 -27 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1375/1372, 2080/2079, 10648/10647
Mapping: {{mapping| 4 0 60 119 185 224 | 0 1 -8 -17 -27 -33 }}

=== Sesquiquartififths
Subgroup: 2.3.5.7
Comma list: 2401/2400, 32805/32768
Mapping: {{mapping|legend=1| 1 1 7 5 | 0 4 -32 -15 }}

==== Sesquart
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 16384/16335
Mapping: {{mapping| 1 1 7 5 2 | 0 4 -32 -15 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440, 3584/3575
Mapping: {{mapping| 1 1 7 5 2 -2 | 0 4 -32 -15 10 39 }}

====== Heartia
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 256/255, 273/272, 364/363, 441/440
Mapping: {{mapping| 1 1 7 5 2 -2 0 | 0 4 -32 -15 10 39 28 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 171/170, 243/242, 256/255, 273/272, 324/323, 441/440
Mapping: {{mapping| 1 1 7 5 2 -2 0 6 | 0 4 -32 -15 10 39 28 -12 }}

====== Sesquartia
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 441/440, 595/594, 3584/3575
Mapping: {{mapping| 1 1 7 5 2 -2 -6 | 0 4 -32 -15 10 39 69 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 243/242, 361/360, 364/363, 441/440, 456/455, 595/594
Mapping: {{mapping| 1 1 7 5 2 -2 -6 6 | 0 4 -32 -15 10 39 69 -12 }}

======= 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 243/242, 323/322, 361/360, 364/363, 441/440, 456/455, 595/594
Mapping: {{mapping| 1 1 7 5 2 -2 -6 6 -6 | 0 4 -32 -15 10 39 69 -12 72 }}

====== Hearty
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 243/242, 364/363, 441/440, 1632/1625
Mapping: {{mapping| 1 1 7 5 2 -2 13 | 0 4 -32 -15 10 39 -61 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 221/220, 243/242, 361/360, 364/363, 441/440, 456/455
Mapping: {{mapping| 1 1 7 5 2 -2 13 6 | 0 4 -32 -15 10 39 -61 -12 }}

======= 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 221/220, 243/242, 276/275, 323/322, 361/360, 364/363, 441/440
Mapping: {{mapping| 1 1 7 5 2 -2 13 6 13 | 0 4 -32 -15 10 39 -61 -12 -58 }}

==== Bisesqui
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 32805/32768
Mapping: {{mapping| 2 2 14 10 23 | 0 4 -32 -15 -55 }}

=== Tsaharuk
Subgroup: 2.3.5.7
Comma list: 32805/32768, 420175/419904
Mapping: {{mapping|legend=1| 1 1 7 0 | 0 5 -40 24 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1331/1323, 19712/19683
Mapping: {{mapping| 1 1 7 0 1 | 0 5 -40 24 21 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384, 729/728, 1331/1323
Mapping: {{mapping| 1 1 7 0 1 3 | 0 5 -40 24 21 6 }}

=== Quanharuk
Subgroup: 2.3.5.7
Comma list: 16875/16807, 32805/32768
Mapping: {{mapping|legend=1| 1 0 15 12 | 0 5 -40 -29 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 32805/32768
Mapping: {{mapping| 1 0 15 12 -7 | 0 5 -40 -29 33 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372, 4096/4095
Mapping: {{mapping| 1 0 15 12 -7 -15 | 0 5 -40 -29 33 59 }}

=== Quintilipyth
Subgroup: 2.3.5.7
Comma list: 32805/32768, 9765625/9680832
Mapping: {{mapping|legend=1| 1 2 -1 -4 | 0 -5 40 82 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4375/4356, 32805/32768
Mapping: {{mapping| 1 2 -1 -4 -7 | 0 -5 40 82 126 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1375/1372, 2080/2079, 4375/4356, 10648/10647
Mapping: {{mapping| 1 2 -1 -4 -7 -9 | 0 -5 40 82 126 153 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 375/374, 595/594, 833/832, 1375/1372, 8624/8619
Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 | 0 -5 40 82 126 153 -11 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 375/374, 400/399, 495/494, 595/594, 1375/1372, 3978/3971
Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 4 | 0 -5 40 82 126 153 -11 3 }}

=== Quintaschis
Subgroup: 2.3.5.7
Comma list: 32805/32768, 49009212/48828125
Mapping: {{mapping|legend=1| 1 2 -1 -5 | 0 -5 40 94 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 32805/32768, 1953125/1951488
Mapping: {{mapping| 1 2 -1 -5 -8 | 0 -5 40 94 138 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 32805/32768, 109512/109375
Mapping: {{mapping| 1 2 -1 -5 -8 -11 | 0 -5 40 94 138 177 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 3757/3750, 32805/32768
Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 | 0 -5 40 94 138 177 -11 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 364/363, 441/440, 476/475, 595/594, 3757/3750, 6885/6859
Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 4 | 0 -5 40 94 138 177 -11 3 }}

==== Quintahelenic
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 8019/8000, 151263/151250
Mapping: {{mapping| 1 2 -1 -5 -9 | 0 -5 40 94 150 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 847/845, 1716/1715, 5632/5625, 8019/8000
Mapping: {{mapping| 1 2 -1 -5 -9 -11 | 0 -5 40 94 150 177 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 561/560, 833/832, 847/845, 1701/1700, 3757/3750
Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 | 0 -5 40 94 150 177 -11 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 476/475, 495/494, 561/560, 833/832, 847/845, 1701/1700
Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 4 | 0 -5 40 94 150 177 -11 3 }}

===== Quintahelenoid
Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 1001/1000, 4096/4095, 86515/86436
Mapping: {{mapping| 1 2 -1 -5 -9 14 | 0 -5 40 94 150 -124 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 561/560, 729/728, 1001/1000, 4096/4095, 14161/14157
Mapping: {{mapping| 1 2 -1 -5 -9 14 5 | 0 -5 40 94 150 -124 -11 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 476/475, 561/560, 729/728, 1001/1000, 4096/4095, 6144/6137
Mapping: {{mapping| 1 2 -1 -5 -9 14 5 4 | 0 -5 40 94 150 -124 -11 3 }}

=== Sextilifourths
Subgroup: 2.3.5.7
Comma list: 32805/32768, 235298/234375
Mapping: {{mapping|legend=1| 1 2 -1 -1 | 0 -6 48 55 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4000/3993, 235298/234375
Mapping: {{mapping| 1 2 -1 -1 0 | 0 -6 48 55 50 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 676/675, 10985/10976
Mapping: {{mapping| 1 2 -1 -1 0 1 | 0 -6 48 55 50 39 }}

=== Septant
Subgroup: 2.3.5.7
Comma list: 32805/32768, 516560652/514714375
Mapping: {{mapping|legend=1| 7 0 105 -56 | 0 1 -8 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 24057/24010, 32805/32768
Mapping: {{mapping| 7 0 105 -56 -120 | 0 1 -8 7 13 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 1716/1715, 2200/2197, 3025/3024
Mapping: {{mapping| 7 0 105 -56 -120 37 | 0 1 -8 7 13 -1 }}

=== Octant
Subgroup: 2.3.5.7
Comma list: 32805/32768, 2259436291848/2251875390625
Mapping: {{mapping|legend=1| 8 0 120 -117 | 0 1 -8 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 32805/32768, 46656/46585
Mapping: {{mapping| 8 0 120 -117 15 | 0 1 -8 11 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655
Mapping: {{mapping| 8 0 120 -117 15 93 | 0 1 -8 11 1 -5 }}

=== Nonant
Subgroup: 2.3.5.7
Comma list: 32805/32768, 40353607/40310784
Mapping: {{mapping|legend=1| 9 0 135 11 | 0 1 -8 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 32805/32768, 42875/42592
Mapping: {{mapping| 9 0 135 11 131 | 0 1 -8 1 -7 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 4096/4095, 16807/16731
Mapping: {{mapping| 9 0 135 11 131 -38 | 0 1 -8 1 -7 5 }}

=== Septiquarschis
Subgroup: 2.3.5.7
Comma list: 32805/32768, 829440/823543
Mapping: {{mapping|legend=1| 1 -4 47 6 | 0 7 56 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 15488/15435, 32805/32768
Mapping: {{mapping| 1 -4 47 6 25 | 0 7 56 -4 -27 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1573/1568, 4096/4095
Mapping: {{mapping| 1 -4 47 6 25 -33 | 0 7 56 -4 -27 46 }}

=== Tridecafifths
Subgroup: 2.3.5.7
Comma list: 32805/32768, {{monzo| -14 -1 -9 13 }}
Mapping: {{mapping|legend=1| 1 1 7 6 | 0 13 -104 -71 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 32805/32768, 55296000/55240493
Mapping: {{mapping| 1 1 7 6 4 | 0 13 -104 -71 -12 }}

=== Subgroup extensions

==== Maqamschismic (2.3.5.11)
Subgroup: 2.3.5.11
Comma list: 2200/2187, 4125/4096
Mapping: {{mapping| 1 0 15 -33 | 0 1 -8 23 }}

===== 2.3.5.11.13 subgroup
Subgroup: 2.3.5.11.13
Comma list: 325/324, 352/351, 4125/4096
Mapping: {{mapping| 1 0 15 -33 -28 | 0 1 -8 23 20 }}

==== Tridecaschismic (2.3.5.13)
Subgroup: 2.3.5.13
Comma list: 325/324, 32805/32768
Mapping: {{mapping| 1 0 15 -28 | 0 1 -8 20 }}

===== 2.3.5.13.19 subgroup
Subgroup: 2.3.5.13.19
Comma list: 325/324, 361/360, 513/512
Mapping: {{mapping| 1 0 15 -28 9 | 0 1 -8 20 -3 }}

==== Photia (2.3.5.17)
Subgroup: 2.3.5.17
Comma list: 256/255, 1458/1445
Mapping: {{mapping|legend=2| 1 0 15 -7 | 0 1 -8 7 }}
Mapping: {{mapping|legend=3| 1 0 15 0 0 0 -7 | 0 1 -8 0 0 0 7 }}

===== 2.3.5.17.19 subgroup
Subgroup: 2.3.5.17.19
Comma list: 171/170, 256/255, 324/323
Mapping: {{mapping| 1 0 15 -7 9 | 0 1 -8 7 -3 }}

==== Nestoria (2.3.5.19)
Subgroup: 2.3.5.19
Comma list: 361/360, 513/512
Mapping: {{mapping|legend=2| 1 0 15 9 | 0 1 -8 -3 }}
Mapping: {{mapping|legend=3| 1 0 15 0 0 0 0 9 | 0 1 -8 0 0 0 0 -3 }}

==== Taylor (2.3.5.13)
Subgroup: 2.3.5.13
Comma list: 676/675, 32805/32768
Mapping: {{mapping|legend=2| 1 0 15 14 | 0 2 -16 -13 }}
Mapping: {{mapping|legend=3| 1 0 15 0 0 14 | 0 2 -16 0 0 -13 }}

===== Dakota (2.3.5.13.19)
Subgroup: 2.3.5.13.19
Comma list: 361/360, 513/512, 676/675
Mapping: {{mapping| 1 0 15 14 9 | 0 2 -16 -13 -6 }}

====== 2.3.5.13.19.37 subgroup
Subgroup: 2.3.5.13.19.37
Comma list: 361/360, 481/480, 513/512, 676/675
Mapping: {{mapping| 1 0 15 14 9 6 | 0 2 -16 -13 -6 -1 }}

==== Quintilischis (2.3.5.17)
Subgroup: 2.3.5.17
Comma list: 32805/32768, 1419857/1417176
Mapping: {{mapping|legend=2| 1 2 -1 5 | 0 -5 40 -11 }}
Mapping: {{mapping|legend=3| 1 2 -1 0 0 0 5 | 0 -5 40 0 0 0 -11 }}

===== 2.3.5.17.19 subgroup
Subgroup: 2.3.5.17.19
Comma list: 4624/4617, 6144/6137, 6885/6859
Mapping: {{mapping| 1 2 -1 5 4 | 0 -5 40 -11 3 }}


= Semicomma family

=== Orson
Subgroup: 2.3.5
Comma list: 2109375/2097152
Mapping: {{mapping|legend=1| 1 0 3 | 0 7 -3 }}

==== Overview to extensions

=== Orwell
Subgroup: 2.3.5.7
Comma list: 225/224, 1728/1715
Mapping: {{mapping|legend=1| 1 0 3 1 | 0 7 -3 8 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 176/175
Mapping: {{mapping| 1 0 3 1 3 | 0 7 -3 8 2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 176/175, 275/273
Mapping: {{mapping| 1 0 3 1 3 8 | 0 7 -3 8 2 -19 }}

===== Blair
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 78/77, 91/90, 99/98
Mapping: {{mapping| 1 0 3 1 3 3 | 0 7 -3 8 2 3 }}

===== Winston
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 99/98, 105/104, 121/120
Mapping: {{mapping| 1 0 3 1 3 1 | 0 7 -3 8 2 12 }}

===== Doublethink
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 169/168, 176/175
Mapping: {{mapping| 1 0 3 1 3 2 | 0 14 -6 16 4 15 }}

==== Newspeak
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 1728/1715
Mapping: {{mapping| 1 0 3 1 -4 | 0 7 -3 8 33 }}

==== Borwell
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 1728/1715
Mapping: {{mapping| 1 -7 6 -7 -18 | 0 14 -6 16 35 }}

=== Sabric
Subgroup: 2.3.5.7
Comma list: 4375/4374, 2109375/2097152
Mapping: {{mapping|legend=1| 1 0 3 -11 | 0 7 -3 61 }}

=== Triwell
Subgroup: 2.3.5.7
Comma list: 1029/1024, 235298/234375
Mapping: {{mapping|legend=1| 1 -14 9 8 | 0 21 -9 -7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 456533/455625
Mapping: {{mapping| 1 -14 9 8 -24 | 0 21 -9 -7 37 }}

=== Quadrawell
Subgroup: 2.3.5.7
Comma list: 2401/2400, 2109375/2097152
Mapping: {{mapping|legend=1| 1 -21 12 2 | 0 28 -12 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 14641/14580
Mapping: {{mapping| 1 -21 12 2 -28 | 0 28 -12 1 39 }}

=== Rainwell
Subgroup: 2.3.5.7
Comma list: 16875/16807, 2100875/2097152
Mapping: {{mapping|legend=1| 1 -21 12 -3 | 0 35 -15 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 2100875/2097152
Mapping: {{mapping| 1 -21 12 -3 -43 | 0 35 -15 9 72 }}

=== Quinwell
Subgroup: 2.3.5.7
Comma list: 420175/419904, 2109375/2097152
Mapping: {{mapping|legend=1| 1 0 3 0 | 0 35 -15 62 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4375/4356, 2109375/2097152
Mapping: {{mapping| 1 0 3 0 5 | 0 35 -15 62 -34 }}

==== Quinbetter
Subgroup: 2.3.5.7.11
Comma list: 385/384, 24057/24010, 43923/43750
Mapping: {{mapping| 1 0 3 0 4 | 0 35 -15 62 -12 }}


= Semaphoresmic family

=== Semaphoresmic a.k.a. semiphore
Subgroup: 2.3.5.7
Comma list: 49/48
Mapping: {{mapping|legend=1| 1 0 2 2 | 0 2 0 1 | 0 0 1 0 }}

==== 2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: 49/48, 91/90

=== Selenium
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55
Mapping: {{mapping|legend=1| 1 0 2 2 5 | 0 2 0 1 1 | 0 0 1 0 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 91/90
Mapping: {{mapping| 1 0 2 2 5 -1 | 0 2 0 1 1 3 | 0 0 1 0 -1 1 }}

=== Negric
Subgroup: 2.3.5.7.11
Comma list: 49/48, 225/224
Mapping: {{mapping|legend=1| 1 2 2 3 0 | 0 -4 3 -2 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90
Mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 | 0 0 0 0 1 0 }}


= Sengic family

=== Sengic
Subgroup: 2.3.5.7
Comma list: [[686/675]]
Mapping: {{mapping|legend=1| 1 0 2 1 | 0 1 0 1 | 0 0 3 2 }}

==== Overview to extensions

==== 2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: 91/90, 169/168
Mapping: {{mapping| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 1 }}

=== Demeter
Subgroup: 2.3.5.7.11
Comma list: 441/440, 686/675
Mapping: {{mapping|legend=1| 1 0 2 1 -3 | 0 1 0 1 4 | 0 0 3 2 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 169/168, 352/351
Mapping: {{mapping| 1 0 2 1 -3 2 | 0 1 0 1 4 1 | 0 0 3 2 1 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 136/135, 154/153, 169/168
Mapping: {{mapping| 1 0 2 1 -3 2 -1 | 0 1 0 1 4 1 3 | 0 0 3 2 1 1 3 }}

=== Krypton
Subgroup: 2.3.5.7.11
Comma list: 56/55, 540/539
Mapping: {{mapping|legend=1| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90
Mapping: {{mapping| 1 0 2 1 2 2 | 0 1 0 1 1 1 | 0 0 3 2 -1 1 }}

=== Sensigh
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/243
Mapping: {{mapping|legend=1| 1 -1 -1 -2 3 | 0 7 9 13 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168
Mapping: {{mapping| 1 -1 -1 -2 3 0 | 0 7 9 13 0 10 | 0 0 0 0 1 0 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 154/153, 169/168
Mapping: {{mapping| 1 -1 -1 -2 3 0 4 | 0 7 9 13 0 10 -1 | 0 0 0 0 1 0 1 }}

=== References


= Sensamagic clan

=== BPS
Subgroup: 3.5.7
Comma list: 245/243
Mapping: {{mapping|legend=2| 1 1 2 | 0 2 -1 }}

==== Overview to extensions

=== Bohpier
Subgroup: 2.3.5.7
Comma list: 245/243, 3125/3087
Mapping: {{mapping|legend=1| 1 0 0 0 | 0 13 19 23 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243, 1344/1331
Mapping: {{mapping| 1 0 0 0 2 | 0 13 19 23 12 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 196/195, 275/273
Mapping: {{mapping| 1 0 0 0 2 2 | 0 13 19 23 12 14 }}

==== Triboh
Subgroup: 2.3.5.7.11
Comma list: 245/243, 1331/1323, 3125/3087
Mapping: {{mapping| 1 0 0 0 0 | 0 39 57 69 85 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 245/243, 275/273, 847/845, 1331/1323
Mapping: {{mapping| 1 0 0 0 0 0 | 0 39 57 69 85 91 }}

=== Pycnic
Subgroup: 2.3.5.7
Comma list: 245/243, 525/512
Mapping: {{mapping|legend=1| 1 0 6 -3 | 0 3 -7 11 }}

=== Xenia
Subgroup: 2.3.5.7
Comma list: 245/243, 1029/1000
Mapping: {{mapping|legend=1| 1 -6 -12 -9 | 0 9 17 14 }}

=== Magus
Subgroup: 2.3.5.7
Comma list: 245/243, 28672/28125
Mapping: {{mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 245/243, 1331/1323
Mapping: {{mapping| 1 -2 2 -6 -6 | 0 11 1 27 29 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 176/175, 245/243, 1331/1323
Mapping: {{mapping| 1 -2 2 -6 -6 5 | 0 11 1 27 29 -4 }}

=== Superenneadecal
Subgroup: 2.3.5.7
Comma list: 245/243, 395136/390625
Mapping: {{mapping|legend=1| 19 0 14 -7 | 0 1 1 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 2560/2541, 3773/3750
Mapping: {{mapping| 19 0 14 -7 96 | 0 1 1 2 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 832/825, 1001/1000
Mapping: {{mapping| 19 0 14 -7 96 10 | 0 1 1 2 -1 2 }}

=== Superthird
Subgroup: 2.3.5.7
Comma list: 245/243, 78125/76832
Mapping: {{mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243, 78125/76832
Mapping: {{mapping| 1 -5 -5 -10 2 | 0 18 20 35 4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 196/195, 1375/1352
Mapping: {{mapping| 1 -5 -5 -10 2 -8 | 0 18 20 35 4 32 }}

=== Leapweek
Subgroup: 2.3.5.7
Comma list: 245/243, 2097152/2066715
Mapping: {{mapping|legend=1| 1 0 42 -21 | 0 1 -25 15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 1331/1323
Mapping: {{mapping| 1 0 42 -21 -14 | 0 1 -25 15 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 245/243, 352/351, 364/363
Mapping: {{mapping| 1 0 42 -21 -14 -9 | 0 1 -25 15 11 8 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 154/153, 169/168, 245/243, 256/255, 273/272
Mapping: {{mapping| 1 0 42 -21 -14 -9 -34 | 0 1 -25 15 11 8 24 }}

===== Leapweeker
Subgroup: 2.3.5.7.11.13.17
Comma list: 136/135, 169/168, 221/220, 245/243, 364/363
Mapping: {{mapping| 1 0 42 -21 -14 -9 39 | 0 1 -25 15 11 8 -22 }}


= Sensamagic family

=== Sensamagic
Subgroup: 2.3.5.7
Comma list: 245/243
Mapping: {{mapping|legend=1| 1 0 0 0 | 0 1 1 2 | 0 0 2 -1 }}
Mapping to lattice: [{{val| 0 1 1 2 }}, {{val| 0 0 2 -1 }}]

==== Overview to extensions

=== Undecimal sensamagic
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384
Mapping: {{mapping|legend=1| 1 0 0 0 7 | 0 1 1 2 -2 | 0 0 2 -1 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 245/243, 352/351, 364/363
Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}

=== Sensawer
Subgroup: 2.3.5.7.11
Comma list: 245/243, 441/440
Mapping: {{mapping|legend=1| 1 0 0 0 -3 | 0 1 1 2 5 | 0 0 2 -1 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 352/351
Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }}

=== Octarod
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243
Mapping: {{mapping|legend=1| 1 0 0 0 2 | 0 1 1 2 0 | 0 0 2 -1 4 }}

=== Shrusus
Subgroup: 2.3.5.7.11
Comma list: 176/175, 245/243
Mapping: {{mapping|legend=1| 1 0 0 0 -4 | 0 1 1 2 4 | 0 0 2 -1 3 }}

==== Shrusic
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 176/175, 245/243
Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }}

=== Bisector
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243
Mapping: {{mapping|legend=1| 2 0 0 0 3 | 0 1 1 2 1 | 0 0 2 -1 1 }}


= Sensipent family

=== Sensipent
Subgroup: 2.3.5
Comma list: 78732/78125
Mapping: {{mapping|legend=1| 1 -1 -1 | 0 7 9 }}

==== Overview to extensions

==== Sensible
Subgroup: 2.3.5.11
Comma list: 8019/8000, 16384/16335
Mapping: {{mapping| 1 -1 -1 9 | 0 7 9 -15 }}

===== 2.3.5.11.17 subgroup
Subgroup: 2.3.5.11.17
Comma list: 256/255, 1089/1088, 1377/1375
Mapping: {{mapping| 1 -1 -1 9 10 | 0 7 9 -15 -16 }}

===== 2.3.5.11.17.23 subgroup
Subgroup: 2.3.5.11.17.23
Comma list: 256/255, 576/575, 1089/1088, 1377/1375
Mapping: {{mapping| 1 -1 -1 9 10 6 | 0 7 9 -15 -16 -4 }}

===== 2.3.5.11.17.23.31 subgroup
Subgroup: 2.3.5.11.17.23.31
Comma list: 256/255, 576/575, 961/960, 1089/1088, 1377/1375
Mapping: {{mapping| 1 -1 -1 9 10 6 2 | 0 7 9 -15 -16 -4 8 }}

=== Sensi

==== Septimal sensi
Subgroup: 2.3.5.7
Comma list: 126/125, 245/243
Mapping: {{mapping|legend=1| 1-1 -1 -2 | 0 7 9 13 }}

===== 2.3.5.7.13 subgroup (sensation)
Subgroup: 2.3.5.7.13
Comma list: 91/90, 126/125, 169/168
Mapping: {{mapping| 1 -1 -1 -2 0| 0 7 9 13 10 }}

==== Sensor
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/243, 385/384
Mapping: {{mapping| 1 -1 -1 -2 9 | 0 7 9 13 -15 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 385/384
Mapping: {{mapping| 1 -1 -1 -2 9 0 | 0 7 9 13 -15 10 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255
Mapping: {{mapping| 1 -1 -1 -2 9 0 10 | 0 7 9 13 -15 10 -16 }}

==== Sensus
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 245/243
Mapping: {{mapping| 1 -1 -1 -2 -8| 0 7 9 13 31 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 352/351
Mapping: {{mapping| 1 -1 -1 -2 -8 0 | 0 7 9 13 31 10 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168
Mapping: {{mapping| 1 -1 -1 -2 -8 0 -7 | 0 7 9 13 31 10 30 }}

==== Sensis
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: {{mapping| 1 -1 -1 -2 2| 0 7 9 13 4 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 -1 -1 -2 2 0 | 0 7 9 13 4 10 }}

==== Sensa
Subgroup: 2.3.5.7.11
Comma list: 55/54, 77/75, 99/98
Mapping: {{mapping| 1 -1 -1 -2 -1| 0 7 9 13 12 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 66/65, 77/75, 143/140
Mapping: {{mapping| 1 -1 -1 -2 -1 0 | 0 7 9 13 12 10}}

==== Bisensi
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 245/243
Mapping: {{mapping| 2 -2 -2 -4 1 | 0 7 9 13 8 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 126/125, 169/168
Mapping: {{mapping| 2 -2 -2 -4 1 0 | 0 7 9 13 8 10 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 121/120, 126/125, 154/153, 169/168
Mapping: {{mapping| 2 -2 -2 -4 1 0 3 | 0 7 9 13 8 10 7 }}

==== Hemisensi
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 245/242
Mapping: {{mapping| 1 -1 -1 -2 -3 | 0 14 18 26 35 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 243/242
Mapping: {{mapping| 1 -1 -1 -2 -3 0 | 0 14 18 26 35 20 }}

=== Sensei
Subgroup: 2.3.5.7
Comma list: 225/224, 78732/78125
Mapping: {{mapping|legend=1| 1 -1 -1 -9 | 0 7 9 32 }}

=== Warrior
Subgroup: 2.3.5.7
Comma list: 5120/5103, 78732/78125
Mapping: {{mapping|legend=1| 1 -1 -1 15 | 0 7 9 -33 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 5120/5103
Mapping: {{mapping| 1 -1 -1 15 9 | 0 7 9 -33 -15 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 847/845, 1331/1323
Mapping: {{mapping| 1 -1 -1 15 9 17 | 0 7 9 -33 -15 -36 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 351/350, 442/441, 715/714
Mapping: {{mapping| 1 -1 -1 15 9 17 10 | 0 7 9 -33 -15 -36 -16 }}

=== Bison
Subgroup: 2.3.5.7
Comma list: 6144/6125, 78732/78125
Mapping: {{mapping|legend=1| 2 -2 -2 13 | 0 7 9 -10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 8019/8000
Mapping: {{mapping| 2 -2 -2 13 18 | 0 7 9 -10 -15 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440, 10985/10976
Mapping: {{mapping| 2 -2 -2 13 18 17 | 0 7 9 -10 -15 -13 }}

=== Subpental
Subgroup: 2.3.5.7
Comma list: 3136/3125, 19683/19600
Mapping: {{mapping|legend=1| 1 -8 -10 -28 | 0 14 18 45 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3136/3125, 8019/8000
Mapping: {{mapping| 1 -8 -10 -28 24 | 0 14 18 45 -30 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 3136/3125
Mapping: {{mapping| 1 -8 -10 -28 24 -23 | 0 14 18 45 -30 39 }}

=== Heinz
Subgroup: 2.3.5.7
Comma list: 1029/1024, 78732/78125
Mapping: {{mapping|legend=1| 1 -8 -10 6 | 0 21 27 -7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 78732/78125
Mapping: {{mapping| 1 -8 -10 6 3 | 0 21 27 -7 1}}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440, 847/845
Mapping: {{mapping| 1 -8 -10 6 3 11 | 0 21 27 -7 1 -16}}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
Mapping: {{mapping| 1 -8 -10 6 3 11 5 | 0 21 27 -7 1 -16 -2}}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968
Mapping: {{mapping| 1 -8 -10 6 3 11 5 12 | 0 21 27 -7 1 -16 -2 -17 }}

=== Trisensory
Subgroup: 2.3.5.7
Comma list: 1728/1715, 78732/78125
Mapping: {{mapping|legend=1| 3 4 6 8 | 0 7 9 4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 78732/78125
Mapping: {{mapping| 3 4 6 8 8 | 0 7 9 4 22 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539, 9295/9261
Mapping: {{mapping| 3 4 6 8 8 11 | 0 7 9 4 22 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 351/350, 442/441, 540/539, 715/714
Mapping: {{mapping| 3 4 6 8 8 11 10 | 0 7 9 4 22 1 21 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 286/285, 324/323, 351/350, 400/399, 476/475
Mapping: {{mapping| 3 4 6 8 8 11 10 12 | 0 7 9 4 22 1 21 7 }}

=== Other subgroup extensions

==== Sensipent (2.3.5.31 subgroup)
Subgroup: 2.3.5.31
Comma list: 961/960, 2511/2500
Mapping: {{mapping| 1 -1 -1 2 | 0 7 9 8 }}

==== Sendai
Subgroup: 2.3.5.23.29.31
Comma list: 465/464, 576/575, 621/620, 900/899
Mapping: {{mapping| 1 -1 -1 6 -4 2| 0 7 9 -4 24 8 }}


= Septisemi temperaments

=== Fluorine
Subgroup: 2.3.5.7
Comma list: 21/20, 243/224
Mapping: {{mapping|legend=1| 1 0 -7 -5 | 0 1 6 5 }}

=== Sodium
Subgroup: 2.3.5.7
Comma list: 21/20, 54/49
Mapping: {{mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}


= Semaphoresmic clan

=== Semaphore
Subgroup: 2.3.7
Comma list: 49/48
Mapping: {{mapping|legend=2| 1 0 2 | 0 2 1 }}
Mapping: {{mapping|legend=3| 1 0 0 2 | 0 2 0 1 }}

==== Overview to extensions

==== Semaerophore
Subgroup: 2.3.7.11
Comma list: 49/48, 729/704
Mapping: {{mapping| 1 0 2 -6 | 0 2 1 12 }}

===== 2.3.7.11.19 subgroup
Subgroup: 2.3.7.11.19
Comma list: 49/48, 77/76, 729/704
Mapping: {{mapping| 1 0 2 -6 -6 | 0 2 1 12 13 }}

=== Godzilla

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 49/48, 81/80
Mapping: {{mapping|legend=1| 1 0 -4 2 | 0 2 8 1 }}

===== 2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 81/80, 91/90
Mapping: {{mapping| 1 0 -4 2 -5 | 0 2 8 1 11 }}

==== Undecimal godzilla
Subgroup: 2.3.5.7.11
Comma list: 45/44, 49/48, 81/80
Mapping: {{mapping| 1 0 -4 2 -6 | 0 2 8 1 12 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 49/48, 78/77, 81/80
Mapping: {{mapping| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}

==== Semafour
Subgroup: 2.3.5.7.11
Comma list: 33/32, 49/48, 55/54
Mapping: {{mapping| 1 0 -4 2 5 | 0 2 8 1 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 33/32, 49/48, 55/54, 91/90
Mapping: {{mapping| 1 0 -4 2 5 -5 | 0 2 8 1 -2 11 }}

==== Varan
Subgroup: 2.3.5.7.11
Comma list: 49/48, 77/75, 81/80
Mapping: {{mapping| 1 0 -4 2 -10 | 0 2 8 1 17 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 77/75, 81/80
Mapping: {{mapping| 1 0 -4 2 -10 -5 | 0 2 8 1 17 11 }}

==== Baragon
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 81/80
Mapping: {{mapping| 1 0 -4 2 9 | 0 2 8 1 -7 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 81/80, 91/90
Mapping: {{mapping| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}

=== Helayo
Subgroup: 2.3.5.7
Comma list: 49/48, 3645/3584
Mapping: {{mapping|legend=1| 1 0 11 2 | 0 2 -11 1 }}

=== Superpelog
Subgroup: 2.3.5.7
Comma list: 49/48, 135/128
Mapping: {{mapping|legend=1| 1 0 7 2 | 0 2 -6 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 49/48
Mapping: {{mapping| 1 0 7 2 5 | 0 2 -6 1 -2 }}

=== Baba
Subgroup: 2.3.5.7
Comma list: 16/15, 49/45
Mapping: {{mapping|legend=1| 1 0 4 2 | 0 2 -2 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 49/45
Mapping: {{mapping| 1 0 4 2 1 | 0 2 -2 1 3 }}

=== Negri

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 49/48, 225/224
Mapping: {{mapping|legend=1| 1 2 2 3 | 0 -4 3 -2 }}

===== 2.3.5.7.13 subgroup (negra)
Subgroup: 2.3.5.7.13
Comma list: 49/48, 65/64, 91/90
Mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -3 }}

==== Undecimal negri
Subgroup: 2.3.5.7.11
Comma list: 45/44, 49/48, 56/55
Mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 49/48, 56/55, 78/77
Mapping: {{mapping| 1 2 2 3 4 4 | 0 -4 3 -2 -5 -3 }}

==== Negril
Subgroup: 2.3.5.7.11
Comma list: 49/48, 100/99, 225/224
Mapping: {{mapping| 1 2 2 3 2 | 0 -4 3 -2 14 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90, 875/858
Mapping: {{mapping| 1 2 2 3 2 4 | 0 -4 3 -2 14 -3 }}

==== Negric
Subgroup: 2.3.5.7.11
Comma list: 33/32, 49/48, 77/75
Mapping: {{mapping| 1 2 2 3 3 | 0 -4 3 -2 4 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 33/32, 49/48, 65/64, 91/90
Mapping: {{mapping| 1 2 2 3 3 4 | 0 -4 3 -2 4 -3 }}

==== Negroni
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 225/224
Mapping: {{mapping| 1 2 2 3 5 | 0 -4 3 -2 -15 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 65/64, 91/90
Mapping: {{mapping| 1 2 2 3 5 4 | 0 -4 3 -2 -15 -3 }}

==== Wilsec
Subgroup: 2.3.5.7.11
Comma list: 49/48, 121/120, 225/224
Mapping: {{mapping| 1 -2 5 1 3 | 0 8 -6 4 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90, 121/120
Mapping: {{mapping| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
Mapping: {{mapping| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
Mapping: {{mapping| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}

=== Nuke
Subgroup: 2.3.5.7
Comma list: 49/48, 3584/3375
Mapping: {{mapping|legend=1| 1 2 2 3 | 0 -6 5 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 77/75, 512/495
Mapping: {{mapping| 1 2 2 3 3 | 0 -6 5 -3 7 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 77/75, 448/429
Mapping: {{mapping| 1 2 2 3 3 4 | 0 -6 5 -3 7 -4 }}


= Starling family

=== Starling
Subgroup: 2.3.5.7
Comma list: [[126/125]]
Mapping: {{mapping|legend=1| 1 0 0 -1 | 0 1 0 -2 | 0 0 1 3 }}
Mapping to lattice: [{{val| 0 1 0 -2 }}, {{val| 0 1 1 1 }}]

==== Overview to extensions

=== Thrush
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175
Mapping: {{mapping|legend=1| 1 0 0 -1 -5 | 0 1 0 -2 -2 | 0 0 1 3 5 }}
Mapping to lattice: [{{val| 0 1 1 1 3 }}, {{val| 0 1 0 -2 -2 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195
Mapping: {{mapping| 1 0 0 -1 -5 0 | 0 1 0 -2 -2 -5 | 0 0 1 3 5 5 }}

==== Bluebird
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 176/175
Mapping: {{mapping| 1 0 0 -1 -5 9 | 0 1 0 -2 -2 4 | 0 0 1 3 5 -5 }}

==== Nightingale
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 126/125, 176/175
Mapping: {{mapping| 1 0 0 -1 -5 -4 | 0 1 0 -2 -2 -1 | 0 0 1 3 5 4 }}

==== Veery
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 176/175
Mapping: {{mapping| 1 0 0 -1 -5 2 | 0 1 0 -2 -2 4 | 0 0 1 3 5 -2 }}

=== Starnova
Subgroup: 2.3.5.7.11
Comma list: 126/125, 385/384
Mapping: {{mapping|legend=1| 1 0 0 -1 8 | 0 1 0 -2 3 | 0 0 1 3 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 385/384
Mapping: {{mapping| 1 0 0 -1 8 0 | 0 1 0 -2 3 -5 | 0 0 1 3 -4 5 }}

=== Thrasher
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99
Mapping: {{mapping|legend=1| 1 0 0 -1 2 | 0 1 0 -2 -2 | 0 0 1 3 2 }}
Mapping to lattice: [{{val| 0 1 0 -2 -2 }}, {{val| 0 1 1 1 0 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 91/90, 100/99
Mapping: {{mapping| 1 0 0 -1 2 2 | 0 1 0 -2 -2 4 | 0 0 1 3 2 -2 }}

==== Mockingbird
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 56/55, 100/99
Mapping: {{mapping| 1 0 0 -1 2 3 | 0 1 0 -2 -2 -1 | 0 0 1 3 2 1 }}

==== Catbird
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 100/99
Mapping: {{mapping| 1 0 0 -1 2 0 | 0 1 0 -2 -2 -5 | 0 0 1 3 2 5 }}

=== Aplonis
Subgroup: 2.3.5.7.11
Comma list: 126/125, 540/539
Mapping: {{mapping|legend=1| 1 0 0 -1 4 | 0 1 0 -2 7 | 0 0 1 3 -5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 196/195
Mapping: {{mapping| 1 0 0 -1 4 0 | 0 1 0 -2 7 -5 | 0 0 1 3 -5 5 }}

=== Treecreeper
Subgroup: 2.3.5.7.11
Comma list: 126/125, 1232/1215
Mapping: {{mapping|legend=1| 1 0 0 -1 -3 | 0 1 0 -2 7 | 0 0 1 3 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 352/351
Mapping: {{mapping| 1 0 0 -1 -3 2 | 0 1 0 -2 7 4 | 0 0 1 3 -2 -2 }}


= Starling temperaments

=== Myna
Subgroup: 2.3.5.7
Comma list: 126/125, 1728/1715
Mapping: {{mapping|legend=1| 1 -1 0 1 | 0 10 9 7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 243/242
Mapping: {{mapping| 1 -1 0 1 -3 | 0 10 9 7 25 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 176/175, 196/195
Mapping: {{mapping| 1 -1 0 1 -3 5 | 0 10 9 7 25 -5 }}

===== Minah
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 91/90, 126/125, 176/175
Mapping: {{mapping| 1 -1 0 1 -3 -2 | 0 10 9 7 25 22 }}

===== Maneh
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 126/125, 243/242
Mapping: {{mapping| 1 -1 0 1 -3 -3 | 0 10 9 7 25 26 }}

==== Myno
Subgroup: 2.3.5.7.11
Comma list: 99/98, 126/125, 385/384
Mapping: {{mapping| 1 -1 0 1 5 | 0 10 9 7 -6 }}

==== Coleto
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 1728/1715
Mapping: {{mapping| 1 -1 0 1 4 | 0 10 9 7 -2 }}

=== Nusecond
Subgroup: 2.3.5.7
Comma list: 126/125, 2430/2401
Mapping: {{mapping|legend=1| 1 -8 -9 -12 | 0 11 13 17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 126/125
Mapping: {{mapping| 1 -8 -9 -12 -7 | 0 11 13 17 12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 99/98, 121/120, 126/125
Mapping: {{mapping| 1 -8 -9 -12 -7 -5 | 0 11 13 17 12 10 }}

=== Oolong
Subgroup: 2.3.5.7
Comma list: 126/125, 117649/116640
Mapping: {{mapping|legend=1| 1 -11 -11 -12 | 0 17 18 20 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 26411/26244
Mapping: {{mapping| 1 -11 -11 -12 -38 | 0 17 18 20 56 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 13013/12960
Mapping: {{mapping| 1 -11 -11 -12 -38 0 | 0 17 18 20 56 5 }}

=== Vines
Subgroup: 2.3.5.7
Comma list: 126/125, 84035/82944
Mapping: {{mapping|legend=1| 2 -1 1 3 | 0 8 7 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 385/384, 2401/2376
Mapping: {{mapping| 2 -1 1 3 9 | 0 8 7 5 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 364/363, 385/384
Mapping: {{mapping| 2 -1 1 3 9 10 | 0 8 7 5 -4 -5 }}

=== Xenial
Subgroup: 2.3.5.7
Comma list: 126/125, 177147/175616
Mapping: {{mapping|legend=1| 1 -6 -12 -25 | 0 9 17 33 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 540/539, 16384/16335
Mapping: {{mapping| 1 -6 -12 -25 22 | 0 9 17 33 -22 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 169/168, 540/539, 729/728
Mapping: {{mapping| 1 -6 -12 -25 22 -14 | 0 9 17 33 -22 21 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 169/168, 221/220, 256/255, 540/539
Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 | 0 9 17 33 -22 21 -26 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 126/125, 169/168, 171/170, 221/220, 256/255, 540/539
Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 27 | 0 9 17 33 -22 21 -26 -27 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 126/125, 162/161, 169/168, 171/170, 208/207, 221/220, 231/230
Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 27 2 | 0 9 17 33 -22 21 -26 -27 3 }}

=== Kumonga
Subgroup: 2.3.5.7
Comma list: 126/125, 12288/12005
Mapping: {{mapping|legend=1| 1 -9 -5 2 | 0 13 9 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 864/847
Mapping: {{mapping| 1 -9 -5 2 -12 | 0 13 9 1 19 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 126/125, 144/143, 176/175
Mapping: {{mapping| 1 -9 -5 2 -12 -2 | 0 13 9 1 19 7 }}

=== Bisemidim
Subgroup: 2.3.5.7
Comma list: 126/125, 118098/117649
Mapping: {{mapping|legend=1| 2 1 2 2 | 0 9 11 15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 540/539, 1344/1331
Mapping: {{mapping| 2 1 2 2 5 | 0 9 11 15 8 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 196/195, 364/363
Mapping: {{mapping| 2 1 2 2 5 5 | 0 9 11 15 8 10 }}

=== Cypress
Subgroup: 2.3.5.7
Comma list: 126/125, 19683/19208
Mapping: {{mapping|legend=1| 1 -5 -7 -12 | 0 12 17 27 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 126/125, 243/242
Mapping: {{mapping| 1 -5 -7 -12 -13 | 0 12 17 27 30 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 99/98, 126/125, 243/242
Mapping: {{mapping| 1 -5 -7 -12 -13 -10 | 0 12 17 27 30 25 }}

=== Casablanca
Subgroup: 2.3.5.7
Comma list: 126/125, 589824/588245
Mapping: {{mapping|legend=1| 1 -7 -4 1 | 0 19 14 4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 385/384, 2420/2401
Mapping: {{mapping| 1 -7 -4 1 3 | 0 19 14 4 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 385/384, 2420/2401
Mapping: {{mapping| 1 -7 -4 1 3 1 | 0 19 14 4 1 6 }}

==== Marrakesh
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 14641/14580
Mapping: {{mapping| 1 -7 -4 1 -11 | 0 19 14 4 32 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 14641/14580
Mapping: {{mapping| 1 -7 -4 1 -11 15 | 0 19 14 4 32 -25 }}

===== Murakuc
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 176/175, 1540/1521
Mapping: {{mapping| 1 -7 -4 1 -11 1 | 0 19 14 4 32 6 }}

=== Amigo
Subgroup: 2.3.5.7
Comma list: 126/125, 2097152/2083725
Mapping: {{mapping|legend=1| 1 -2 2 9 | 0 11 1 -19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 16384/16335
Mapping: {{mapping| 1 -2 2 9 9 | 0 11 1 -19 -17 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 169/168, 176/175, 364/363
Mapping: {{mapping| 1 -2 2 9 9 5 | 0 11 1 -19 -17 -4 }}

=== Gilead
Subgroup: 2.3.5.7
Comma list: 126/125, 343/324
Mapping: {{mapping|legend=1| 1 -5 -5 -6 | 0 9 10 12 }}

=== Supersensi
Subgroup: 2.3.5.7
Comma list: 126/125, 17496/16807
Mapping: {{mapping|legend=1| 1 -4 -4 -5 | 0 15 17 21 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 126/125, 864/847
Mapping: {{mapping| 1 -4 -4 -5 -1 | 0 15 17 21 12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 99/98, 126/125, 144/143
Mapping: {{mapping| 1 -4 -4 -5 -1 -3 | 0 15 17 21 12 18 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 78/77, 99/98, 120/119, 126/125, 144/143
Mapping: {{mapping| 1 -4 -4 -5 -1 -3 0 | 0 15 17 21 12 18 11 }}

=== Cobalt
Subgroup: 2.3.5.7
Comma list: 126/125, 40353607/40310784
Mapping: {{mapping|legend=1| 27 0 20 33 | 0 1 1 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 540/539, 21609/21296
Mapping: {{mapping| 27 0 20 33 8 | 0 1 1 1 2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 196/195, 21609/21296
Mapping: {{mapping| 27 0 20 33 8 100 | 0 1 1 1 2 0 }}

====== Cobaltous
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 144/143, 189/187, 196/195, 1452/1445
Mapping: {{mapping| 27 0 20 33 8 100 79 | 0 1 1 1 2 0 2 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 126/125, 144/143, 171/170, 189/187, 196/195, 969/968
Mapping: {{mapping| 27 0 20 33 8 100 79 99 | 0 1 1 1 2 0 2 1 }}

====== Cobaltic
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 144/143, 196/195, 221/220, 12005/11968
Mapping: {{mapping| 27 0 20 33 8 100 -18 | 0 1 1 1 2 0 3 }}

======= 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 126/125, 144/143, 196/195, 210/209, 221/220, 1088/1083
Mapping: {{mapping| 27 0 20 33 8 100 -18 72 | 0 1 1 1 2 0 3 1 }}

===== Cobaltite
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 169/168, 540/539, 975/968
Mapping: {{mapping| 27 0 20 33 8 57 | 0 1 1 1 2 1 }}

=== References


= Stearnsmic clan

=== No-five stearnsmic
Subgroup: 2.3.7
Comma list: 118098/117649
Mapping: {{mapping|legend=2| 2 1 2 | 0 3 5 }}
Mapping: {{mapping|legend=3| 2 1 0 2 | 0 3 0 5 }}

==== Overview to extensions

=== Pogo
Subgroup: 2.3.5.7
Comma list: 32805/32768, 118098/117649
Mapping: {{mapping|legend=1| 2 1 22 2 | 0 3 -24 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 32805/32768
Mapping: {{mapping| 2 1 22 2 25 | 0 3 -24 5 -25 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573, 4096/4095
Mapping: {{mapping| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}

=== Supers
Subgroup: 2.3.5.7
Comma list: 5120/5103, 118098/117649
Mapping: {{mapping|legend=1| 2 1 -12 2 | 0 3 23 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 5120/5103
Mapping: {{mapping| 2 1 -12 2 -9 | 0 3 23 5 22 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 1575/1573
Mapping: {{mapping| 2 1 -12 2 -9 -2 | 0 3 23 5 22 13 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 289/288, 352/351, 442/441, 561/560
Mapping: {{mapping| 2 1 -12 2 -9 -2 6 | 0 3 23 5 22 13 3 }}

=== Stearnscape
Subgroup: 2.3.5.7
Comma list: 118098/117649, 250047/250000
Mapping: {{mapping|legend=1| 6 3 2 6 | 0 6 11 10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 137781/137500
Mapping: {{mapping| 6 3 2 6 11 | 0 6 11 10 9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573, 34398/34375
Mapping: {{mapping| 6 3 2 6 11 -6 | 0 6 11 10 9 26 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 540/539, 729/728, 936/935, 1156/1155, 1575/1573
Mapping: {{mapping| 6 3 2 6 11 -6 5 | 0 6 11 10 9 26 18 }}

=== Garistearn
Subgroup: 2.3.5.7
Comma list: 118098/117649, 33554432/33480783
Mapping: {{mapping|legend=1| 94 149 0 264 | 0 0 1 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 33554432/33480783
Mapping: {{mapping| 94 149 0 264 107 | 0 0 1 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573, 28672/28561
Mapping: {{mapping| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873
Mapping: {{mapping| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}

=== Decistearn
Subgroup: 2.3.5.7
Comma list: 3136/3125, 118098/117649
Mapping: {{mapping|legend=1| 10 2 14 5 | 0 3 2 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3136/3125, 4000/3993
Mapping: {{mapping| 10 2 14 5 30 | 0 3 2 5 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539, 3136/3125
Mapping: {{mapping| 10 2 14 5 30 37 | 0 3 2 5 1 0 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 289/288, 351/350, 540/539, 1632/1625
Mapping: {{mapping| 10 2 14 5 30 37 27 | 0 3 2 5 1 0 3 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475
Mapping: {{mapping| 10 2 14 5 30 37 27 24 | 0 3 2 5 1 0 3 4 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475, 897/896
Mapping: {{mapping| 10 2 14 5 30 37 27 24 36 | 0 3 2 5 1 0 3 4 2 }}


= Subgroup temperaments

== Composite subgroup temperaments

=== 2.9.5.7 subgroup

==== Commatose
Subgroup: 2.9.5.7
Comma list: {{monzo| 28 -2 -19 8 }}, {{monzo| 9 -25 23 6 }}
Mapping: {{mapping|legend=2| 1 9 6 13 | 0 -298 -188 -521 }}

===== 2.9.5.7.11
Subgroup: 2.9.5.7.11
Comma list: {{monzo| -7 7 -3 2 -4 }}, {{monzo| 17 0 -13 1 3 }}, {{monzo| 11 -2 -6 7 -3 }}

===== 2.9.5.7.11.13
Subgroup: 2.9.5.7.11.13
Comma list: 123201/123200, 1016064/1015625, 2250423/2249390, 2599051/2598156

==== Daemotertiaschis
Subgroup: 2.9.5.7.33.13.17
Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976
Mapping: {{mapping|legend=2|1 1 11 -16 13 -18 20|0 3 -12 26 -11 30 -22}}

==== Baldy
Subgroup: 2.9.5.7
Comma list: 225/224, 3125/3087
Mapping: {{mapping|legend=2| 1 3 3 4 | 0 1 -4 -7 }}

===== 2.9.5.7.13
Subgroup: 2.9.5.7.13
Comma list: [[225/224]], [[325/324]], [[640/637]]
Mapping: {{mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}
Mapping: {{mapping|legend=3| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}

===== Baldanders
Subgroup: 2.9.5.7.11
Comma list: 100/99, 225/224, 245/242
Mapping: {{mapping|legend=2| 1 3 3 4 5 | 0 1 -4 -7 -9 }}

====== 2.9.5.7.11.13
Subgroup: 2.9.5.7.11.13
Comma list: 100/99, 144/143, 225/224, 245/242
Mapping: {{mapping|legend=2| 1 3 3 4 5 2 | 0 1 -4 -7 -9 10 }}

=== 2.9.5.11 subgroup

==== Glacial
Subgroup: 2.9.5.11.13
Comma list: 45/44, 65/64, 81/80
Mapping: {{mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}
Mapping: {{mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}

=== 2.9.7 subgroup

==== Mabon
Subgroup: 2.9.7
Comma list: 44957696/43046721
Mapping: [{{val|1 1 -3}}, {{val|0 3 8}}]

===== 2.9.7.11 subgroup
Subgroup: 2.9.7.11
Comma list: 896/891, 1331/1296
Mapping: [{{val|1 1 -3 2}}, {{val|0 3 8 2}}]

=== 2.9.7.11 subgroup

==== Apparatus
Subgroup: 2.9.7.11
Comma list: 41503/41472, 322102/321489
Mapping: {{mapping|legend=2| 1 5 3 5 | 0 -19 -2 -16 }}
Mapping: {{mapping|legend=3| 1 5/2 0 3 5 | 0 -19/2 0 -2 -16 }}

==== Joan
Subgroup: 2.9.7.11
Comma list: 99/98, 9317/9216
Mapping: {{mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}
Mapping: {{mapping|legend=3| 1 0 0 1 3 | 0 7/2 0 4 1 }}

==== Machine
Subgroup: 2.9.7.11
Comma list: 64/63, 99/98
Mapping: {{mapping|legend=2| 1 0 6 13 | 0 1 -1 -3 }}
Mapping: {{mapping|legend=3| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }}

==== Penta a.k.a. mechanism
Subgroup: 2.9.7.11
Comma list: 896/891, 26411/26244
Mapping: {{mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}
Mapping: {{mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}

=== 2.9.11 subgroup

==== Demon
Subgroup: 2.9.11
Comma list: [[1331/1296]]
Mapping: {{mapping|legend=2|1 1 2|0 3 2}}

==== Genius
Subgroup: 2.9.11
Comma list: [[131769/131072]]
Mapping: {{mapping|legend=2|1 1 4|0 4 -1}}

=== 2.9.15.7 subgroup

==== Stacks (a.k.a. 2magic)
Subgroup: 2.9.15.7
Comma list: 225/224, 245/243
Mapping: {{mapping|legend=2| 1 0 2 -1 | 0 5 3 6 }}
Mapping: {{mapping|legend=3| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }}

===== 2.9.15.7.11
Subgroup: 2.9.15.7.11
Comma list: 100/99, 225/224, 245/243

===== 2.9.15.7.11.13
Subgroup: 2.9.15.7.11.13
Comma list: 100/99, 105/104, 144/143, 196/195

=== 2.9.21 subgroup

==== A-team
Subgroup: 2.9.21
Comma list: 1029/1024
Mapping: {{mapping|legend=2| 1 2 4 | 0 3 1 }}
Mapping: {{mapping|legend=3| 1 1 0 3 | 0 3/2 0 -1/2 }}

===== 2.9.5.21
Subgroup: 2.9.5.21

====== 2.9.5.21.11
Subgroup: 2.9.5.21.11
Comma list: 81/80, 99/98, 385/384

===== B-team
Subgroup: 2.9.15.21.33
Comma list: 245/243, 385/384, 441/440

=== 2.15.55 subgroup

==== Spog
Subgroup: 2.15.55
Comma list: [[100663296/100656875]]
Mapping: {{mapping|legend=2| 1 0 5 | 0 5 1 }}

===== 2.15.55.325
Subgroup: 2.15.55.325
Comma list: [[4225/4224]], [[6656/6655]]
Mapping: {{mapping|legend=2| 1 0 5 6 | 0 5 1 3 }}

===== 2.15.189.55.325
Subgroup: 2.15.189.55.325
Comma list: [[2080/2079]], [[3025/3024]], [[4096/4095]]
Mapping: {{mapping|legend=2| 1 0 6 5 6 | 0 5 2 1 3 }}

===== 2.15.189.55.325.725
Subgroup: 2.15.189.55.325.725
Comma list: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
Mapping: {{mapping|legend=2| 1 0 6 5 6 -3 | 0 5 2 1 3 16 }}

===== 2.15.189.55.325.725.279
Subgroup: 2.15.189.55.325.725.279
Comma list: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
Mapping: {{mapping|legend=2| 1 0 6 5 6 -3 5 | 0 5 2 1 3 16 4 }}

=== 4.3.5 subgroup

==== Tetrahanson
Subgroup: 4.3.5
Comma list: 15625/15552
Mapping: {{mapping|legend=2| 1 3 3 | 0 -6 -5 }}

==== Tetrameantone
Subgroup: 4.3.5
Comma list: 81/80
Mapping: {{mapping|legend=2| 1 1 2 | 0 -1 -4 }}

==== Tetramagic
Subgroup: 4.3.5
Comma list: 3125/3072
Mapping: {{mapping|legend=2| 1 0 1 | 0 5 1 }}

==== Blacktetra
Subgroup: 4.3.5
Comma list: 256/243
Mapping: {{mapping|legend=2| 5 4 6 | 0 0 -1 }}

=== 4.6.5 subgroup

==== Meanquad
Subgroup: 4.6.5
Comma list: [[81/80]] = {{monzo| -4 4 -1 }}
Mapping: {{mapping|legend=2| 1 0 -4| 0 1 4 }}

===== 4.6.5.7 subgroup (tetrominant)
Subgroup: 4.6.5.7
Comma list: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
Mapping: {{mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}

=== 4.9.25 subgroup

==== Meansquared
Subgroup: 4.9.25
Comma list: [[6561/6400]]
Mapping: {{mapping|legend=2| 1 3 4 | 0 1 4 }}

=== 4.9.49 subgroup

==== Archsquared
Subgroup: 4.9.49
Comma list: 4096/3969
Mapping: {{mapping|legend=2| 1 3 0 | 0 1 -2 }}

=== 8.9.7 subgroup

==== Sixscared
Subgroup: 8.9.7
Comma list: 64/63
Mapping: {{mapping|legend=2| 1 0 2 | 0 1 -1 }}


= Swetismic temperaments

=== Hades
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993
Mapping: {{mapping|legend=1| 2 1 0 2 3 | 0 3 0 5 -1 | 0 0 1 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573
Mapping: {{mapping| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}

==== Cerberus
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539
Mapping: {{mapping| 2 1 0 2 3 1 | 0 3 0 5 -1 -4 | 0 0 1 0 1 2 }}

=== Minos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 12005/11979
Mapping: {{mapping|legend=1| 1 0 -3 0 -1 | 0 2 4 3 4 | 0 0 5 1 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675
Mapping: {{mapping| 1 0 -3 0 -1 -4 | 0 2 4 3 4 7 | 0 0 5 1 3 5 }}

=== Persephone
Subgroup: 2.3.5.7.11
Comma list: 540/539, 88209/87500
Mapping: {{mapping|legend=1| 1 0 -6 4 -12 | 0 1 4 0 7 | 0 0 5 -3 11 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845
Mapping: {{mapping| 1 0 -6 4 -12 -7 | 0 1 4 0 7 5 | 0 0 5 -3 11 7 }}

=== Hypnos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 72171/71680
Mapping: {{mapping|legend=1| 1 0 0 -3 8 | 0 3 0 11 -13 | 0 0 1 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 540/539, 729/728
Mapping: {{mapping| 1 0 0 -3 8 0 | 0 3 0 11 -13 7 | 0 0 1 0 1 0 }}


= Sycamore family

=== Sycamore
Subgroup: 2.3.5
Comma list: 48828125/47775744
Mapping: {{mapping|legend=1| 1 1 2 | 0 11 6 }}

=== Septimal sycamore
Subgroup: 2.3.5.7
Comma list: 686/675, 875/864
Mapping: {{mapping|legend=1| 1 1 2 2 | 0 11 6 15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 686/675
Mapping: {{mapping| 1 1 2 2 4 | 0 11 6 15 -10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 100/99, 169/168, 385/384
Mapping: {{mapping| 1 1 2 2 4 3 | 0 11 6 15 -10 13 }}

=== Betic
Subgroup: 2.3.5.7
Comma list: 225/224, 1071875/1062882
Mapping: {{mapping|legend=1| 1 1 2 1 | 0 11 6 34 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 218750/216513
Mapping: {{mapping| 1 1 2 1 5 | 0 11 6 34 -29 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 1875/1859
Mapping: {{mapping| 1 1 2 1 5 2 | 0 11 6 34 -29 32 }}


= Tetracot family

=== Tetracot
Subgroup: 2.3.5
Comma list: 20000/19683
Mapping: {{mapping|legend=1| 1 1 1 | 0 4 9 }}

==== Overview to extensions

===== Subgroup extensions

===== Full 7-limit extensions

==== 2.3.5.11 subgroup
Subgroup: 2.3.5.11
Comma list: 100/99, 243/242
Mapping: {{mapping| 1 1 1 2 | 0 4 9 10 }}

===== 2.3.5.11.13 subgroup
Subgroup: 2.3.5.11.13
Comma list: 100/99, 144/143, 243/242
Mapping: {{mapping| 1 1 1 2 4 | 0 4 9 10 -2 }}

=== Monkey
Subgroup: 2.3.5.7
Comma list: 875/864, 5120/5103
Mapping: {{mapping|legend=1| 1 1 1 5 | 0 4 9 -15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 243/242, 385/384
Mapping: {{mapping| 1 1 1 5 2 | 0 4 9 -15 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 243/242
Mapping: {{mapping| 1 1 1 5 2 4 | 0 4 9 -15 10 -2 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 144/143, 154/153, 170/169
Mapping: {{mapping| 1 1 1 5 2 4 6 | 0 4 9 -15 10 -2 -13 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 144/143, 154/153, 170/169, 171/169
Mapping: {{mapping| 1 1 1 5 2 4 6 6 | 0 4 9 -15 10 -2 -13 -12 }}

=== Bunya
Subgroup: 2.3.5.7
Comma list: 225/224, 15625/15309
Mapping: {{mapping|legend=1| 1 1 1 -1 | 0 4 9 26 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 243/242
Mapping: {{mapping| 1 1 1 -1 2 | 0 4 9 26 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 225/224, 243/242
Mapping: {{mapping| 1 1 1 -1 2 4 | 0 4 9 26 10 -2 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 120/119, 144/143, 170/169, 225/224
Mapping: {{mapping| 1 1 1 -1 2 4 6 | 0 4 9 26 10 -2 -13 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 144/143, 170/169, 190/189, 225/224
Mapping: {{mapping| 1 1 1 -1 2 4 6 0 | 0 4 9 26 10 -2 -13 29 }}

=== Modus
Subgroup: 2.3.5.7
Comma list: 64/63, 4375/4374
Mapping: {{mapping|legend=1| 1 1 1 4 | 0 4 9 -8 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 243/242
Mapping: {{mapping| 1 1 1 4 2 | 0 4 9 -8 10 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 78/77, 100/99, 144/143
Mapping: {{mapping| 1 1 1 4 2 4 | 0 4 9 -8 10 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 64/63, 78/77, 100/99, 120/119, 144/143
Mapping: {{mapping| 1 1 1 4 2 4 1 | 0 4 9 -8 10 -2 21 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 64/63, 78/77, 96/95, 100/99, 120/119, 144/143
Mapping: {{mapping| 1 1 1 4 2 4 1 5 | 0 4 9 -8 10 -2 21 -5 }}

==== Ponens
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 363/350
Mapping: {{mapping| 1 1 1 4 3 | 0 4 9 -8 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 66/65, 143/140
Mapping: {{mapping| 1 1 1 4 3 4 | 0 4 9 -8 3 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 52/51, 55/54, 64/63, 66/65, 143/140
Mapping: {{mapping| 1 1 1 4 3 4 5 | 0 4 9 -8 3 -2 -6 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 52/51, 55/54, 64/63, 66/65, 77/76, 143/140
Mapping: {{mapping| 1 1 1 4 3 4 5 5 | 0 4 9 -8 3 -2 -6 -5 }}

=== Wollemia
Subgroup: 2.3.5.7
Comma list: 126/125, 2240/2187
Mapping: {{mapping|legend=1| 1 1 1 0 | 0 4 9 19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 243/242
Mapping: {{mapping| 1 1 1 0 2 | 0 4 9 19 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 91/90, 100/99, 243/242
Mapping: {{mapping| 1 1 1 0 2 4 | 0 4 9 19 10 -2 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 56/55, 91/90, 100/99, 136/135, 154/153
Mapping: {{mapping| 1 1 1 0 2 4 1 | 0 4 9 19 10 -2 21 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 56/55, 76/75, 91/90, 100/99, 136/135, 154/153
Mapping: {{mapping| 1 1 1 0 2 4 1 1 | 0 4 9 19 10 -2 21 22 }}

=== Octacot
Subgroup: 2.3.5.7
Comma list: 245/243, 2401/2400
Mapping: {{mapping|legend=1| 1 1 1 2 | 0 8 18 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 243/242, 245/242
Mapping: {{mapping| 1 1 1 2 2 | 0 8 18 11 20 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 196/195, 243/242
Mapping: {{mapping| 1 1 1 2 2 4 | 0 8 18 11 20 -4 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 120/119, 144/143, 154/153, 189/187
Mapping: {{mapping| 1 1 1 2 2 4 3 | 0 8 18 11 20 -4 15 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 133/132, 144/143, 154/153, 189/187
Mapping: {{mapping| 1 1 1 2 2 4 3 3 | 0 8 18 11 20 -4 15 17 }}

===== Octocat
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 91/90, 100/99, 245/242
Mapping: {{mapping| 1 1 1 2 2 2 | 0 8 18 11 20 23 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 52/51, 78/77, 91/90, 100/99, 189/187
Mapping: {{mapping| 1 1 1 2 2 2 3 | 0 8 18 11 20 23 15 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 52/51, 78/77, 91/90, 100/99, 133/132, 189/187
Mapping: {{mapping| 1 1 1 2 2 2 3 3 | 0 8 18 11 20 23 15 17 }}

===== Octopod
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 243/242, 245/242
Mapping: {{mapping| 1 1 1 2 2 1 | 0 8 18 11 20 37 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 120/119, 154/153, 243/242
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 8 18 11 20 37 15 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 105/104, 120/119, 133/132, 154/153, 209/208
Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 8 18 11 20 37 15 17 }}

===== Dificot
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 243/242, 245/242, 343/338
Mapping: {{mapping| 1 -7 -17 -9 -18 -14 | 0 16 36 22 40 33 }}

==== October
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 1375/1372
Mapping: {{mapping| 1 1 1 2 5 | 0 8 18 11 -21 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 275/273, 385/384
Mapping: {{mapping| 1 1 1 2 5 4 | 0 8 18 11 -21 -4 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 154/153, 170/169, 196/195, 245/243, 256/255
Mapping: {{mapping| 1 1 1 2 5 4 6 | 0 8 18 11 -21 -4 -26 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 154/153, 170/169, 190/189, 196/195, 209/208, 245/243
Mapping: {{mapping| 1 1 1 2 5 4 6 3 | 0 8 18 11 -21 -4 -26 17 }}

=== Dodecacot
Subgroup: 2.3.5.7
Comma list: 3125/3087, 10976/10935
Mapping: {{mapping|legend=1| 1 1 1 1 | 0 12 27 37 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 243/242, 1375/1372
Mapping: {{mapping| 1 1 1 1 2 | 0 12 27 37 30 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 243/242, 275/273
Mapping: {{mapping| 1 1 1 1 2 2 | 0 12 27 37 30 35 }}

=== Weasel
Subgroup: 2.3.5.7
Comma list: 50/49, 19683/19208
Mapping: {{mapping|legend=1| 2 2 2 3 | 0 4 9 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98, 243/242
Mapping: {{mapping| 2 2 2 3 4 | 0 4 9 9 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 78/77, 99/98, 243/242
Mapping: {{mapping| 2 2 2 3 4 3 | 0 4 9 9 10 15 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 78/77, 85/84, 99/98, 243/242
Mapping: {{mapping| 2 2 2 3 4 3 7 | 0 4 9 9 10 15 4 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 50/49, 78/77, 85/84, 99/98, 135/133, 243/242
Mapping: {{mapping| 2 2 2 3 4 3 7 5 | 0 4 9 9 10 15 4 12 }}

==== Weasly
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 99/98, 144/143, 243/242
Mapping: {{mapping| 2 2 2 3 4 8 | 0 4 9 9 10 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 85/84, 99/98, 144/143, 243/242
Mapping: {{mapping| 2 2 2 3 4 8 7 | 0 4 9 9 10 -2 4 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 85/84, 99/98, 144/143, 190/189, 243/242
Mapping: {{mapping| 2 2 2 3 4 8 7 5 | 0 4 9 9 10 -2 4 12}}

=== Other subgroup extensions

==== Tetracot (2.3.5.13)
Subgroup: 2.3.5.13
Comma list: 325/324, 512/507
Mapping: {{mapping| 1 1 1 4 | 0 4 9 -2 }}

==== Devisemi (2.3.5.19)
Subgroup: 2.3.5.19
Comma list: 361/360, 20000/19683
Mapping: {{mapping|legend=2| 1 1 1 3 | 0 8 18 17 }}
Mapping: {{mapping|legend=3| 1 1 1 0 0 0 0 3 | 0 8 18 0 0 0 0 17 }}

==== Devisemi (2.3.5.7.19)
Subgroup: 2.3.5.7.19
Comma list: 190/189, 245/243, 361/360
Mapping: {{mapping| 1 1 1 2 3 | 0 8 18 11 17 }}

=== Notes

=== References


= Alphatricot family

=== Alphatricot
Subgroup: 2.3.5
Comma list: {{monzo| 39 -29 3 }}
Mapping: {{mapping|legend=1| 1 0 -13 | 0 3 29 }}

==== Alphatrimot (2.3.5.13 subgroup)
Subgroup: 2.3.5.13
Comma list: 2197/2187, 41067/40960
Mapping: {{mapping| 1 0 -13 0 | 0 3 29 7 }}

==== Alphatrillium (2.3.5.13 subgroup)
Subgroup: 2.3.5.13
Comma list: 140628/140625, 256000/255879
Mapping: {{mapping| 1 0 -13 -28 | 0 3 29 60 }}

=== Alphatrillium
Subgroup: 2.3.5.7
Comma list: 4375/4374, {{monzo| 40 -22 -1 -1 }}
Mapping: {{mapping|legend=1| 1 0 -13 53 | 0 3 29 -95 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 131072/130977, 759375/758912
Mapping: {{mapping| 1 0 -13 53 -89 | 0 3 29 -95 175 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078
Mapping: {{mapping| 1 0 -13 53 -89 -28 | 0 3 29 -95 175 60 }}

==== Pseudotrillium
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 5632/5625, 4108797/4096000
Mapping: {{mapping| 1 0 -13 53 -61 | 0 3 29 -95 122 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374
Mapping: {{mapping| 1 0 -13 53 -61 -28 | 0 3 29 -95 122 60 }}

=== Alphatrident
Subgroup: 2.3.5.7
Comma list: 6144/6125, 14348907/14336000
Mapping: {{mapping|legend=1| 1 0 -13 25 | 0 3 29 -42 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3388/3375, 6144/6125, 8019/8000
Mapping: {{mapping| 1 0 -13 25 -33 | 0 3 29 -42 69 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125
Mapping: {{mapping| 1 0 -13 25 -33 0 | 0 3 29 -42 69 7 }}

=== Alphatrimot
Subgroup: 2.3.5.7
Comma list: 2430/2401, 5120/5103
Mapping: {{mapping|legend=1| 1 0 -13 -3 | 0 3 29 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 5120/5103
Mapping: {{mapping| 1 0 -13 -3 -5 | 0 3 29 11 16 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 169/168, 352/351
Mapping: {{mapping| 1 0 -13 -3 -5 0 | 0 3 29 11 16 7 }}

=== Tritricot
Subgroup: 2.3.5.7
Comma list: 250047/250000, {{monzo| 35 -23 -3 3 }}
Mapping: {{mapping|legend=1| 3 0 -39 -74 | 0 3 29 52 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 4000/3993, 166698/166375, 200704/200475
Mapping: {{mapping| 3 0 -39 -74 -34 | 0 3 29 52 28 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875
Mapping: {{mapping| 3 0 -39 -74 -34 -84 | 0 3 29 52 28 60 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619
Mapping: {{mapping| 3 0 -39 -74 -34 -84 -2 | 0 3 29 52 28 60 9 }}

==== Noletaland
Subgroup: 2.3.5.7.11
Comma list: 250047/250000, 56723625/56689952, 78675968/78594219
Mapping: {{mapping| 3 6 19 30 35 | 0 -9 -87 -156 -178 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 10648/10647, 43904/43875, 85750/85683, 250047/250000
Mapping: {{mapping| 3 6 19 30 35 36 | 0 -9 -87 -156 -178 -180 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2058/2057, 4914/4913, 8624/8619, 12376/12375, 250047/250000
Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 2058/2057, 2926/2925, 3136/3135, 4200/4199, 4914/4913, 250047/250000
Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}

===== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 2058/2057, 2926/2925, 3136/3135, 3381/3380, 3520/3519, 4914/4913, 18515/18513
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 | 0 -9 -87 -156 -178 -180 -121 -38 -126 }}

===== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 2058/2057, 2755/2754, 2926/2925, 3136/3135, 3381/3380, 3451/3450, 3520/3519, 4914/4913
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 19 | 0 -9 -87 -156 -178 -180 -121 -38 -126 -32 }}

=== Notes


= Trienstonic clan

=== Trienstonian
Subgroup: 2.3.7
Comma list: 28/27
Mapping: {{mapping|legend=2| 1 0 -2 | 0 1 3 }}
Mapping: {{mapping|legend=3| 1 0 0 -2 | 0 1 0 3 }}

==== Overview to extensions

=== Uncle
Subgroup: 2.3.5.7
Comma list: 28/27, 256/245
Mapping: {{mapping|legend=1| 1 0 12 -2 | 0 1 -6 3 }}

=== Octokaidecal
Subgroup: 2.3.5.7
Comma list: 28/27, 50/49
Mapping: {{mapping|legend=1| 2 0 -5 -4 | 0 1 3 3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 50/49, 55/54
Mapping: {{mapping| 2 0 -5 -4 7 | 0 1 3 3 0 }}

=== Parakangaroo
Subgroup: 2.3.5.7
Comma list: 28/27, 1029/1000
Mapping: {{mapping|legend=1| 1 0 -3 -2 | 0 3 10 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 77/75, 245/242
Mapping: {{mapping| 1 0 -3 -2 -4 | 0 3 10 9 14 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 66/65, 147/143
Mapping: {{mapping| 1 0 -3 -2 -4 0 | 0 3 10 9 14 7 }}


= Unicorn family

=== Unicorn
Subgroup: 2.3.5
Comma list: 1594323/1562500
Mapping: {{mapping|legend=1| 1 2 3 | 0 -8 -13 }}

=== Septimal unicorn
Subgroup: 2.3.5.7
Comma list: [[126/125]], [[10976/10935]]
Mapping: {{mapping|legend=1| 1 2 3 4 | 0 -8 -13 -23 }}

==== 2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: [[126/125]], [[196/195]], [[676/675]]
Mapping: {{mapping|legend=1| 1 2 3 4 5 | 0 -8 -13 -23 -25 }}

===== 2.3.5.7.13.29 subgroup
Subgroup: 2.3.5.7.13.29
Comma list: [[126/125]], [[196/195]], [[261/260]], [[377/375]]
Mapping: {{mapping|legend=1| 1 2 3 4 5 6 | 0 -8 -13 -23 -25 -22 }}

===== 2.3.5.7.13.29.43 subgroup
Subgroup: 2.3.5.7.13.29.43
Comma list: [[126/125]], [[196/195]], [[216/215]], [[261/260]], [[377/375]]
Mapping: {{mapping|legend=1| 1 2 3 4 5 6 6 | 0 -8 -13 -23 -25 -22 -11 }}

==== Alicorn
Subgroup: 2.3.5.7.11
Comma list: 126/125, 540/539, 896/891
Mapping: {{mapping| 1 2 3 4 3 | 0 -8 -13 -23 9 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 196/195, 676/675
Mapping: {{mapping| 1 2 3 4 3 5 | 0 -8 -13 -23 9 -25 }}

==== Camahueto
Subgroup: 2.3.5.7.11
Comma list: 126/125, 385/384, 10976/10935
Mapping: {{mapping| 1 2 3 4 2 | 0 -8 -13 -23 28 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 385/384, 676/675
Mapping: {{mapping| 1 2 3 4 2 5 | 0 -8 -13 -23 28 -25 }}

==== Qilin
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 10976/10935
Mapping: {{mapping| 1 2 3 4 6 | 0 -8 -13 -23 -49 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 2200/2197
Mapping: {{mapping| 1 2 3 4 6 5 | 0 -8 -13 -23 -49 -25 }}

==== Monocerus
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 5488/5445
Mapping: {{mapping| 2 4 6 8 9 | 0 -8 -13 -23 -20 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 196/195, 243/242, 364/363
Mapping: {{mapping| 2 4 6 8 9 10 | 0 -8 -13 -23 -20 -25 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 196/195, 221/220, 243/242, 289/288
Mapping: {{mapping| 2 4 6 8 9 10 9 | 0 -8 -13 -23 -20 -25 -8 }}

=== Rhinoceros
Subgroup: 2.3.5.7
Comma list: 49/48, 4375/4374
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -8 -13 -4 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 100/99, 126/121
Mapping: {{mapping|  1 2 3 3 4 | 0 -8 -13 -4 -10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 78/77, 100/99, 126/121
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -8 -13 -4 -10 -6 }}


= Valinorsmic clan

=== Valinor
Subgroup: 2.5.7.11
Comma list: 176/175
Mapping: {{mapping|legend=2| 1 0 0 -4 | 0 1 0 2 | 0 0 1 1 }}

==== Overview to extensions

=== Manwe
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323
Mapping: {{mapping|legend=1| 1 0 0 12 8 | 0 1 0 3 3 | 0 0 1 -6 -4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 1331/1323
Mapping: {{mapping| 1 0 0 12 8 13 | 0 1 0 3 3 0 | 0 0 1 -6 -4 -4 }}

=== Augenic
Subgroup: 2.3.5.7.11
Comma list: 56/55, 128/125
Mapping: {{mapping|legend=1| 3 0 7 0 2 | 0 1 0 0 0 | 0 0 0 1 1 }}


= Vishnuzmic family

=== Vishnu
Subgroup: 2.3.5
Comma list: 6115295232/6103515625
Mapping: {{mapping|legend=1| 2 4 5 | 0 -7 -3 }}

=== Septimal vishnu
Subgroup: 2.3.5.7
Comma list: 4375/4374, 29360128/29296875
Mapping: {{mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5632/5625
Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}

===== Ananta
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}

===== Acyuta
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}

=== Vishnean
Subgroup: 2.3.5.7
Comma list: 126/125, 540225/524288
Mapping: {{mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 385/384, 1350/1331
Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 126/125, 144/143, 847/845
Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}

=== Narayana
Subgroup: 2.3.5.7
Comma list: 65625/65536, 321489/320000
Mapping: {{mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 65625/65536
Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}

=== Quarvish
Subgroup: 2.3.5.7
Comma list: 2401/2400, 6115295232/6103515625
Mapping: {{mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 172032/171875
Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}

=== Decavish
Subgroup: 2.3.5.7
Comma list: 420175/419904, 2202927104/2197265625
Mapping: {{mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 41503/41472, 172032/171875
Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}


= Vulture family

=== Vulture
Subgroup: 2.3.5
Comma list: 10485760000/10460353203
Mapping: {{mapping|legend=1| 1 0 -6 | 0 4 21 }}

==== Overview to extensions

=== Septimal vulture
Subgroup: 2.3.5.7
Comma list: 4375/4374, 33554432/33480783
Mapping: {{mapping|legend=1| 1 0 -6 25 | 0 4 21 -56 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 5632/5625, 41503/41472
Mapping: {{mapping| 1 0 -6 25 -33 | 0 4 21 -56 92 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095, 4375/4374
Mapping: {{mapping| 1 0 -6 25 -33 -7 | 0 4 21 -56 92 27 }}

===== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 676/675, 1001/1000, 1216/1215, 1540/1539, 1729/1728
Mapping: {{mapping| 1 0 -6 25 -33 -7 -12 | 0 4 21 -56 92 27 41 }}

==== Semivulture
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 33554432/33480783
Mapping: {{mapping| 2 0 -12 50 41 | 0 4 21 -56 -43 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374
Mapping: {{mapping| 2 0 -12 50 41 -14 | 0 4 21 -56 -43 27 }}

=== Terture
Subgroup: 2.3.5.7
Comma list: 250047/250000, 359661568/358722675
Mapping: {{mapping|legend=1| 3 0 -18 -32 | 0 4 21 34 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 19712/19683, 102487/102400
Mapping: {{mapping| 3 0 -18 -32 8 | 0 4 21 34 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
Mapping: {{mapping| 3 0 -18 -32 8 -21 | 0 4 21 34 2 27 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 | 0 4 21 34 2 27 12 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 -36 | 0 4 21 34 2 27 12 41 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 -36 10 | 0 4 21 34 2 27 12 41 3 }}

=== Condor
Subgroup: 2.3.5.7
Comma list: 10976/10935, 40353607/40000000
Mapping: {{mapping|legend=1| 1 -4 -27 -20 | 0 12 63 49 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4000/3993, 10976/10935
Mapping: {{mapping| 1 -4 -27 -20 -24 | 0 12 63 49 59 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 676/675, 10976/10935
Mapping: {{mapping| 1 -4 -27 -20 -24 -34 | 0 12 63 49 59 81 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 676/675, 8624/8619
Mapping: {{mapping| 1 -4 -27 -20 -24 -34 12 | 0 12 63 49 59 81 -17 }}

=== Eagle
Subgroup: 2.3.5.7
Comma list: 2401/2400, 10485760000/10460353203
Mapping: {{mapping|legend=1| 2 4 9 8 | 0 -8 -42 -23 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 19712/19683
Mapping: {{mapping| 2 4 9 8 12 | 0 -8 -42 -23 -49 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715, 10648/10647
Mapping: {{mapping| 2 4 9 8 12 13 | 0 -8 -42 -23 -49 -54 }}

=== Turkey
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 5250987/5242880
Mapping: {{mapping|legend=1| 1 -8 -48 7 | 0 16 84 -7 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 19712/19683, 42875/42768, 160083/160000
Mapping: {{mapping| 1 -8 -48 7 -87 | 0 16 84 -7 151 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104
Mapping: {{mapping| 1 -8 -48 7 -87 -61 | 0 16 84 -7 151 108 }}


= Werckismic temperaments

=== History
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4000/3993
Mapping: {{mapping|legend=1| 1 2 0 0 1 | 0 -6 0 7 2 | 0 0 1 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 676/675
Mapping: {{mapping| 1 2 0 0 1 2 | 0 -6 0 7 2 -9 | 0 0 1 1 1 1 }}

=== Varuna
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000
Mapping: {{mapping|legend=1| 2 0 0 9 12 | 0 1 0 -4 -6 | 0 0 1 2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440
Mapping: {{mapping| 2 0 0 9 12 11 | 0 1 0 -4 -6 -7 | 0 0 1 2 3 4 }}

=== Trimyna
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375
Mapping: {{mapping|legend=1| 1 -1 0 1 -3 | 0 5 0 -1 8 | 0 0 1 1 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 1001/1000
Mapping: {{mapping| 1 -1 0 1 -3 5 | 0 5 0 -1 8 -7 | 0 0 1 1 1 1 }}

===== Trimy
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 676/675, 847/845
Mapping: {{mapping| 1 -6 0 2 -11 -10 | 0 10 0 -2 16 15 | 0 0 1 1 1 1 }}

=== Seminaiad
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1127357/1125000
Mapping: {{mapping|legend=1| 1 5 0 -2 3 | 0 -11 0 8 -6 | 0 0 1 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 847/845, 1001/1000
Mapping: {{mapping| 1 5 0 -2 3 2 | 0 -11 0 8 -6 -2 | 0 0 1 1 1 1 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 221/220, 441/440, 847/845
Mapping: {{mapping| 1 5 0 -2 3 2 3 | 0 -11 0 8 -6 -2 -4 | 0 0 1 1 1 1 1 }}

===== Seminaiadia
Subgroup: 2.3.5.7.11.13.17
Comma list: 441/440, 833/832, 847/845, 1001/1000
Mapping: {{mapping| 1 5 0 -2 3 2 12 | 0 -11 0 8 -6 -2 -18 | 0 0 1 1 1 1 -1 }}

=== References


= Wesley family

=== Wesley
Subgroup: 2.3.5
Comma list: 78125/73728
Mapping: {{mapping|legend=1| 1 4 3 | 0 -7 -2 }}

=== Septimal wesley
Subgroup: 2.3.5.7
Comma list: 405/392, 875/864
Mapping: {{mapping|legend=1| 1 4 3 8 | 0 -7 -2 -15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 875/864
Mapping: {{mapping| 1 4 3 8 9 | 0 -7 -2 -15 -16 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 78/77, 99/98, 325/324
Mapping: {{mapping| 1 4 3 8 9 12 | 0 -7 -2 -15 -16 -24 }}

=== Snipes
Subgroup: 2.3.5.7
Comma list: 225/224, 6125/5832
Mapping: {{mapping|legend=1| 1 4 3 9 | 0 -7 -2 -18 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 55/54, 225/224, 245/242
Mapping: {{mapping| 1 4 3 9 10 | 0 -7 -2 -18 -19 }}

=== Roman

==== 7-limit a.k.a. crusher
Subgroup: 2.3.5.7
Comma list: 525/512, 3125/3024
Mapping: {{mapping|legend=1| 1 4 3 -1 | 0 -7 -2 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 525/512
Mapping: {{mapping| 1 4 3 -1 0 | 0 -7 -2 11 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 100/99, 105/104, 245/242
Mapping: {{mapping| 1 4 3 -1 0 3 | 0 -7 -2 11 10 2 }}

=== Dubbla
Subgroup: 2.3.5.7
Comma list: 50/49, 78125/73728
Mapping: {{mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 125/121, 1344/1331
Mapping: {{mapping| 2 1 4 5 6 | 0 7 2 2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 105/104, 125/121, 144/143
Mapping: {{mapping| 2 1 4 5 6 4 | 0 7 2 2 3 11 }}


= Würschmidt family

=== Würschmidt
Subgroup: 2.3.5
Comma list: 393216/390625
Mapping: {{mapping|legend=1| 1 -1 2 | 0 8 1 }}

==== Overview to extensions

===== 7-limit extensions

===== Subgroup extensions

==== 2.3.5.23 subgroup
Subgroup: 2.3.5.23
Comma list: 576/575, 12167/12150

===== 2.3.5.11.23 subgroup
Subgroup: 2.3.5.11.23
Comma list: 243/242, 276/275, 529/528

=== Septimal würschmidt
Subgroup: 2.3.5.7
Comma list: 225/224, 8748/8575
Mapping: {{mapping|legend=1| 1 -1 2 -3 | 0 8 1 18 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 243/242
Mapping: {{mapping| 1 -1 2 -3 -3 | 0 8 1 18 20 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 144/143, 176/175, 275/273
Mapping: {{mapping| 1 -1 2 -3 -3 5 | 0 8 1 18 20 -4 }}

===== Worseschmidt
Subgroup: 2.3.5.7.11.13
Mapping: {{mapping| 1 -1 2 -3 -3 -5 | 0 8 1 18 20 27 }}

=== Worschmidt
Subgroup: 2.3.5.7
Comma list: 126/125, 33075/32768
Mapping: {{mapping|legend=1| 1 -1 2 7 | 0 8 1 -13 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 385/384
Mapping: {{mapping| 1 -1 2 7 -3 | 0 8 1 -13 20 }}

=== Whirrschmidt
Subgroup: 2.3.5.7
Comma list: 4375/4374, 393216/390625
Mapping: {{mapping|legend=1| 1 -1 2 -14 | 0 8 1 52 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 896/891, 4375/4356
Mapping: {{mapping| 1 -1 2 -14 -3 | 0 8 1 52 20 }}


= Quintosec family

=== Quintosec
Subgroup: 2.3.5
Comma list: {{monzo| 47 -15 -10 }}
Mapping: {{mapping|legend=1| 5 1 22 | 0 2 -3 }}

==== 2.3.5.11 subgroup
Subgroup: 2.3.5.11
Comma list: 5632/5625, 26214400/26198073
Mapping: {{mapping| 5 1 22 45 | 0 2 -3 -8 }}

=== Qintosec
Subgroup: 2.3.5.7
Comma list: 225/224, 2560000/2470629
Mapping: {{mapping|legend=1| 5 1 22 21 | 0 2 -3 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 3840/3773
Mapping: {{mapping| 5 1 22 21 0 | 0 2 -3 -2 5 }}

==== Qinto
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 332750/321489
Mapping: {{mapping| 5 1 22 21 -7 | 0 2 -3 -2 7 }}

=== Sengasec
Subgroup: 2.3.5.7
Comma list: 686/675, 16807/16384
Mapping: {{mapping|legend=1| 5 1 22 14 | 0 2 -3 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384, 686/675
Mapping: {{mapping| 5 1 22 14 0 | 0 2 -3 0 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 243/242, 686/675
Mapping: {{mapping| 5 1 22 14 0 22 | 0 2 -3 0 5 -1 }}

=== Decoid
Subgroup: 2.3.5.7
Comma list: 2401/2400, 67108864/66976875
Mapping: {{mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 5632/5625, 9801/9800
Mapping: {{mapping| 10 0 47 36 98 | 0 2 -3 -1 -8 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
Mapping: {{mapping| 10 0 47 36 98 37 | 0 2 -3 -1 -8 0 }}

==== Triacontoid
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 42592/42525, 1771561/1769472
Mapping: {{mapping| 30 0 141 108 80 | 0 2 -3 -1 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 2401/2400, 4096/4095, 6656/6655
Mapping: {{mapping| 30 0 141 108 80 111 | 0 2 -3 -1 1 0 }}

=== Notes


= Trisedodge family

=== Trisedodge
Subgroup: 2.3.5
Comma list: 30958682112/30517578125
Mapping: {{mapping|legend=1| 5 1 7 | 0 3 2 }}

==== Countdown
Subgroup: 2.3.5.11
Comma list: 4000/3993, 6912/6875

=== Septimal trisedodge
Subgroup: 2.3.5.7
Comma list: 4000/3969, 110592/109375
Mapping: {{mapping|legend=1| 5 1 7 21 | 0 3 2 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 2560/2541
Mapping: {{mapping| 5 1 7 21 15 | 0 3 2 -3 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 1040/1029, 1331/1323
Mapping: {{mapping| 5 1 7 21 15 37 | 0 3 2 -3 1 -8 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255
Mapping: {{mapping| 5 1 7 21 15 37 32 | 0 3 2 -3 1 -8 -5 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255, 190/189,
Mapping: {{mapping| 5 1 7 21 15 37 32 12 | 0 3 2 -3 1 -8 -5 4 }}

===== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255, 190/189, 253/252
Mapping: {{mapping| 5 1 7 21 15 37 32 12 18 | 0 3 2 -3 1 -8 -5 4 2 }}

===== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255, 190/189, 253/252, 232/231
Mapping: {{mapping| 5 1 7 21 15 37 32 12 18 22 | 0 3 2 -3 1 -8 -5 4 2 1 }}

===== Trisey
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 325/324, 364/363, 640/637
Mapping: {{mapping| 5 1 7 21 15 0 | 0 3 2 -3 1 8 }}

=== Coblack
Subgroup: 2.3.5.7
Comma list: 126/125, 16807/16384
Mapping: {{mapping|legend=1| 5 1 7 14 | 0 3 2 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 385/384
Mapping: {{mapping| 5 1 7 14 15 | 0 3 2 0 1 }}

=== References


= Garischismic clan

=== Gary
Subgroup: 2.3.7
Comma list: 33554432/33480783
Mapping: {{mapping|legend=2| 1 0 25 | 0 1 -14 }}

==== Overview to extensions

==== 2.3.7.11 subgroup
Subgroup: 2.3.7.11
Comma list: 19712/19683, 41503/41472
Mapping: {{mapping| 1 0 25 -33 | 0 1 -14 23 }}

=== Cotoneum
Subgroup: 2.3.5.7
Comma list: 10976/10935, 823543/819200
Mapping: {{mapping|legend=1| 1 0 80 25 | 0 1 -49 -14 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 10976/10935, 16384/16335
Mapping: {{mapping| 1 0 80 25 -33 | 0 1 -49 -14 23 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 3584/3575, 10976/10935
Mapping: {{mapping| 1 0 80 25 -33 -93 | 0 1 -49 -14 23 61 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262
Mapping: {{mapping| 1 0 80 25 -33 -93 -137 | 0 1 -49 -14 23 61 89 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728
Mapping: {{mapping| 1 0 80 25 -33 -93 -137 74 | 0 1 -49 -14 23 61 89 -44 }}

=== World calendar
Subgroup: 2.3.5.7
Comma list: 390625/388962, 33554432/33480783
Mapping: {{mapping|legend=1| 4 1 -44 86 | 0 2 -13 -28 }}

==== 2.3.5.7.17 subgroup
Subgroup: 2.3.5.7.17
Comma list: 2025/2023, 24576/24565, 390625/388962
Mapping: {{mapping| 4 1 -44 86 3 | 0 2 -13 -28 5 }}

==== 2.3.5.7.17.19 subgroup
Subgroup: 2.3.5.7.17.19
Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000
Mapping: {{mapping| 4 1 -44 86 3 25 | 0 2 -13 -28 5 -3 }}


= Canou family

=== Canou
Subgroup: 2.3.5.7
Comma list: [[4802000/4782969]]
Mapping: {{mapping|legend=1| 1 0 0 -1 | 0 1 2 2 | 0 0 -4 3 }}

=== Undecimal canou
Subgroup: 2.3.5.7.11
Comma list: 19712/19683, 42875/42768
Mapping: {{mapping|legend=1| 1 0 0 -1 -7 | 0 1 2 2 7 | 0 0 -4 3 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 19712/19683, 42875/42768
Mapping: {{mapping| 1 0 0 -1 -7 -13 | 0 1 2 2 7 10 | 0 0 -4 3 -3 4 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 833/832, 1156/1155, 19712/19683
Mapping: {{mapping| 1 0 0 -1 -7 -13 -5 | 0 1 2 2 7 10 6 | 0 0 -4 3 -3 4 -2 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215
Mapping: {{mapping| 1 0 0 -1 -7 -13 -5 -6 | 0 1 2 2 7 10 6 7 | 0 0 -4 3 -3 4 -2 -4 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1156/1155
Mapping: {{mapping| 1 0 0 -1 -7 -13 -5 -6 4 | 0 1 2 2 7 10 6 7 1 | 0 0 -4 3 -3 4 -2 -4 -5 }}

=== Canta
Subgroup: 2.3.5.7.11
Comma list: 896/891, 472392/471625
Mapping: {{mapping|legend=1| 1 0 0 -1 6 | 0 1 2 2 -2 | 0 0 4 -3 -3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 472392/471625
Mapping: {{mapping| 1 0 0 -1 6 11 | 0 1 2 2 -2 -5 | 0 0 4 -3 -3 -3 }}

=== Semicanou
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 14641/14580
Mapping: {{mapping|legend=1| 2 0 0 -2 1 | 0 1 2 2 2 | 0 0 -4 3 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 14641/14580
Mapping: {{mapping| 2 0 0 -2 1 -11 | 0 1 2 2 2 5 | 0 0 -4 3 -1 6 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 1089/1088, 1225/1224, 14641/14580
Mapping: {{mapping| 2 0 0 -2 1 -11 -10 | 0 1 2 2 2 5 6 | 0 0 -4 3 -1 6 -2 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 715/714, 1089/1088, 1216/1215, 1225/1224, 1445/1444
Mapping: {{mapping| 2 0 0 -2 1 -11 -10 -12 | 0 1 2 2 2 5 6 7 | 0 0 -4 3 -1 6 -2 -4 }}

==== Semicanoumint
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 9801/9800, 14641/14580
Mapping: {{mapping| 2 0 0 -2 1 11 | 0 1 2 2 2 -1 | 0 0 -4 3 -1 -1 }}

==== Semicanouwolf
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 11011/10935
Mapping: {{mapping| 2 0 0 -2 1 0 | 0 1 2 2 2 3 | 0 0 -4 3 -1 -5 }}


= Canousmic temperaments

=== Satin
Subgroup: 2.3.5.7
Comma list: 2100875/2097152, 4802000/4782969
Mapping: {{mapping|legend=1| 1 2 12 -3 | 0 -3 -70 42 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 4000/3993, 19712/19683, 41503/41472
Mapping: {{mapping| 1 2 12 -3 13 | 0 -3 -70 42 -69 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689
Mapping: {{mapping| 1 2 12 -3 13 -1 | 0 -3 -70 42 -69 34 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095
Mapping: {{mapping| 1 2 12 -3 13 -1 11 | 0 -3 -70 42 -69 34 -50 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573
Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 | 0 -3 -70 42 -69 34 -50 -85 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155
Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 16 | 0 -3 -70 42 -69 34 -50 -85 -83 }}

=== Superlimmal
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 52734375/52706752
Mapping: {{mapping|legend=1| 1 8 12 18 | 0 -57 -86 -135 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 1479016/1476225
Mapping: {{mapping| 1 8 12 18 11 | 0 -57 -86 -135 -67 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 4000/3993, 4225/4224, 4459/4455
Mapping: {{mapping| 1 8 12 18 11 1 | 0 -57 -86 -135 -67 24 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 1275/1274, 2500/2499, 3025/3024, 4225/4224
Mapping: {{mapping| 1 8 12 18 11 1 6 | 0 -57 -86 -135 -67 24 -17 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 969/968, 1275/1274, 1445/1444, 1729/1728, 2500/2499
Mapping: {{mapping| 1 8 12 18 11 1 6 11 | 0 -57 -86 -135 -67 24 -17 -60 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 760/759, 969/968, 1105/1104, 1275/1274, 1445/1444, 1496/1495
Mapping: {{mapping| 1 8 12 18 11 1 6 11 7 | 0 -57 -86 -135 -67 24 -17 -60 -22 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 595/594, 760/759, 784/783, 969/968, 1045/1044, 1105/1104, 1275/1274, 1496/1495
Mapping: {{mapping| 1 8 12 18 11 1 6 11 7 16 | 0 -57 -86 -135 -67 24 -17 -60 -22 -99 }}

==== No-31's 37-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29.37
Comma list: 595/594, 760/759, 784/783, 925/924, 969/968, 1000/999, 1045/1044, 1105/1104, 1275/1274
Mapping: {{mapping| 1 8 12 18 11 1 6 11 7 16 15 | 0 -57 -86 -135 -67 24 -17 -60 -22 -99 -87 }}


= Semicanousmic clan

=== Deuteromere
Subgroup: 2.3.5.11
Comma list: 14641/14580
Mapping: {{mapping|legend=2| 1 0 2 1 | 0 1 2 2 | 0 0 -4 -1 }}

==== 2.3.5.11.17 subgroup
Subgroup: 2.3.5.11.17
Comma list: 1089/1088, 14641/14580

==== 2.3.5.11.17.19 subgroup
Subgroup: 2.3.5.11.17.19
Comma list: 1089/1088, 1216/1215, 1445/1444

=== Syndeute
Subgroup: 2.3.5.7.11
Comma list: 14641/14580, 19712/19683
Mapping: {{mapping|legend=1| 1 0 2 -9 1 | 0 1 2 7 2 | 0 0 -4 1 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1573/1568, 2080/2079, 14641/14580
Mapping: {{mapping| 1 0 2 -9 1 -15 | 0 1 2 7 2 10 | 0 0 -4 1 -1 4 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 442/441, 561/560, 715/714, 14641/14580
Mapping: {{mapping| 1 0 2 -9 1 -15 -4 | 0 1 2 7 2 10 6 | 0 0 -4 1 -1 4 -2 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 442/441, 561/560, 715/714, 1216/1215, 1445/1444
Mapping: {{mapping| 1 0 2 -9 1 -15 -4 -4 | 0 1 2 7 2 10 6 7 | 0 0 -4 1 -1 4 -2 -4 }}

=== Hemireiwa
Subgroup: 2.3.5.7.11
Comma list: 14641/14580, 160083/160000
Mapping: {{mapping|legend=1| 1 0 2 7 1 | 0 2 0 -6 3 | 0 0 4 7 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 14641/14580
Mapping: {{mapping| 1 0 2 7 1 1 | 0 2 0 -6 3 3 | 0 0 4 7 1 4 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 1001/1000, 14641/14580
Mapping: {{mapping| 1 0 2 7 1 1 -4 | 0 2 0 -6 3 3 10 | 0 0 4 7 1 4 2 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 676/675, 715/714, 1001/1000, 1216/1215, 1445/1444
Mapping: {{mapping| 1 0 2 7 1 1 -4 -4 | 0 2 0 -6 3 3 10 10 | 0 0 4 7 1 4 2 4 }}


= Nexus family

=== Nexus
Subgroup: 2.3.5.7.11
Comma list: [[1771561/1769472]]
Mapping: [{{val| 3 0 0 0 8}}, {{val| 0 2 0 0 1}}, {{val| 0 0 1 0 0}}, {{val| 0 0 0 1 0}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: [[1771561/1769472]], [[676/675]]
Mapping: [⟨3 0 0 0 8 -3], ⟨0 2 0 0 1 3], ⟨0 0 1 0 0 1], ⟨0 0 0 1 0 0]⟩


= Alphaxenic rank-3 clan

=== Alphaxenic
Subgroup: 2.3.5.7.11
Comma list: 131769/131072
Mapping: {{mapping|legend=1| 2 1 0 0 8 | 0 2 0 0 -1 | 0 0 1 0 0 | 0 0 0 1 0 }}

=== Rabic
Subgroup: 2.3.5.7.11
Comma list: 243/242, 131769/131072
Mapping: {{mapping|legend=1| 24 38 0 0 83 | 0 0 1 0 0 | 0 0 0 1 0 }}


= Mercator family

=== Mercator
Subgroup: 2.3.5
Comma list: {{monzo| -84 53 }}
Mapping: [{{val| 53 84 0 }}, {{val| 0 0 1 }}]

=== Schismerc
Subgroup: 2.3.5.7
Comma list: 15625/15552, 32805/32768
Mapping: [{{val| 53 84 123 0 }}, {{val| 0 0 0 1 }}]

==== Cartography
Subgroup: 2.3.5.7.11
Comma list: 385/384, 6250/6237, 19712/19683
Mapping: [{{val| 53 84 123 0 332 }}, {{val| 0 0 0 1 -1 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 625/624, 19712/19683
Mapping: [{{val| 53 84 123 0 332 196 }}, {{val| 0 0 0 1 -1 0 }}

==== Pentacontatritonic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 15625/15552, 32805/32768
Mapping: [{{val| 53 84 123 0 481 }}, {{val| 0 0 0 1 -2 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 4096/4095, 13750/13689
Mapping: [{{val| 53 84 123 0 481 345 }}, {{val| 0 0 0 1 -2 1 }}

==== Boiler
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 15625/15552, 32805/32768
Mapping: [{{val| 106 168 246 0 69 }}, {{val| 0 0 0 1 1 }}]

=== Joliet
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1728/1715, 3125/3087
Mapping: [{{val| 53 84 123 149 0 }}, {{val| 0 0 0 0 1 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 325/324, 640/637
Mapping: [{{val| 53 84 123 149 0 196 }}, {{val| 0 0 0 0 1 0 }}]

=== Iodine
Subgroup: 2.3.5.7
Comma list: {{monzo| -19 14 -5 3 }}, {{monzo| 8 3 -20 12 }}
Mapping: [{{val| 53 84 2 -53 }}, {{val| 0 0 3 5 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 160083/160000, 820125/819896, 4302592/4296875
Mapping: [{{val| 53 84 2 -53 143 }}, {{val| 0 0 3 5 1 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 6656/6655, 34398/34375, 43904/43875, 59535/59488
Mapping: [{{val| 53 84 2 -53 143 -46 }}, {{val| 0 0 3 5 1 6 }}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1701/1700, 6656/6655, 8624/8619, 12376/12375, 14875/14872
Mapping: [{{val| 53 84 2 -53 143 -46 257 }}, {{val| 0 0 3 5 1 6 -1 }}]


= Ripple family

=== Ripple
Subgroup: 2.3.5
Comma list: 6561/6250
Mapping: {{mapping|legend=1| 1 2 3 | 0 -5 -8 }}

==== Overview to extensions

=== Septimal ripple
Subgroup: 2.3.5.7
Comma list: [[126/125]], [[405/392]]
Mapping: {{mapping|legend=1| 1 2 3 4 | 0 -5 -8 -14 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: [[45/44]], [[99/98]], [[126/125]]
Mapping: {{mapping| 1 2 3 4 5 | 0 -5 -8 -14 -18 }}

=== Rip
Subgroup: 2.3.5.7
Comma list: 36/35, 2560/2401
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -5 -8 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 80/77, 126/121
Mapping: {{mapping| 1 2 3 3 4 | 0 -5 -8 -2 -6 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 40/39, 66/65, 147/143
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -5 -8 -2 -6 -3 }}

=== Hemiripple
Subgroup: 2.3.5.7
Comma list: 49/48, 6561/6250
Mapping: {{mapping|legend=1| 1 2 3 3 | 0 -10 -16 -5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 121/120, 567/550
Mapping: {{mapping| 1 2 3 3 4 | 0 -10 -16 -5 -13 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 121/120, 351/350
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -10 -16 -5 -13 -7 }}

=== Cohemiripple
Subgroup: 2.3.5.7
Comma list: 245/243, 1323/1250
Mapping: {{mapping|legend=1| 1 -3 -5 -5 | 0 10 16 17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 77/75, 243/242, 245/242
Mapping: {{mapping| 1 -3 -5 -5 -8 | 0 10 16 17 25 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 77/75, 147/143, 243/242
Mapping: {{mapping| 1 -3 -5 -5 -8 -5 | 0 10 16 17 25 19 }}


= Smate family

=== Smate
Subgroup: 2.3.5
Comma list: 2048/1875
Mapping: {{mapping|legend=1| 1 -1 3 | 0 4 -1 }}

=== Septimal smate
Subgroup: 2.3.5.7
Comma list: 36/35, 2048/1875
Mapping: {{mapping|legend=1| 1 -1 3 -3 | 0 4 -1 9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 56/55, 243/242
Mapping: {{mapping| 1 -1 3 -3 -3 | 0 4 -1 9 10 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 36/35, 56/55, 243/242
Mapping: {{mapping| 1 -1 3 -3 -3 -5 | 0 4 -1 9 10 -2 }}

=== Hemismate
Subgroup: 2.3.5.7
Comma list: 256/245, 392/375
Mapping: {{mapping|legend=1| 1 -5 4 2 | 0 8 -2 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 77/75, 256/245
Mapping: {{mapping| 1 -5 4 2 1 | 0 8 -2 1 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 56/55, 77/75, 256/245
Mapping: {{mapping| 1 -5 4 2 1 7 | 0 8 -2 1 3 -4 }}


= Cloudy clan

=== Coblack
Subgroup: 2.3.5.7
Comma list: 126/125, 16807/16384
Mapping: {{mapping|legend=1| 5 1 7 14 | 0 3 2 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 385/384
Mapping: {{mapping| 5 1 7 14 15 | 0 3 2 0 1 }}

=== Decic
Subgroup: 2.3.5.7
Comma list: 225/224, 16807/16384
Mapping: {{mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 3087/3025
Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 2200/2197
Mapping: {{mapping| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
Mapping: {{mapping| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}

==== Splendecic
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1617/1600, 2401/2376
Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 1001/1000, 1188/1183
Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}

==== Prodecic
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 5929/5832
Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 275/273, 5929/5832
Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
Mapping: {{mapping| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}

=== Pentadecal
Subgroup: 2.3.5.7
Comma list: 875/864, 16807/16384
Mapping: {{mapping|legend=1| 15 0 11 42 | 0 1 1 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1372/1331
Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 1372/1331
Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}

==== Quindecal
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 875/864
Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 196/195, 352/351, 875/864
Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}

=== Quinkee
Subgroup: 2.3.5.7
Comma list: 1029/1000, 6144/6125
Mapping: {{mapping|legend=1| 5 9 12 14 | 0 -3 -1 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 1029/1000
Mapping: {{mapping| 5 9 12 14 18 | 0 -3 -1 0 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 637/625
Mapping: {{mapping| 5 9 12 14 18 20 | 0 -3 -1 0 -2 -4 }}

=== References


= Varunismic temperaments

=== Essence
Subgroup: 2.3.5.7
Comma list: 321489/320000, 823543/820125
Mapping: {{mapping|legend=1| 2 10 27 23 | 0 -11 -36 -28 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 456533/455625
Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 729/728, 847/845, 1001/1000
Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }}

=== Octowerck
Subgroup: 2.3.5.7
Comma list: 321489/320000, 420175/419904
Mapping: {{mapping|legend=1| 8 0 -11 14 | 0 3 7 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 41503/41472
Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 729/728, 1001/1000, 6656/6655
Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}

===== Octowerckis
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440, 2197/2187
Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}


= Compton family

=== Compton
Subgroup: 2.3.5
Comma list: 531441/524288
Mapping: {{mapping|legend=1| 12 19 0 | 0 0 1 }}

=== Septimal compton
Subgroup: 2.3.5.7
Comma list: 225/224, 250047/250000
Mapping: {{mapping|legend=1| 12 19 0 -22 | 0 0 1 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 4375/4356
Mapping: {{mapping| 12 19 0 -22 -42 | 0 0 1 2 3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 364/363, 441/440
Mapping: {{mapping| 12 19 0 -22 -42 -67 | 0 0 1 2 3 4 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440
Mapping: {{mapping| 12 19 0 -22 -42 -67 49 | 0 0 1 2 3 4 0 }}

===== Comptone
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 441/440, 1001/1000
Mapping: {{mapping| 12 19 0 -22 -42 100 | 0 0 1 2 3 -2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440
Mapping: {{mapping| 12 19 0 -22 -42 100 49 | 0 0 1 2 3 -2 0 }}

=== Catler
Subgroup: 2.3.5.7
Comma list: 81/80, 128/125
Mapping: {{mapping|legend=1| 12 19 28 0 | 0 0 0 1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 81/80, 99/98, 128/125
Mapping: {{mapping| 12 19 28 0 -26 | 0 0 0 1 2 }}

==== Catlat
Subgroup: 2.3.5.7.11
Comma list: 81/80, 128/125, 540/539
Mapping: {{mapping| 12 19 28 0 109 | 0 0 0 1 -2 }}

==== Catnip
Subgroup: 2.3.5.7.11
Comma list: 56/55, 81/80, 128/125
Mapping: {{mapping| 12 19 28 0 8 | 0 0 0 1 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 66/65, 81/80, 105/104
Mapping: {{mapping| 12 19 28 0 8 11 | 0 0 0 1 1 1 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 51/50, 56/55, 66/65, 81/80, 105/104
Mapping: {{mapping| 12 19 28 0 8 11 49 | 0 0 0 1 1 1 0 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 51/50, 56/55, 66/65, 76/75, 81/80, 96/95
Mapping: {{mapping| 12 19 28 0 8 11 49 51 | 0 0 0 1 1 1 0 0 }}

===== Duodecic
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 81/80, 91/90, 128/125
Mapping: {{mapping| 12 19 28 0 8 78 | 0 0 0 1 1 -1 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 51/50, 56/55, 81/80, 91/90, 128/125
Mapping:{{mapping| 12 19 28 0 8 78 49 | 0 0 0 1 1 -1 0 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95
Mapping: {{mapping| 12 19 28 0 8 78 49 51 | 0 0 0 1 1 -1 0 0 }}

=== Duodecim
Subgroup: 2.3.5.7.11
Comma list: 36/35, 50/49, 64/63
Mapping: {{mapping|legend=1| 12 19 28 34 0 | 0 0 0 0 1 }}

=== Hours
Subgroup: 2.3.5.7
Comma list: 19683/19600, 33075/32768
Mapping: {{mapping|legend=1| 24 38 0 123 | 0 0 1 -1 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384, 9801/9800
Mapping: {{mapping| 24 38 0 123 83 | 0 0 1 -1 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 364/363, 385/384
Mapping: {{mapping| 24 38 0 123 83 33 | 0 0 1 -1 0 1 }}

=== Gamelstearn
Subgroup: 2.3.5.7
Comma list: 1029/1024, 118098/117649
Mapping: {{mapping|legend=1| 36 57 0 101 | 0 0 1 0 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1029/1024, 4000/3993
Mapping: {{mapping| 36 57 0 101 41 | 0 0 1 0 1 }}

=== Omicronbeta
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 385/384, 4000/3993
Mapping: {{mapping|legend=1| 72 114 167 202 249 0 | 0 0 0 0 0 1 }}


= Mirwomo temperaments

=== Caleb
Subgroup: 2.3.5.7
Comma list: 33075/32768, 250047/250000
Mapping: {{mapping|legend=1| 3 -1 6 18 | 0 6 1 -10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4125/4096, 4375/4356
Mapping: {{mapping| 3 -1 6 18 19 | 0 6 1 -10 -9 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 364/363, 441/440, 625/624
Mapping: {{mapping| 3 -1 6 18 19 13 | 0 6 1 -10 -9 -2 }}


= Mistismic temperaments

=== Neutron
Subgroup: 2.3.5.7
Comma list: 458752/455625, 40353607/39813120
Mapping: [{{val| 7 12 15 20 }}, {{val| 0 -5 7 -2 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 166012/164025, 585640/583443
Mapping: [{{val| 7 12 15 20 26 }}, {{val| 0 -5 7 -2 -10 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 352/351, 10192/10125, 50421/50336
Mapping: [{{val| 7 12 15 20 26 -10 }}, {{val| 0 -5 7 -2 -10 5 }}]


= Hewuermera temperaments

=== Hemidimfi
Subgroup: 2.3.5.7
Comma list: 589824/588245, 2460375/2458624
Mapping: [{{val|1 -4 14 -1}}, {{val|0 22 -46 15}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 12005/11979, 16384/16335
Mapping: [{{val|1 -4 14 -1 6}}, {{val|0 22 -46 15 -10}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675, 4096/4095
Mapping: [{{val|1 -4 14 -1 6 7}}, {{val|0 22 -46 15 -10 -13}}]


= Septiennealimmal clan

=== No-five septiennealimmal
Subgroup: 2.3.7
Comma list: 40353607/40310784
Mapping: {{mapping|legend=2| 9 0 11 | 0 1 1 }}

==== Ennea
Subgroup: 2.3.7.11
Comma list: 41503/41472, 43923/43904
Mapping: {{mapping| 9 0 11 24 | 0 2 2 1 }}

=== Ennealimmal
Subgroup: 2.3.5.7
Comma list: 2401/2400, 4375/4374
Mapping: {{mapping|legend=1| 9 1 1 12 | 0 2 3 2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 5632/5625
Mapping: {{mapping| 9 1 1 12 -75 | 0 2 3 2 16 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 4096/4095, 4375/4374
Mapping: {{mapping| 9 1 1 12 -75 93 | 0 2 3 2 16 -9 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 1001/1000, 1716/1715, 4096/4095, 4375/4374
Mapping: {{mapping| 9 1 1 12 -75 93 -3 | 0 2 3 2 16 -9 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 715/714, 1001/1000, 1216/1215, 1716/1715, 4096/4095, 4375/4374
Mapping: {{mapping| 9 1 1 12 -75 93 -3 -48 | 0 2 3 2 16 -9 6 13 }}

===== Ennealimmalis
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4375/4374, 5632/5625
Mapping: {{mapping| 9 1 1 12 -75 -106 | 0 2 3 2 16 21 }}

==== Ennealimmia
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 131072/130977
Mapping: {{mapping| 9 1 1 12 124 | 0 2 3 2 -14 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095, 4375/4374
Mapping: {{mapping| 9 1 1 12 124 93 | 0 2 3 2 -14 -9 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1225/1224, 1701/1700, 2401/2400, 4096/4095
Mapping: {{mapping| 9 1 1 12 124 93 -3 | 0 2 3 2 -14 -9 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 936/935, 1216/1215, 1225/1224, 1701/1700, 1729/1728, 2401/2400
Mapping: {{mapping| 9 1 1 12 124 93 -3 -48 | 0 2 3 2 -14 -9 6 13 }}

==== Ennealimnic
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 4375/4356
Mapping: {{mapping| 9 1 1 12 -2 | 0 2 3 2 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440, 625/624
Mapping: {{mapping| 9 1 1 12 -2 -33 | 0 2 3 2 5 10 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 375/374, 441/440, 595/594
Mapping: {{mapping| 9 1 1 12 -2 -33 -3 | 0 2 3 2 5 10 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 243/242, 364/363, 375/374, 441/440, 513/512, 595/594
Mapping: {{mapping| 9 1 1 12 -2 -33 -3 78  | 0 2 3 2 5 10 6 -6 }}

===== Ennealim
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 243/242, 325/324, 441/440
Mapping: {{mapping| 9 1 1 12 -2 20 | 0 2 3 2 5 2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 243/242, 325/324, 441/440
Mapping: {{mapping| 9 1 1 12 -2 20 -3 | 0 2 3 2 5 2 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 169/168, 221/220, 243/242, 325/324, 441/440
Mapping: {{mapping| 9 1 1 12 -2 20 -3 25 | 0 2 3 2 5 2 6 2 }}

==== Ennealiminal
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 4375/4374
Mapping: {{mapping| 9 1 1 12 51 | 0 2 3 2 -3 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 385/384, 1375/1372
Mapping: {{mapping| 9 1 1 12 51 20 | 0 2 3 2 -3 2 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 221/220, 325/324, 385/384, 1375/1372
Mapping: {{mapping| 9 1 1 12 51 20 50 | 0 2 3 2 -3 2 -2 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 153/152, 169/168, 221/220, 325/324, 385/384, 1375/1372
Mapping: {{mapping| 9 1 1 12 51 20 50 25 | 0 2 3 2 -3 2 -2 2 }}

==== Hemiennealimmal
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 4375/4374
Mapping: {{mapping| 18 0 -1 22 48 | 0 2 3 2 1 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715, 3025/3024
Mapping: {{mapping| 18 0 -1 22 48 -19 | 0 2 3 2 1 6 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 1001/1000, 1716/1715, 3025/3024
Mapping: {{mapping| 18 0 -1 22 48 -19 -12 | 0 2 3 2 1 6 6 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 676/675, 715/714, 1001/1000, 1331/1330, 1716/1715, 3025/3024
Mapping: {{mapping| 18 0 -1 22 48 -19 -12 48 105 | 0 2 3 2 1 6 6 -2 }}

===== Semihemiennealimmal
Subgroup: 2.3.5.7.11.13
Comma list: 2401/2400, 3025/3024, 4225/4224, 4375/4374
Mapping: {{mapping| 18 0 -1 22 48 88 | 0 4 6 4 2 -3 }}

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2401/2400, 2431/2430, 3025/3024, 4225/4224, 4375/4374
Mapping: {{mapping| 18 0 -1 22 48 88 -119 | 0 4 6 4 2 -3 27 }}

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 2401/2400, 2431/2430, 2926/2925, 3025/3024, 4225/4224, 4375/4374
Mapping: {{mapping| 18 0 -1 22 48 88 -119 -2 | 0 4 6 4 2 -3 27 11 }}

==== Semiennealimmal
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4000/3993, 4375/4374
Mapping: {{mapping| 9 3 4 14 18 | 0 6 9 6 7 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1575/1573, 2080/2079, 2401/2400, 4375/4374
Mapping: {{mapping| 9 3 4 14 18 -8 | 0 6 9 6 7 22 }}

==== Quadraennealimmal
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 234375/234256
Mapping: {{mapping| 9 1 1 12 -7 | 0 8 12 8 23 }}

==== Trinealimmal
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 2097152/2096325
Mapping: {{mapping| 27 1 0 34 177 | 0 2 3 2 -4 }}

==== Rhodium
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 117440512/117406179
Mapping: {{mapping| 45 1 -1 56 226 | 0 2 3 2 -2 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2401/2400, 4225/4224, 4375/4374, 6656/6655
Mapping: {{mapping| 45 1 -1 56 226 272 | 0 2 3 2 -2 -3 }}

=== Undecentic
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3136/3125, 4375/4374
Mapping: {{mapping|legend=1| 99 157 230 278 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 2401/2400, 3136/3125
Mapping: {{mapping| 99 157 230 278 0 24 | 0 0 0 0 1 1 }}

=== Schisennealimmal
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 32805/32768
Mapping: {{mapping|legend=1| 171 271 397 480 0 | 0 0 0 0 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 729/728, 2205/2197, 2401/2400
Mapping: {{mapping| 171 271 397 480 0 633 | 0 0 0 0 1 0 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 729/728, 833/832, 1225/1224, 2205/2197
Mapping: {{mapping| 171 271 397 480 0 633 699 | 0 0 0 0 1 0 0 }}

==== Schisennealimmic
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4375/4374, 32805/32768
Mapping: {{mapping| 171 271 397 480 0 41 | 0 0 0 0 1 1 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1225/1224, 1701/1700, 2025/2023, 11271/11264
Mapping: {{mapping| 171 271 397 480 0 41 699 | 0 0 0 0 1 1 0 }}

=== Lunennealimmal
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 274877906944/274658203125
Mapping: {{mapping|legend=1| 441 699 1024 1238 1526 | 0 0 0 0 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2401/2400, 4096/4095, 4375/4374, 85750/85683
Mapping: {{mapping| 441 699 1024 1238 1526 1632 | 0 0 0 0 -1 0 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2401/2400, 4096/4095, 4375/4374, 8624/8619, 14161/14157
Mapping: {{mapping| 441 699 1024 1238 1526 1632 1803 | 0 0 0 0 -1 0 -1 }}

=== Other subgroup extensions

==== Septiennealic (2.3.7.13)
Subgroup: 2.3.7.13
Comma list: 169/168, 31213/31104
Mapping: {{mapping| 9 0 11 19 | 0 1 1 1 }}


= Nexus clan

=== Tribilo
Subgroup: 2.3.11
Comma list: 1771561/1769472
Mapping: {{mapping|legend=2| 3 0 8 | 0 2 1 }}

=== Triblet
Subgroup: 2.3.11.13
Comma list: 352/351, 1771561/1769472
Mapping: {{mapping|legend=2| 3 0 8 23 | 0 2 1 -5 }}

=== Trilobite
Subgroup: 2.3.11.13
Comma list: 85293/85184, 1771561/1769472
Mapping: {{mapping|legend=2| 3 0 8 42 | 0 2 1 -13 }}


= Pentacircle clan

=== Parapythic
Subgroup: 2.3.7.11
Comma list: 896/891
Mapping: {{mapping|legend=2| 1 0 0 7 | 0 1 0 -4 | 0 0 1 1 }}

==== Overview to extensions

===== Subgroup extensions

===== Full 11-limit extensions

==== Parapyth
Subgroup: 2.3.7.11.13
Comma list: 352/351, 364/363
Mapping: {{mapping| 1 0 0 7 12 | 0 1 0 -4 -7 | 0 0 1 1 1 }}

===== Etypyth
Subgroup: 2.3.7.11.13.17
Comma list: 352/351, 364/363, 442/441
Mapping: {{mapping| 1 0 0 7 12 -13 | 0 1 0 -4 -7 9 | 0 0 1 1 1 1 }}

=== Terrapyth
Subgroup: 2.3.5.7.11
Comma list: 896/891, 585640/583443
Mapping: {{mapping|legend=1| 1 0 -31 0 7 | 0 1 21 0 -4 | 0 0 0 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 9295/9261
Mapping: {{mapping| 1 0 -31 0 7 12 | 0 1 0 21 0 4 -7 | 0 0 0 1 1 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 364/363, 442/441, 715/714
Mapping: {{mapping| 1 0 -31 0 7 12 -13 | 0 1 0 21 0 4 -7 9 | 0 0 0 1 1 1 1 1 }}

=== Pentafrost
Subgroup: 2.3.5.7.11
Comma list: 245/242, 896/891
Mapping: {{mapping|legend=1| 1 0 15 0 7 | 0 1 -8 0 -4 | 0 0 0 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 245/242, 352/351
Mapping: {{mapping| 1 0 15 0 7 12 | 0 1 -8 0 -4 -7 | 0 0 0 1 1 1 }}

==== Permafrost
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 245/242, 896/891
Mapping: {{mapping| 1 0 15 0 7 -3 | 0 1 -8 0 -4 6 | 0 0 0 1 1 -1 }}

=== Tolerant
Subgroup: 2.3.5.7.11
Comma list: 896/891, 2200/2187
Mapping: {{mapping|legend=1| 1 0 0 -10 -3 | 0 1 0 11 7 | 0 0 1 -2 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363
Mapping: {{mapping| 1 0 0 -10 -3 2 | 0 1 0 11 7 4 | 0 0 1 -2 -2 -2 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 325/324, 352/351, 364/363
Mapping: {{mapping| 1 0 0 -10 -3 2 8 | 0 1 0 11 7 4 -1 | 0 0 1 -2 -2 -2 -1 }}

=== Kujuku
Subgroup: 2.3.5.7.11
Comma list: 896/891, 14700/14641
Mapping: {{mapping|legend=1| 1 0 0 -13 -6 | 0 2 0 17 9 | 0 0 1 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 676/675
Mapping: {{mapping| 1 0 0 -13 -6 -1 | 0 2 0 17 9 3 | 0 0 1 1 1 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 364/363, 676/675
Mapping: {{mapping| 1 0 0 -13 -6 -1 8 | 0 2 0 17 9 3 -2 | 0 0 1 1 1 1 -1 }}

=== Trienparapyth
Subgroup: 2.3.5.7.11
Comma list: 896/891, 3388/3375
Mapping: {{mapping|legend=1| 1 2 0 2 1 | 0 -3 0 -11 1 | 0 0 1 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 1001/1000
Mapping: {{mapping| 1 2 0 2 1 0 | 0 -3 0 -11 1 10 | 0 0 1 1 1 1 }}

==== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 286/285, 352/351, 364/363, 400/399
Mapping: {{mapping| 1 2 0 2 1 0 0 | 0 -3 0 -11 1 10 14 | 0 0 1 1 1 1 1 }}

==== 2.3.5.7.11.13.19.23 subgroup
Subgroup: 2.3.5.7.11.13.19.23
Comma list: 208/207, 286/285, 352/351, 364/363, 400/399
Mapping: {{mapping| 1 2 0 2 1 0 0 0 | 0 -3 0 -11 1 10 14 16 | 0 0 1 1 1 1 1 1 }}


= Ptolemismic clan

=== Ptolemic
Subgroup: 2.3.5.11
Comma list: 100/99
Mapping: {{mapping|legend=2| 1 0 0 2 | 0 1 0 -2 | 0 0 1 2 }}

=== Apollo

=== Keemic

=== Thrasher

=== Ares


= Gariboh clan

=== Sirius
Subgroup: 3.5.7
Comma list: 3125/3087
Mapping: {{mapping|legend=2| 1 1 1 | 0 3 5 }}

==== Overview to extensions


= Countercomp family

=== Countercomp
Subgroup: 2.3.5
Comma list: {{monzo| 65 -41 }}
Mapping: [{{val| 41 65 0 }}, {{val| 0 0 1 }}]

=== Gamelacomp
Subgroup: 2.3.5.7
Comma list: 1029/1024, 537824/531441
Mapping: [{{val| 41 65 0 115 }}, {{val| 0 0 1 0 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 537824/531441
Mapping: [{{val| 41 65 0 115 237 }}, {{val| 0 0 1 0 -1 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 59150/59049
Mapping: [{{val| 41 65 0 115 237 247 }}, {{val| 0 0 1 0 -1 -1 }}]

=== Mermacomp
Subgroup: 2.3.5.7
Comma list: 5120/5103, 2500000/2470629
Mapping: [{{val| 41 65 0 20 }}, {{val| 0 0 1 1 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5120/5103, 75625/75264
Mapping: [{{val| 41 65 0 20 237 }}, {{val| 0 0 1 1 -1 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 75625/75264
Mapping: [{{val| 41 65 0 20 237 247 }}, {{val| 0 0 1 1 -1 -1 }}]

=== Hemicountercomp
Subgroup: 2.3.5.7
Comma list: 2401/2400, 52613349376/52301766015
Mapping: [{{val| 41 65 1 68 }}, {{val| 0 0 2 1 }}]

==== Hemicocomp
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 16384/16335, 19712/19683
Mapping: [{{val| 41 65 1 68 189 }}, {{val| 0 0 2 1 -1 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 3584/3575, 10648/10647
Mapping: [{{val| 41 65 1 68 189 246 }}, {{val| 0 0 2 1 -1 -2 }}]

==== Hemermacomp
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 59290/59049, 131072/130977
Mapping: [{{val| 41 65 1 68 236 }}, {{val| 0 0 2 1 -2 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095, 59290/59049
Mapping: [{{val| 41 65 1 68 236 293 }}, {{val| 0 0 2 1 -2 -3 }}]


= Hemfiness temperaments

=== Undesemi
Subgroup: 2.3.5.7
Comma list: 4096000/4084101, 95703125/95551488
Mapping: [{{val|1 5 5 1}}, {{val|0 -51 -40 27}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 180224/180075
Mapping: [{{val|1 5 5 1 5}}, {{val|0 -51 -40 27 -23}}]

=== Piracy
Subgroup: 2.3.5.7
Comma list: 4096000/4084101, 48828125/48771072
Mapping: [{{val|1 -6 0 9}}, {{val|0 49 15 -40}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 12005/11979, 16384/16335
Mapping: [{{val|1 -6 0 9 16}}, {{val|0 49 15 -40 -81}}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2205/2197, 12005/11979
Mapping: [{{val|1 -6 0 9 16 2}}, {{val|0 49 15 -40 -81 11}}]

===== Pirateship
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 1716/1715, 4096/4095, 6250/6237
Mapping: [{{val|1 -6 0 9 16 15}}, {{val|0 49 15 -40 -81 -73}}]


= Mitonismic temperaments

=== Meridic
Subgroup: 2.3.5.7
Comma list: 5250987/5242880, 2202927104/2197265625
Mapping: [{{val| 43 0 168 257 }}, {{val| 0 1 -1 -2 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 41503/41472, 172032/171875, 1240029/1239040
Mapping: [{{val| 43 0 168 257 -192 }}, {{val| 0 1 -1 -2 5 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2200/2197, 4096/4095, 21168/21125, 39366/39325
Mapping: [{{val| 43 0 168 257 -192 91 }}, {{val| 0 1 -1 -2 5 1 }}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 833/832, 1701/1700, 2200/2197, 4096/4095, 11016/11011
Mapping: [{{val| 43 0 168 257 -192 91 -165 }}, {{val| 0 1 -1 -2 5 1 5 }}]


= Keenanismic temperaments

=== Uniwiz
Subgroup: 2.3.5.7.11
Comma list: 385/384, 9801/9800
Mapping: {{mapping|legend=1| 2 1 0 7 8 | 0 2 0 3 -1 | 0 0 1 -1 0 }}

==== 2.3.5.7.11.17 subgroup
Subgroup: 2.3.5.7.11.17
Comma list: 289/288, 385/384, 561/560
Mapping: {{mapping| 2 1 0 7 8 6 | 0 2 0 3 -1 2 | 0 0 1 -1 0 0 }}

=== Tritiwiz
Subgroup: 2.3.5.7.11
Comma list: 385/384, 4000/3993
Mapping: {{mapping|legend=1| 1 2 0 8 1 | 0 -3 0 -4 1 | 0 0 1 -2 1 }}


= Passion family

=== Passion
Subgroup: 2.3.5
Comma list: 262144/253125
Mapping: {{mapping|legend=1| 1 2 2 | 0 -5 4 }}

==== Overview to extensions

=== Septimal passion
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/3087
Mapping: {{mapping|legend=1| 1 2 2 2 | 0 -5 4 10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 1375/1372
Mapping: {{mapping| 1 2 2 2 2 | 0 -5 4 10 18 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 196/195, 275/273
Mapping: {{mapping| 1 2 2 2 2 2 | 0 -5 4 10 18 21 }}

=== Passionate
Subgroup: 2.3.5.7
Comma list: 126/125, 131072/127575
Mapping: {{mapping|legend=1| 1 2 2 1 | 0 -5 4 22 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 8192/8019
Mapping: {{mapping| 1 2 2 1 1 | 0 -5 4 22 30 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 343/338, 364/363
Mapping: {{mapping| 1 2 2 1 1 1 | 0 -5 4 22 30 33 }}

===== Pash
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 1352/1331
Mapping: {{mapping| 1 2 2 1 1 0 | 0 -5 4 22 30 45 }}

=== Passive
Subgroup: 2.3.5.7
Comma list: 225/224, 256/245
Mapping: {{mapping|legend=1| 1 2 2 3 | 0 -5 4 -2 }}

=== Freivald
Subgroup: 2.3.5.7
Comma list: 6144/6125, 6272/6075
Mapping: {{mapping|legend=1| 1 -3 6 -5 | 0 10 -8 17 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2744/2673
Mapping: {{mapping| 1 -3 6 -5 3 | 0 10 -8 17 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 176/175, 512/507
Mapping: {{mapping| 1 7 -2 12 4 1 | 0 -10 8 -17 -1 5 }}


= Parkleiness temperaments

=== Majvamic
Subgroup: 2.3.5.7
Comma list: 1959552/1953125, 67108864/66976875
Mapping: [{{val|1 10 5 -32}}, {{val|0 -22 -7 91}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 46656/46585, 131072/130977
Mapping: [{{val|1 10 5 -32 31}}, {{val|0 -22 -7 91 -72}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095, 39366/39325
Mapping: [{{val|1 10 5 -32 31 19}}, {{val|0 -22 -7 91 -72 -40}}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 936/935, 1001/1000, 1156/1155, 4096/4095
Mapping: [{{val|1 10 5 -32 31 19 6}}, {{val|0 -22 -7 91 -72 -40 -5}}]

=== Octogintic
Subgroup: 2.3.5.7
Comma list: 1959552/1953125, 645700815/645657712
Mapping: [{{val|80 127 186 225}}, {{val|0 -1 -1 -2}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 46656/46585, 391314/390625
Mapping: [{{val|80 127 186 225 277}}, {{val|0 -1 -1 -2 -1}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 4225/4224, 4459/4455, 46656/46585
Mapping: [{{val|80 127 186 225 277 296}}, {{val|0 -1 -1 -2 -1 0}}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1001/1000, 1377/1375, 4225/4224, 4459/4455
Mapping: [{{val|80 127 186 225 277 296 327}}, {{val|0 -1 -1 -2 -1 0 0}}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 936/935, 969/968, 1001/1000, 1377/1375, 1521/1520, 3136/3135
Mapping: [{{val|80 127 186 225 277 296 327 340}}, {{val|0 -1 -1 -2 -1 0 0 -1}}]


= Limmic temperaments

=== Blackwood

==== 5-limit
Subgroup: 2.3.5
Comma list: 256/243
Mapping: {{mapping|legend=1| 5 8 0 | 0 0 1 }}

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 28/27, 49/48
Mapping: {{mapping|legend=1| 5 8 0 14 | 0 0 1 0 }}

===== Undecimal blackwood
Subgroup: 2.3.5.7.11
Comma list: 28/27, 49/48, 55/54
Mapping: {{mapping| 5 8 0 14 29 | 0 0 1 0 -1 }}

====== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 49/48, 55/54
Mapping: {{mapping| 5 8 0 14 29 7 | 0 0 1 0 -1 1 }}

===== Farrier
Subgroup: 2.3.5.7.11
Comma list: 28/27, 49/48, 77/75
Mapping: {{mapping| 5 8 0 14 -6 | 0 0 1 0 2 }}

====== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 49/48, 66/65
Mapping: {{mapping| 5 8 0 14 -6 7 | 0 0 1 0 2 1 }}

===== Ferrum
Subgroup: 2.3.5.7.11
Comma list: 28/27, 35/33, 49/48
Mapping: {{mapping| 5 8 0 14 6 | 0 0 1 0 1 }}

=== Blackweed
Subgroup: 2.3.11/7
Comma list: {{monzo| 8 -5 }} (256/243)
Mapping: {{mapping|legend=2| 5 8 0 | 0 0 1 }}


= Llywelynsmic clan

=== Llywelyn a.k.a. shoe
Subgroup: 2.5.7
Comma list: 4194304/4117715
Mapping: {{mapping|legend=2| 1 1 3 | 0 7 -1 }}
Mapping: {{mapping|legend=3| 1 0 1 3 | 0 0 7 -1 }}

==== 2.5.7.11 subgroup
Subgroup: 2.5.7.11
Comma list: 176/175, 1310720/1294139

==== 2.5.7.11.13 subgroup
Subgroup: 2.5.7.11.13
Comma list: 176/175, 640/637, 847/845

==== 2.5.7.11.13.17 subgroup
Subgroup: 2.5.7.11.13.17
Comma list: 176/175, 221/220, 640/637, 847/845


= Semiporwellismic clan

=== Semiporwellic
Subgroup: 2.3.5.11
Comma list: 16384/16335
Mapping: {{mapping|legend=2| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 }}


= No-elevens subgroup temperaments

=== Ultrapyth
Subgroup: 2.3.5.7.13
Comma list: 64/63, 91/90, 4394/4375
Mapping: [{{val|1 2 8 2 11}}, {{val|0 -1 -14 2 -18}}]

=== Beet
Subgroup: 2.3.5.7.13
Comma list: 64/63, 91/90, 196/195
Mapping: {{mapping| 1 1 5 4 4 | 0 2 -9 -4 -1 }}

=== Meanpop
Subgroup: 2.3.5.7.13
Comma list: 81/80, 105/104, 126/125
Mapping: [{{val|1 2 4 7 10}}, {{val|0 -1 -4 -10 -15}}]

=== Sensi (aka sensation)
Subgroup: 2.3.5.7.13
Comma list: 91/90, 126/125, 169/168
Mapping: [{{val|1 6 8 11 10}}, {{val|0 -7 -9 -13 -10}}]

=== Decic
Subgroup: 2.3.5.7.13
Comma list: 105/104, 196/195, 8281/8192
Mapping: [{{val|10 16 23 28 37}}, {{val|0 -1 1 0 0}}]

==== 2.3.5.7.13.17
Subgroup: 2.3.5.7.13.17
Comma list: 105/104, 170/169, 196/195, 289/288
Mapping: [{{val|10 16 23 28 37 41}}, {{val|0 -1 1 0 0 -1}}]

=== Quartonic
Subgroup: 2.3.5.7.13
Comma list: 169/168, 325/324, 640/637
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -11 -18 -5 -8}}]

=== Unicorn
Subgroup: 2.3.5.7.13
Comma list: 126/125, 196/195, 676/675
Mapping: [{{val|1 2 3 4 5}}, {{val|0 -8 -13 -23 -25}}]

=== Septidiasemi
Subgroup: 2.3.5.7.13
Comma list: 2205/2197, 2401/2400, 4096/4095
Mapping: [{{val|1 -1 6 4 4}}, {{val|0 26 -37 -12 -3}}]

==== 2.3.5.7.13.17
Subgroup: 2.3.5.7.13.17
Comma list: 833/832, 1275/1274, 2025/2023, 2205/2197
Mapping: [{{val|1 -1 6 4 4 2}}, {{val|0 26 -37 -12 -3 21}}]

=== Pontiac
Subgroup: 2.3.5.7.13
Comma list: 625/624, 729/728, 4096/4095
Mapping: [{{val|1 2 -1 19 -10}}, {{val|0 -1 8 -39 33}}]

==== 2.3.5.7.13.17
Subgroup: 2.3.5.7.13.17
Comma list: 625/624, 729/728, 1225/1224, 2880/2873
Mapping: [{{val|1 2 -1 19 -10 29}}, {{val|0 -1 8 -39 33 -60}}]

=== Mitonic
Subgroup: 2.3.5.7.13
Comma list: 4096/4095, 4375/4374, 13720/13689
Mapping: [{{val|1 -1 -3 6 11}}, {{val|0 17 35 -21 -48}}]

==== 2.3.5.7.13.17
Subgroup: 2.3.5.7.13.17
Comma list: 833/832, 1225/1224, 1701/1700, 4096/4095
Mapping: [{{val|1 -1 -3 6 11 5}}, {{val|0 17 35 -21 -48 -6}}]

=== Tertiaseptal
Subgroup: 2.3.5.7.13
Comma list: 625/624, 2401/2400, 4096/4095
Mapping: [{{val|1 3 2 3 1}}, {{val|0 -22 5 -3 42}}]

==== 2.3.5.7.13.17
Subgroup: 2.3.5.7.13.17
Comma list: 625/624, 833/832, 1225/1224, 4096/4095
Mapping: [{{val|1 3 2 3 1 1}}, {{val|0 -22 5 -3 42 48}}]

=== Oquatonic
Subgroup: 2.3.5.7.13
Comma list: 625/624, 4096/4095, 10985/10976
Mapping: [{{val|28 44 65 79 104}}, {{val|0 1 0 -1 -1}}]

=== Garibaldia
Subgroup: 2.3.5.7.17
Comma list: 120/119, 225/224, 1458/1445
Mapping: [{{val|1 2 -1 -3 7}}, {{val|0 -1 8 14 -7}}]

==== 2.3.5.7.17.19
Subgroup: 2.3.5.7.17.19
Comma list: 120/119, 171/170, 190/189, 225/224
Mapping: [{{val|1 2 -1 -3 7 3}}, {{val|0 -1 8 14 -7 3}}]

=== Devisemi
Subgroup: 2.3.5.7.19
Comma list: 190/189, 245/243, 361/360
Mapping: [{{val|1 1 1 2 3}}, {{val|0 8 18 11 17}}]

=== Pontia
Subgroup: 2.3.5.7.19
Comma list: 361/360, 513/512, 4375/4374
Mapping: [{{val|1 2 -1 19 3}}, {{val|0 -1 8 -39 3}}]

=== Cotoneum
Subgroup: 2.3.5.7.19
Comma list: 343/342, 1216/1215, 48013/48000
Mapping: [{{val|1 2 -18 -3 -14}}, {{val|0 -1 49 14 44}}]

=== Devimarvel (rank 3)
Subgroup: 2.3.5.7.19
Comma list: 225/224, 400/399
Mapping: [{{val|1 0 0 -5 9}}, {{val|0 1 0 2 -3}}, {{val|0 0 1 2 0}}]

=== Devichrome (rank 4)
Subgroup: 2.3.5.7.19
Comma list: [[400/399]]
Mapping: [{{val|1 0 0 0 4}}, {{val|0 1 0 0 -1}}, {{val|0 0 1 0 2}}, {{val|0 0 0 1 -1}}]


= No-sevens subgroup temperaments

=== 2.3.5.11 temperaments

==== Twentcufo
Subgroup: 2.3.5.11
Comma list: 8019/8000, 14641/14580
Mapping: [{{val|1 0 -2 0}}, {{val|0 11 30 24}}]

==== Emka
Subgroup: 2.3.5.11
Comma list: 4000/3993, 9453125/9437184
Mapping: [{{val|1 14 6 3}}, {{val|0 -27 -8 1}}]

===== 2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 625/624, 2200/2197, 4000/3993
Mapping: [{{val|1 14 6 3 6}}, {{val|0 -27 -8 1 -5}}]

==== Tremka
Subgroup: 2.3.5.11
Comma list: 6912/6875, 526153617/524288000
Mapping: [{{val|1 -4 -2 4}}, {{val|0 31 24 -3}}]

===== 2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 2200/2197, 3267/3250, 6656/6655
Mapping: [{{val|1 -4 -2 4 1}}, {{val|0 31 24 -3 15}}]

==== Yarman
Subgroup: 2.3.5.11
Comma list: 4000/3993, 390625000/387420489
Mapping: [{{val|1 2 3 4}}, {{val|0 -33 -54 -43}}]

===== 2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 325/324, 4000/3993, 85683/85184
Mapping: [{{val|1 2 3 4 4}}, {{val|0 -33 -54 -43 -24}}]

==== Superpine
Subgroup: 2.3.5.11
Comma list: 81/80, 1350/1331
Mapping: {{mapping| 1 2 4 5 | 0 -3 -12 -11 }}

===== 2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 81/80, 144/143, 975/968
Mapping: {{mapping| 1 2 4 5 | 0 -3 -12 -11 5 }}

==== Dicot

==== Mavila

==== Tetracot

==== Porkypine

==== Mohaha

==== Larry

==== Dequarter

==== Hypnotone

=== 2.3.5.13 temperaments

==== Majvam
Subgroup: 2.3.5.13
Comma list: 676/675, 127401984/126953125
Mapping: [{{val|1 10 5 19}}, {{val|0 -22 -7 -40}}]

===== 2.3.5.13.17
Subgroup: 2.3.5.13.17
Comma list: 676/675, 2601/2600, 24576/24565
Mapping: [{{val|1 10 5 19 6}}, {{val|0 -22 -7 -40 -5}}]

==== Tricot

==== Taylor

==== Vulture
Subgroup: 2.3.5.13
Comma list: 676/675, 256000/255879
Mapping: {{mapping|legend=2| 1 0 -6 -7 | 0 4 21 27 }}

===== 2.3.5.13.19
Subgroup: 2.3.5.13.19
Comma list: 676/675, 1216/1215, 20007/20000

=== 2.3.5.17 temperaments

==== Quintaleap

==== Quindromeda

==== Photia

==== Quintilischis

==== Srutal Archagall

=== 2.3.5.19 temperaments

==== Rarity
Subgroup: 2.3.5.19.23
Comma list: 1035/1024, 16875/16606, 192375/188416
Mapping: {{mapping|legend=2| 1 11 -10 -3 -2 | 0 -13 17 10 9 }}

==== Devisemi

==== Nestoria

==== Stützel

=== Higher-limit subgroup temperaments

==== Reversed marvel
Subgroup: 2.3.5.113
Comma list: 226/225
Mapping: {{mapping|legend=2|1 0 0 -1|0 1 0 2|0 0 1 2}}


= No-fives subgroup temperaments

=== Temperaments with a 2.3.7 gene

==== Archy

===== Supra

====== Supraphon

===== Suhajira

===== Flutterpyth
Subgroup: 2.3.7.11.13
Comma list: 64/63, 364/363, 1078/1053
Mapping: {{mapping| 1 0 6 21 34 | 0 1 -2 -11 -19 }}

====== 2.3.7.11.13.19 subgroup
Subgroup: 2.3.7.11.13.19
Comma list: 64/63, 209/208, 343/342, 364/363
Mapping: {{mapping| 1 0 6 21 34 17 | 0 1 -2 -11 -19 -8 }}

==== Semaphore

==== Slendric

==== Slendroschismic

===== Pentadecoid

==== Navy
Subgroup: 2.3.7
Comma list: 282429536481/281974669312
Mapping: {{mapping|legend=2| 1 1 0| 0 5 24 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 1331/1323, 19712/19683
Mapping: {{mapping| 1 1 0 1 | 0 5 24 21 }}

===== 2.3.7.11.13
Subgroup: 2.3.7.11.13
Comma list: 352/351, 729/728, 1331/1323
Mapping: {{mapping| 1 1 0 1 3 | 0 5 24 21 6 }}

==== Lee
Subgroup: 2.3.7
Comma list: 177147/175616
Mapping: {{mapping|legend=2| 1 0 -3 | 0 3 11 }}
Mapping: {{mapping|legend=3| 1 0 0 -3 | 0 3 0 11 }}

==== Buzzard

==== Hemif
Subgroup: 2.3.7
Comma list: 1605632/1594323
Mapping: {{mapping|legend=2| 1 1 -1 | 0 2 13 }}
Mapping: {{mapping|legend=3| 1 1 0 -1 | 0 2 0 13 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 243/242, 896/891
Mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}

====== 2.3.7.11.13
Subgroup: 2.3.7.11.13
Comma list: 144/143, 243/242, 364/363

====== Heartful
Subgroup: 2.3.7.11.19
Comma list: 243/242, 896/891, 1083/1078
Mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}

==== Hearts
Subgroup: 2.3.7
Comma list: 34451725707/34359738368
Mapping: {{mapping|legend=2| 1 1 5 | 0 4 -15 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 243/242, 65536/65219
Mapping: {{mapping| 1 1 5 2 | 0 4 -15 10 }}

===== 2.3.7.11.19
Subgroup: 2.3.7.11.19
Comma list: 243/242, 513/512, 1083/1078
Mapping: {{mapping| 1 1 5 2 6 | 0 4 -15 10 -12 }}

==== Magi
Subgroup: 2.3.7
Comma list: 537824/531441
Mapping: {{mapping|legend=2| 1 0 -1 | 0 5 12 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 896/891, 26411/26244
Mapping: {{mapping| 1 0 -1 6 | 0 5 12 -8 }}

====== Caspar
Subgroup: 2.3.7.11.13
Comma list: 144/143, 343/338, 729/728
Mapping: {{mapping| 1 0 -1 6 -2 | 0 5 12 -8 18 }}

======= Twenothology
Subgroup: 2.3.7.11.13.29
Comma list: 144/143, 232/231, 343/338, 729/728
Mapping: {{mapping| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}

====== Melchior
Subgroup: 2.3.7.11.13
Comma list: 352/351, 364/363, 26411/26244
Mapping: {{mapping| 1 0 -1 6 11 | 0 5 12 -8 -23 }}

====== Balthazar
Subgroup: 2.3.7.11.13
Comma list: 169/168, 896/891, 26411/26244
Mapping: {{mapping| 1 0 -1 6 1 | 0 10 24 -16 17 }}

===== Hogwarts
Subgroup: 2.3.7.29
Comma list: 784/783, 5887/5832
Mapping: {{mapping| 1 0 -1 2 | 0 5 12 9 }}

==== Skwares
Subgroup: 2.3.7
Comma list: 19683/19208
Mapping: {{mapping|legend=2| 1 -1 -3 | 0 4 9 }}
Mapping: {{mapping|legend=3| 1 -1 0 -3 | 0 4 0 9 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 99/98, 243/242
Mapping: {{mapping| 1 -1 -3 -3 | 0 4 9 10 }}

====== 2.3.7.11.13
Subgroup: 2.3.7.11.13
Comma list: 78/77, 99/98, 243/242
Mapping: {{mapping| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}

====== Skwairs
Subgroup: 2.3.7.11.13
Comma list: 99/98, 144/143, 243/242
Mapping: {{mapping| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}

====== Byhearted
Subgroup: 2.3.7.11.19
Comma list: 99/98, 243/242, 363/361
Mapping: {{mapping| 2 2 3 4 5 | 0 4 9 10 12 }}

==== Harrison
Subgroup: 2.3.7
Comma list: [[59049/57344]]
Mapping: {{mapping|legend=2| 1 0 -13 | 0 1 10 }}
Mapping: {{mapping|legend=3| 1 0 0 -13 | 0 1 0 10 }}

==== Bleu
Subgroup: 2.3.7
Comma list: 17496/16807
Mapping: {{mapping|legend=2| 1 1 2 | 0 5 7 }}
Mapping: {{mapping|legend=3| 1 1 0 2 | 0 5 0 7 }}

===== 2.3.7.11 subgroup
Subgroup: 2.3.7.11
Comma list: 99/98, 864/847
Mapping: {{mapping| 1 1 2 3 | 0 5 7 4 }}

===== 2.3.7.11.13 subgroup
Subgroup: 2.3.7.11.13
Comma list: 78/77, 99/98, 144/143
Mapping: {{mapping| 1 1 2 3 3 | 0 5 7 4 6 }}

==== Doublehearted
Subgroup: 2.3.7
Comma list: 5764801/5668704
Mapping: {{mapping|legend=2| 1 1 2 | 0 8 11 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 243/242, 2401/2376
Mapping: {{mapping| 1 1 2 2 | 0 8 11 20 }}

===== 2.3.7.11.19
Subgroup: 2.3.7.11.19
Comma list: 133/132, 243/242, 343/342
Mapping: {{mapping| 1 1 2 2 3 | 0 8 11 20 17 }}

==== Purpleheart
Subgroup: 2.3.7
Comma list: 2187/2048
Mapping: {{mapping|legend=2| 7 11 0 | 0 0 1 }}

==== Chrysanthemum
Subgroup: 2.3.7
Comma list: {{monzo| 83 -1 -29 }}
Mapping: {{mapping|legend=2| 1 -4 3 | 0 29 -1 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 43923/43904, 5767168/5764801
Mapping: {{mapping| 1 -4 3 5 | 0 29 -1 -8 }}

==== Leapfrog
Subgroup: 2.3.7
Comma list: 14680064/14348907
Mapping: {{mapping|legend=2| 1 0 -21 | 0 1 15 }}
Mapping: {{mapping|legend=3| 1 0 0 -21 | 0 1 0 15 }}

===== 2.3.7.11
Subgroup: 2.3.7.11
Comma list: 896/891, 1331/1323
Mapping: {{mapping| 1 0 -21 -14 | 0 1 15 11 }}

===== 2.3.7.11.13
Subgroup: 2.3.7.11.13
Comma list: 169/168, 352/351, 364/363
Mapping: {{mapping| 1 0 -21 -14 -9 | 0 1 15 11 8 }}

====== Skidoo
Subgroup: 2.3.7.11.13.23
Comma list: 169/168, 208/207, 352/351, 364/363
Mapping: {{mapping| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}

======= 2.3.7.11.13.23.29
Subgroup: 2.3.7.11.13.23.29
Comma list: 169/168, 208/207, 232/231, 352/351, 364/363
Mapping: {{mapping| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}

==== Superslendric
Subgroup: 2.3.7
Comma list: 17294403/16777216
Mapping: {{mapping|legend=2| 1 0 3 | 0 8 -1 }}

==== Hectosaros leap week
Subgroup: 2.3.7
Comma list: {{monzo| -50 -746 439 }}
Mapping: {{mapping|legend=2| 1 -126 -214 | 0 439 746 }}

===== 2.3.7.13 subgroup
Subgroup: 2.3.7.13
Comma list: {{monzo| -42 -2 -5 16 }}, {{monzo| 10 -46 29 -5 }}
Mapping: {{mapping| 1 -126 -214 -80 | 0 439 746 288 }}

===== 2.3.7.13.17 subgroup
Subgroup: 2.3.7.13.17
Comma list: 39337984/39328497, {{monzo| 0 -14 7 4 -3 }}, {{monzo| -18 -24 14 -1 5 }}
Mapping: {{mapping| 1 -126 -214 -80 -18 | 0 439 746 288 76 }}

===== 2.3.7.13.17.19 subgroup
Subgroup: 2.3.7.13.17.19
Comma list: 10081799/10077696, 10754912/10744731, 39337984/39328497, 480024727/480020256
Mapping: {{mapping| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }}

==== Heartland (rank 3)
Subgroup: 2.3.7.11.19
Comma list: 243/242, 1083/1078
Mapping: {{mapping|legend=2| 1 1 0 2 1 | 0 4 0 10 3 | 0 0 1 0 1 }}

=== Temperaments with a 2.3.11 gene

==== Neutral

===== Namo

==== Io
Subgroup: 2.3.11
Comma list: 33/32
Mapping: {{mapping|legend=2| 1 0 5 | 0 1 -1 }}

==== Infraug
Subgroup: 2.3.11
Comma list: 729/704
Mapping: {{mapping|legend=2| 1 0 -6 | 0 1 6 }}

===== 2.3.11.13
Subgroup: 2.3.11.13
Comma list: 144/143, 729/704

===== Aerophore
Subgroup: 2.3.11.19
Comma list: 363/361, 729/704

==== Paralimmal
Subgroup: 2.3.11
Comma list: 4096/3993
Mapping: {{mapping|legend=2| 1 0 4 | 0 3 -1 }}

===== Huxley
Subgroup: 2.3.11.13
Comma list: 512/507, 1352/1331
Mapping: {{mapping| 1 -3 5 6 | 0 6 -2 -3 }}

==== Glaishur
Subgroup: 2.3.11
Comma list: 10554638336/10460353203
Mapping: {{mapping|legend=2| 1 1 0 | 0 5 21 }}

===== 2.3.11.13
Subgroup: 2.3.11.13
Comma list: 352/351, 531674/531441
Mapping: {{mapping| 1 1 0 3 | 0 5 21 6 }}

=== Temperaments with a 2.3.13 gene

==== Threedic
Subgroup: 2.3.13
Comma list: 2197/2187
Mapping: {{mapping|legend=2| 1 0 0 | 0 3 7 }}

==== Ultraflat
Subgroup: 2.3.13
Comma list: 27/26
Mapping: {{mapping|legend=2| 1 0 -1 | 0 1 3 }}

==== Superflat
Subgroup: 2.3.13
Comma list: 1053/1024
Mapping: {{mapping|legend=2| 1 0 10 | 0 1 -4 }}

==== Shoal
Subgroup: 2.3.13
Comma list: 816293376/815730721
Mapping: {{mapping|legend=2| 1 -5 -7 | 0 8 13 }}

===== 2.3.13.23
Subgroup: 2.3.13.23
Comma list: 3888/3887, 12168/12167
Mapping: {{mapping| 1 -5 -7 -7 | 0 8 13 14 }}

==== Glacier
Subgroup: 2.3.13
Comma list: 373248/371293
Mapping: {{mapping|legend=2| 1 1 3 | 0 5 6 }}

=== Temperaments with a higher-limit gene

==== Semitonic
Subgroup: 2.3.17
Comma list: [[289/288]]
Mapping: {{mapping|legend=2| 2 0 5 | 0 1 1 }}

==== Boethian
Subgroup: 2.3.19
Comma list: 513/512
Mapping: {{mapping|legend=2| 1 0 9 | 0 1 -3 }}

==== Dog
Subgroup: 2.3.19
Comma list: 81/76
Mapping: {{mapping|legend=2| 1 0 -2 | 0 1 4 }}

==== Lipsett
Subgroup: 2.3.23
Comma list: 2187/2116
Mapping: {{mapping|legend=2| 1 0 -1 | 0 2 7 }}

==== Porpoise
Subgroup: 2.3.29
Comma list: 24576/24389
Mapping: {{mapping|legend=2| 1 2 5 | 0 -3 -1 }}

==== Sematology
Subgroup: 2.3.37
Comma list: 4107/4096
Mapping: {{mapping|legend=2| 1 0 6 | 0 2 -1 }}

==== Reversed mavila
Subgroup: 2.3.37
Comma list: 81/74
Mapping: {{mapping|legend=2| 1 0 -1 | 0 1 4 }}

==== Reversed meantone
Subgroup: 2.3.41
Comma list: 82/81
Mapping: {{mapping|legend=2| 1 0 -1 | 0 1 4 }}


= No-threes subgroup temperaments

=== Overview by mapping of 5

=== 2.5.7 temperaments

==== Frostburn
Subgroup: 2.5.7
Comma list: 78125/76832
Mapping: {{mapping|legend=2| 1 3 4 | 0 -4 -7 }}

===== 2.5.7.11
Subgroup: 2.5.7.11
Comma list: 245/242, 625/616
Mapping: {{mapping|legend=2| 1 3 4 5 | 0 -4 -7 -9 }}

==== Mabilic
Subgroup: 2.5.7
Comma list: 1071875/1048576
Mapping: {{mapping|legend=2| 1 1 5 | 0 3 -5 }}
Mapping: {{mapping|legend=3| 1 0 1 5 | 0 0 3 -5 }}

==== Rainy
Subgroup: 2.5.7
Comma list: [[2100875/2097152]]

==== French decimal
Subgroup: 2.5.7

===== 2.5.7.11 subgroup
Subgroup: 2.5.7.11

===== 2.5.7.11.13 subgroup
Subgroup: 2.5.7.11.13

==== Bastille
Subgroup: 2.5.7
Comma list: {{Monzo|1426 -596 -15}}

==== Augment
Subgroup: 2.5.7.11
Comma list: 56/55, 128/125
Mapping: {{mapping|legend=2| 3 7 0 2 | 0 0 1 1 }}
Mapping: {{mapping|legend=3| 3 0 7 9 11| 0 0 0 -1 -1 }}

==== Ostara
Subgroup: 2.5.7.11
Comma list: 8589934592/8544921875, 53710650917/53687091200
Mapping: [{{val| 1 1 20 -49 }}, {{val| 0 3 -39 119 }}]

===== 2.5.7.11.13 subgroup
Subgroup: 2.5.7.11.13
Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125
Mapping: [{{val| 1 1 20 -49 35 }}, {{val| 0 3 -39 119 -71 }}]

===== 2.5.7.11.13.17 subgroup
Subgroup: 2.5.7.11.13.17
Mapping: [{{val| 1 1 20 -49 35 42 }}, {{val| 0 3 -39 119 -71 -86 }}]
Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251

===== 2.5.7.11.13.17.19 subgroup
Subgroup: 2.5.7.11.13.17.19
Mapping: [{{val| 1 1 20 -49 35 42 21 }}, {{val| 0 3 -39 119 -71 -86 -38 }}]
Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875

==== Tricesimoprimal miracloid
Subgroup: 2.5.7.11.19.29.31
Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688
Mapping: [{{val| 1 419 48 177 157 624 625 }}, {{val| 0 -461 -50 -192 -169 -685 -686 }}]

==== Huntington
Subgroup: 2.5.7.13
Comma list: [[640/637]], [[10985/10976]]
Mapping: {{mapping|legend=2| 1 5 4 4 | 0 -9 -4 -1 }}
Mapping: {{mapping|legend=3| 1 0 5 4 0 4 | 0 0 -9 -4 0 -1 }}

===== Silver
Subgroup: 2.5.7.13.17
Comma list: [[170/169]], [[640/637]], [[5525/5488]]
Mapping: {{mapping|legend=2| 1 5 4 4 2 | 0 -9 -4 -1 7 }}
Mapping: {{mapping|legend=3| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}

==== Pakkanen
Subgroup: 2.5.7.11
Comma list: 625/616
Mapping: {{mapping|legend=2| 1 0 0 -3 | 0 1 0 4 | 0 0 1 -1 }}

==== No-threes naiad
Subgroup: 2.5.7.11
Comma list: 5021863/5000000
Mapping: {{mapping|legend=2| 1 0 2 0 | 0 1 1 1 | 0 0 -4 3 }}

===== 2.5.7.11.13 subgroup
Subgroup: 2.5.7.11.13
Comma list: 847/845, 1001/1000
Mapping: {{mapping| 1 0 2 0 1 | 0 1 1 1 1 | 0 0 -4 3 1 }}

===== 2.5.7.11.13.17 subgroup
Subgroup: 2.5.7.11.13.17
Comma list: 170/169, 221/220, 847/845
Mapping: {{Mapping| 1 0 2 0 1 1 | 0 1 1 1 1 1 | 0 0 -4 3 1 2 }}

=== Higher 2.5 temperaments

==== Movila
Subgroup: 2.5.11
Comma list: 1331/1280
Mapping: [{{val|1 1 3}}, {{val|0 3 1}}]

==== Wizz
Subgroup: 2.5.11
Comma list: [[15625/15488]]
Mapping: {{mapping|legend=2| 2 0 -7 | 0 1 3 }}
Mapping: {{mapping|legend=3| 2 0 4 0 5 | 0 0 1 0 3 }}

==== Insect
Subgroup: 2.5.11
Comma list: 33275/32768
Mapping: {{mapping|legend=2|1 0 5|0 3 -2}}

==== Sephiroth
Subgroup: 2.5.11.13.17
Comma list: 65/64, 170/169, 221/220
Mapping: {{mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
Mapping: {{mapping|legend=3| 1 0 2 0 5 4 5 | 0 0 1 0 -5 -1 -3 }}

==== Trader
Subgroup: 2.5.13
Comma list: [[26/25]]
Mapping: {{mapping|legend=2|1 2 3|0 1 2}}

==== Superquintal
Subgroup: 2.5.13
Comma list: 64000000/62748517
Mapping: {{mapping|legend=2|1 5 6|0 -7 -6}}

==== Vengeance
Subgroup: 2.5.17
Comma list: 78608/78125
Mapping: {{mapping|legend=2|1 1 1|0 3 7}}

=== No-threes-or-fives subgroup temperaments

==== Amaranthine
Subgroup: 2.7.11
Comma list: 5767168/5764801
Mapping: {{mapping|legend=2| 1 2 -3 | 0 1 8 }}

==== Score
Subgroup: 2.7.11.13
Comma list: 343/338, 847/832
Mapping: {{mapping|legend=2| 1 1 3 1 | 0 4 1 6 }}
Mapping: {{mapping|legend=3| 1 0 0 1 3 1| 0 0 0 4 1 6 }}

==== Bossier
Subgroup: 2.7.11.13
Comma list: [[1573/1568]], [[15488/15379]]
Mapping: {{mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}
Mapping: {{mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}

==== Voltage
Subgroup: 2.7.13
Comma list: [[28672/28561]]
Mapping: {{mapping|legend=2| 1 4 4 | 0 -4 -1 }}
Mapping: {{mapping|legend=3| 1 0 0 4 0 4 | 0 0 0 -4 0 -1 }}

==== Ultrakleismic
Subgroup: 2.7.17
Comma list: 4913/4802
Mapping: {{mapping|legend=2|1 2 3|0 3 4}}

==== Counterultrakleismic
Subgroup: 2.7.17
Comma list: 2024782584832/2015993900449
Mapping: {{mapping|legend=2|1 0 1|0 10 11}}

==== Shipwreck
Subgroup: 2.7.53
Comma list: 1048576/1042139
Mapping: [{{val|1 0 6}}, {{val|0 3 -1}}]]

==== Lovecraft
Subgroup: 2.11.13
Comma list: [[1352/1331]]
Mapping: {{mapping|legend=2| 1 3 3 | 0 2 3 }}
Mapping: {{mapping|legend=3| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}

==== Blackbirds
Subgroup: 2.11.13
Comma list: [[29282/28561]]
Mapping: {{mapping|legend=2| 4 0 1 | 0 1 1 }}
Mapping: {{mapping|legend=3| 4 0 0 0 12 13 | 0 0 0 0 1 1 }}

==== Bluebirds
Subgroup: 2.11.13
Comma list: [[265837/262144]]
Mapping: {{mapping|legend=2| 1 0 6 | 0 3 -2 }}
Mapping: {{mapping|legend=3| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}

==== Yamablu
Subgroup: 2.11.13.17.19
Comma list: 209/208, 2057/2048, 83521/83486

==== Mavericks
Subgroup: 2.13.19
Comma list: 47525504/47045881
Mapping: [{{val|1 1 2}}, {{val|0 6 5}}]

==== Yer (rank 3)
Subgroup: 2.11.13.17.19
Comma list: 209/208, 2057/2048


= Lokismic temperaments

=== Septisemitonic
Subgroup: 2.3.5.7
Comma list: 102760448/102515625, 200120949/200000000
Mapping: [{{val|2 5 0 -1}}, {{val|0 -13 33 47}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 131072/130977, 422576/421875
Mapping: [{{val|2 5 0 -1 11}}, {{val|0 -13 33 47 -29}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024, 4096/4095, 405769/405000
Mapping: [{{val|2 5 0 -1 11 15}}, {{val|0 -13 33 47 -29 -54}}]


= Quindromeda family

=== Quindromeda
Subgroup: 2.3.5
Mapping: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]

==== Subgroup temperament

===== 2.3.5.17
Subgroup: 2.3.5.17
Comma list: 24576/24565, 295936/295245
Mapping: [{{val| 1 2 0 5 }}, {{val| 0 -5 28 -11 }}]

===== 2.3.5.17.19
Subgroup: 2.3.5.17.19
Comma list: 1216/1215, 1445/1444, 6144/6137
Mapping: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}]

=== Quintagar
Subgroup: 2.3.5.7
Comma list: 3136/3125, 33554432/33480783
Mapping: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}]

==== Quintoneum
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 7168000/7144929
Mapping: [{{val| 1 2 0 -3 -5 }}, {{val| 0 -5 28 70 102 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 3136/3125, 13720/13689
Mapping: [{{val| 1 2 0 -3 -5 -7 }}, {{val| 0 -5 28 70 102 129 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 3136/3125, 3757/3750
Mapping: [{{val| 1 2 0 -3 -5 -7 5 }}, {{val| 0 -5 28 70 102 129 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 364/363, 441/440, 476/475, 595/594, 1216/1215, 3757/3750
Mapping: [{{val| 1 2 0 -3 -5 -7 5 4 }}, {{val| 0 -5 28 70 102 129 -11 3 }}]

===== Quintoneoid
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049
Mapping: [{{val| 1 2 0 -3 -5 11 }}, {{val| 0 -5 28 70 102 -88 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 441/440, 595/594, 1001/1000, 2601/2600, 3136/3125
Mapping: [{{val| 1 2 0 -3 -5 11 5 }}, {{val| 0 -5 28 70 102 -88 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 441/440, 476/475, 595/594, 1001/1000, 1216/1215, 2601/2600
Mapping: [{{val| 1 2 0 -3 -5 11 5 4 }}, {{val| 0 -5 28 70 102 -88 -11 3 }}]

==== Quinsandra
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 19712/19683, 41503/41472
Mapping: [{{val| 1 2 0 -3 13 }}, {{val| 0 -5 28 70 -115 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3136/3125, 4096/4095, 19712/19683
Mapping: [{{val| 1 2 0 -3 13 11 }}, {{val| 0 -5 28 70 -115 -88 }}]

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1156/1155, 1377/1375, 3136/3125, 4096/4095
Mapping: [{{val| 1 2 0 -3 13 11 5 }}, {{val| 0 -5 28 70 -115 -88 -11 }}]

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 476/475, 936/935, 1156/1155, 1216/1215, 1377/1375, 1729/1728
Mapping: [{{val| 1 2 0 -3 13 11 5 4 }}, {{val| 0 -5 28 70 -115 -88 -11 3 }}]

==== Quinsandric
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 8019/8000, 15488/15435
Mapping: [{{val| 1 2 0 -3 -6 }}, {{val| 0 -5 28 70 114 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 2080/2079, 3136/3125, 10648/10647
Mapping: [{{val| 1 2 0 -3 -6 -8 }}, {{val| 0 -5 28 70 114 141 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 442/441, 561/560, 3136/3125, 7744/7735
Mapping: [{{val| 1 2 0 -3 -6 -8 5 }}, {{val| 0 -5 28 70 114 141 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 351/350, 442/441, 476/475, 561/560, 627/625, 6144/6137
Mapping: [{{val| 1 2 0 -3 -6 -8 5 4 }}, {{val| 0 -5 28 70 114 141 -11 3 }}]

===== Quinsandro
Subgroup: 2.3.5.7.11.13
Comma list: 1573/1568, 3136/3125, 4096/4095, 4459/4455
Mapping: [{{val| 1 2 0 -3 -6 11 }}, {{val| 0 -5 28 70 114 -88 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 561/560, 715/714, 1701/1700, 3136/3125, 4096/4095
Mapping: [{{val| 1 2 0 -3 -6 11 5 }}, {{val| 0 -5 28 70 114 -88 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 286/285, 476/475, 561/560, 627/625, 1216/1215, 1729/1728
Mapping: [{{val| 1 2 0 -3 -6 11 5 4 }}, {{val| 0 -5 28 70 114 -88 -11 3 }}]

=== Quintakwai
Subgroup: 2.3.5.7
Comma list: 5120/5103, 9765625/9680832
Mapping: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4375/4356, 5120/5103
Mapping: [{{val| 1 2 0 -2 -4 }}, {{val| 0 -5 28 58 90 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 1375/1372, 1575/1573, 4096/4095
Mapping: [{{val| 1 2 0 -2 -4 10 }}, {{val| 0 -5 28 58 90 -76 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 375/374, 595/594, 1275/1274, 4096/4095
Mapping: [{{val| 1 2 0 -2 -4 10 5 }}, {{val| 0 -5 28 58 90 -76 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 325/324, 375/374, 400/399, 595/594, 1216/1215, 1275/1274
Mapping: [{{val| 1 2 0 -2 -4 10 5 4 }}, {{val| 0 -5 28 58 90 -76 -11 3 }}]

===== Quinkwai
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1375/1372, 4375/4356
Mapping: [{{val| 1 2 0 -2 -4 -5 }}, {{val| 0 -5 28 58 90 105 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 375/374, 595/594, 833/832, 1375/1372
Mapping: [{{val| 1 2 0 -2 -4 -5 5 }}, {{val| 0 -5 28 58 90 105 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 352/351, 375/374, 400/399, 495/494, 595/594, 1375/1372
Mapping: [{{val| 1 2 0 -2 -4 -5 5 4 }}, {{val| 0 -5 28 58 90 105 -11 3 }}]

===== Quintakwoid
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 625/624, 1375/1372, 5120/5103
Mapping: [{{val| 1 2 0 -2 -4 -6 }}, {{val| 0 -5 28 58 90 117 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 375/374, 442/441, 595/594, 5120/5103
Mapping: [{{val| 1 2 0 -2 -4 -6 5 }}, {{val| 0 -5 28 58 90 117 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215
Mapping: [{{val| 1 2 0 -2 -4 -6 5 4 }}, {{val| 0 -5 28 58 90 117 -11 3 }}]

=== Quindro
Subgroup: 2.3.5.7
Comma list: 4375/4374, 72057594037927936/71489976421753125
Mapping: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 5632/5625, 25165824/25109315
Mapping: [{{val| 1 2 0 15 -5 }}, {{val| 0 -5 28 -147 102 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4375/4374, 5632/5625, 20480/20449
Mapping: [{{val| 1 2 0 15 -5 11 }}, {{val| 0 -5 28 -147 102 -88 }}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1156/1155, 2080/2079, 2431/2430, 4375/4374, 5632/5625
Mapping: [{{val| 1 2 0 15 -5 11 5 }}, {{val| 0 -5 28 -147 102 -88 -11 }}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 1156/1155, 1216/1215, 1445/1444, 2080/2079, 2376/2375, 2431/2430
Mapping: [{{val| 1 2 0 15 -5 11 5 4 }}, {{val| 0 -5 28 -147 102 -88 -11 3 }}]

=== Hemiquindromeda
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 67108864/66976875
Mapping: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 14700/14641, 16384/16335, 19712/19683
Mapping: [{{val|1 2 0 6 4}}, {{val|0 -10 56 -77 -13}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 676/675, 4096/4095, 19712/19683
Mapping: [{{val|1 2 0 6 4 2}}, {{val|0 -10 56 -77 -13 41}}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 595/594, 676/675, 1156/1155, 4096/4095
Mapping: [{{val|1 2 0 6 4 2 5}}, {{val|0 -10 56 -77 -13 41 -22}}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 364/363, 595/594, 676/675, 1156/1155, 1216/1215, 1729/1728
Mapping: [{{val|1 2 0 6 4 2 5 4}}, {{val|0 -10 56 -77 -13 41 -22 6}}]

=== Semiquindromeda
Subgroup: 2.3.5.7
Comma list: 102760448/102515625, 1220703125/1219784832
Mapping: [{{val| 2 4 0 -5 }}, {{val| 0 -5 28 64 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 85937500/85766121
Mapping: [{{val| 2 4 0 -5 -10 }}, {{val| 0 -5 28 64 102 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 5632/5625, 831875/830466
Mapping: [{{val| 2 4 0 -5 -10 -13 }}, {{val| 0 -5 28 64 102 123 }}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876
Mapping: [{{val| 2 4 0 -5 -10 -13 10 }}, {{val| 0 -5 28 64 102 123 -11 }}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499
Mapping: [{{val| 2 4 0 -5 -10 -13 10 8 }}, {{val| 0 -5 28 64 102 123 -11 3 }}]


= Quintaleap family

=== Quintaleap
Subgroup: 2.3.5
Comma list: {{monzo| 37 -16 -5 }} = 137438953472/134521003125
Mapping: [{{val| 1 2 1 }}, {{val| 0 -5 16 }}]

==== Subgroup temperament

===== 2.3.5.17
Subgroup: 2.3.5.17
Comma list: 256/255, 1419857/1417176
Mapping: [{{val| 1 2 1 5 }}, {{val| 0 -5 16 -11 }}]

===== 2.3.5.17.19
Subgroup: 2.3.5.17.19
Comma list: 256/255, 361/360, 4624/4617
Mapping: [{{val| 1 2 1 5 4 }}, {{val| 0 -5 16 -11 3 }}]

=== Quintupole
Subgroup: 2.3.5.7
Comma list: 4000/3969, 458752/455625
Mapping: [{{val| 1 2 1 0 }}, {{val| 0 -5 16 34 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 1375/1372, 4375/4356
Mapping: [{{val| 1 2 1 0 -1 }}, {{val| 0 -5 16 34 54 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 625/624, 2704/2695
Mapping: [{{val| 1 2 1 0 -1 -2 }}, {{val| 0 -5 16 34 54 69 }}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 364/363, 375/374, 442/441
Mapping: [{{val| 1 2 1 0 -1 -2 5 }}, {{val| 0 -5 16 34 54 69 -11 }}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374
Mapping: [{{val| 1 2 1 0 -1 -2 5 4 }}, {{val| 0 -5 16 34 54 69 -11 3 }}]

=== Quintapole
Subgroup: 2.3.5.7
Comma list: 225/224, 7812500/7411887
Mapping: [{{val| 1 2 1 1 }}, {{val| 0 -5 16 22 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 85184/84035
Mapping: [{{val| 1 2 1 1 0 }}, {{val| 0 -5 16 22 42 }}]

===== Galileic
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 225/224, 275/273, 12168/12005
Mapping: [{{val| 1 2 1 1 0 -1 }}, {{val| 0 -5 16 22 42 57 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 120/119, 225/224, 275/273, 2431/2401
Mapping: [{{val| 1 2 1 1 0 -1 5 }}, {{val| 0 -5 16 22 42 57 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 225/224, 247/245, 275/273, 361/357
Mapping: [{{val| 1 2 1 1 0 -1 5 4 }}, {{val| 0 -5 16 22 42 57 -11 3 }}]

===== Catagali
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 225/224, 847/845, 1040/1029
Mapping: [{{val| 1 2 1 1 0 0 }}, {{val| 0 -5 16 22 42 45 }}]

====== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 120/119, 225/224, 442/441, 847/845
Mapping: [{{val| 1 2 1 1 0 0 5 }}, {{val| 0 -5 16 22 42 45 -11 }}]

====== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 209/208, 225/224, 361/357, 442/441
Mapping: [{{val| 1 2 1 1 0 0 5 4 }}, {{val| 0 -5 16 22 42 45 -11 3 }}]

==== Quintain
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/242, 5000/4851
Mapping: [{{val| 1 2 1 1 1 }}, {{val| 0 -5 16 22 30 }}]

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 245/242, 275/273, 1040/1029
Mapping: [{{val| 1 2 1 1 1 0 }}, {{val| 0 -5 16 22 30 45 }}]

=== Quinticosiennic
Subgroup: 2.3.5.7
Comma list: 5120/5103, 395136/390625
Mapping: [{{val| 1 2 1 -1 }}, {{val| 0 -5 16 46 }}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 78408/78125
Mapping: [{{val| 1 2 1 -1 -2 }}, {{val| 0 -5 16 46 66 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 78408/78125
Mapping: [{{val| 1 2 1 -1 -2 -3 }}, {{val| 0 -5 16 46 66 81 }}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750
Mapping: [{{val| 1 2 1 -1 -2 -3 5 }}, {{val| 0 -5 16 46 66 81 -11 }}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475
Mapping: [{{val| 1 2 1 -1 -2 -3 5 4 }}, {{val| 0 -5 16 46 66 81 -11 3 }}]

=== Decimaleap
Subgroup: 2.3.5.7
Comma list: 6144/6125, 393379840/387420489
Mapping: [{{val|1 2 1 5}}, {{val|0 -10 32 -53}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 6144/6125, 14700/14641
Mapping: [{{val|1 2 1 5 4}}, {{val|0 -10 32 -53 -13}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 676/675, 6144/6125
Mapping: [{{val|1 2 1 5 4 3}}, {{val|0 -10 32 -53 -13 17}}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 364/363, 676/675, 1156/1155
Mapping: [{{val|1 2 1 5 4 3 5}}, {{val|0 -10 32 -53 -13 17 -22}}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 256/255, 352/351, 361/360, 364/363, 456/455, 665/663
Mapping: [{{val|1 2 1 5 4 3 5 4}}, {{val|0 -10 32 -53 -13 17 -22 6}}]


= Biyatismic clan

=== Protomere
Subgroup: 2.3.5.11
Comma list: 121/120
Mapping: {{mapping|legend=2| 1 0 1 2 | 0 1 1 1 | 0 0 -2 -1 }}

=== Zeus
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175
Mapping: {{mapping|legend=1| 1 0 1 4 2 | 0 1 1 -1 1 | 0 0 -2 3 1 }}
Mapping to lattice: [{{val| 0 1 -1 2 0 }}, {{val| 0 1 1 -1 1 }}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 351/350
Mapping: {{mapping| 1 0 1 4 2 7 | 0 1 1 -1 1 -2 | 0 0 -2 3 -1 -1 }}
Mapping to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}]

==== Tinia
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 121/120, 176/175
Mapping: {{mapping| 1 0 1 4 2 2 | 0 1 1 -1 1 1 | 0 0 -2 3 -1 -1 }}

=== Artemis
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224
Mapping: {{mapping|legend=1| 1 0 1 -3 2 | 0 1 1 4 1 | 0 0 -2 -4 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 121/120, 196/195
Mapping: {{mapping| 1 0 1 -3 2 -5 | 0 1 1 4 1 6 | 0 0 -2 -4 -1 -6 }}

==== Diana
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273
Mapping: {{mapping| 1 0 1 -3 2 7 | 0 1 1 4 1 -2 | 0 0 -2 -4 -1 -1 }}

=== Oxpecker
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125
Mapping: {{mapping|legend=1| 1 0 1 2 2 | 0 1 1 1 1 | 0 0 -2 -6 -1 }}

==== Woodpecker
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 121/120, 126/125
Mapping: {{mapping| 1 0 1 2 2 2 | 0 1 1 1 1 1 | 0 0 -2 -6 -1 1 }}

=== Kahoupokane
Subgroup: 2.3.5.7.11
Comma list: 121/120, 5120/5103
Mapping: {{mapping|legend=1| 1 0 1 11 2 | 0 1 1 -5 1 | 0 0 -2 -2 -1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 352/351
Mapping: {{mapping| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }}

=== Big brother
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120
Mapping: {{mapping|legend=1| 1 0 -5 -1 -1 | 0 1 3 2 2 | 0 0 4 1 2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 99/98, 121/120
Mapping: {{mapping| 1 0 3 1 3 1 | 0 1 3 2 2 0 | 0 0 -4 -1 -2 2 }}

=== Aphrodite
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440
Mapping: {{mapping|legend=1| 1 0 1 3 2 | 0 1 1 0 1 | 0 0 -4 -3 -2 }}

==== Eros
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 196/195, 352/351
Mapping: {{mapping| 1 0 1 3 2 7 | 0 1 1 0 1 -2 | 0 0 -4 -3 -2 -2 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 196/195, 352/351
Mapping: {{mapping| 1 0 1 3 2 7 6 | 0 1 1 0 1 -2 -1 | 0 0 -4 -3 -2 -2 -5 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 121/120, 154/153, 196/195, 286/285, 352/351
Mapping: {{mapping| 1 0 1 3 2 7 6 9 | 0 1 1 0 1 -2 -1 -3 | 0 0 -4 -3 -2 -2 -5 0 }}

===== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 121/120, 154/153, 161/160, 196/195, 286/285, 352/351
Mapping: {{mapping| 1 0 1 3 2 7 6 9 3 | 0 1 1 0 1 -2 -1 -3 1 | 0 0 -4 -3 -2 -2 -5 0 -1 }}

==== Astarte
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 351/350, 441/440
Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 -4 -3 -2 -11 }}

==== Inanna
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 121/120, 275/273
Mapping: {{mapping| 1 0 1 3 2 1 | 0 1 1 0 1 2 | 0 0 -4 -3 -2 -7 }}

==== Ishtar
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 441/440
Mapping: {{mapping| 1 0 1 3 2 -1 | 0 1 1 0 1 3 | 0 0 -4 -3 -2 -1 }}

=== References


= Undim family

=== Undim
Subgroup: 2.3.5
Comma list: {{monzo| 41 -20 -4 }}
Mapping: {{mapping|legend=1| 4 0 41 | 0 1 -5 }}

==== Overview to extensions

=== Septimal undim
Subgroup: 2.3.5.7
Comma list: 5120/5103, 390625/388962
Mapping: {{mapping|legend=1| 4 0 41 81 | 0 1 -5 -11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 5120/5103, 5632/5625
Mapping: {{mapping| 4 0 41 81 128 | 0 1 -5 -11 -18 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 625/624, 847/845, 1375/1372
Mapping: {{mapping| 4 0 41 81 128 148 | 0 1 -5 -11 -18 -21 }}

=== Unlit
Subgroup: 2.3.5.7
Comma list: 4375/4374, {{monzo| 41 -20 -4 }}
Mapping: {{mapping|legend=1| 4 0 41 -160 | 0 1 -5 27 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5767168/5740875
Mapping: {{mapping| 4 0 41 -160 -113 | 0 1 -5 27 20 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3025/3024, 1835008/1828125
Mapping: {{mapping| 4 0 41 -160 -113 -334 | 0 1 -5 27 20 55 }}

=== Twilight
Subgroup: 2.3.5.7
Comma list: 6144/6125, 31470387200/31381059609
Mapping: {{mapping|legend=1| 8 0 82 -79 | 0 1 -5 8 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 6144/6125, 9801/9800, 19712/19683
Mapping: {{mapping| 8 0 82 -79 15 | 0 1 -5 8 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3584/3575, 14641/14625
Mapping: {{mapping| 8 0 82 -79 15 -186 | 0 1 -5 8 1 17 }}

=== References


= Mabila family

=== Mabila
Subgroup: 2.3.5
Comma list: 268435456/263671875
Mapping: {{mapping|legend=1| 1 -4 4 | 0 10 -3 }}

=== Amavil
Subgroup: 2.3.5.7
Comma list: 225/224, 17496/16807
Mapping: {{mapping|legend=1| 1 -4 4 -5 | 0 10 -3 14 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 864/847
Mapping: {{mapping| 1 -4 4 -5 -1 | 0 10 -3 14 8 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 99/98, 144/143, 176/175
Mapping: {{mapping| 1 -4 4 -5 -1 -3 | 0 10 -3 14 8 12 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 78/77, 99/98, 120/119, 144/143, 176/175
Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 | 0 10 -3 14 8 12 -7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143
Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 -3 | 0 10 -3 14 8 12 -7 13 }}

=== Semabila
Subgroup: 2.3.5.7
Comma list: 49/48, 28672/28125
Mapping: {{mapping|legend=1| 1 -4 4 0 | 0 10 -3 5 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55, 1350/1331
Mapping: {{mapping| 1 -4 4 0 1 | 0 10 -3 5 8 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 91/90, 847/845
Mapping: {{mapping| 1 -4 4 0 1 -3 | 0 10 -3 5 8 12 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 49/48, 56/55, 91/90, 154/153, 375/374
Mapping: {{mapping| 1 -4 4 0 1 -3 8 | 0 10 -3 5 8 12 -7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187
Mapping: {{mapping| 1 -4 4 0 1 -3 8 2 | 0 10 -3 5 8 12 -7 4 }}

=== Tuskaloosa
Subgroup: 2.3.5.7
Comma list: 19683/19600, 110592/109375
Mapping: {{mapping|legend=1| 1 -4 4 -24 | 0 10 -3 48 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 19683/19600
Mapping: {{mapping| 1 -4 4 -24 -20 | 0 10 -3 48 42 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 676/675, 1331/1323
Mapping: {{mapping| 1 -4 4 -24 -20 -3 | 0 10 -3 48 42 12 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 351/350, 676/675, 715/714
Mapping: {{mapping| 1 -4 4 -24 -20 -3 8 | 0 10 -3 48 42 12 -7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475
Mapping: {{mapping| 1 -4 4 -24 -20 -3 8 -22 | 0 10 -3 48 42 12 -7 47 }}

=== Muscogee
Subgroup: 2.3.5.7
Comma list: 126/125, 33756345/33554432
Mapping: {{mapping|legend=1| 1 -4 4 19 | 0 10 -3 -29 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 264627/262144
Mapping: {{mapping| 1 -4 4 19 23 | 0 10 -3 -29 -35 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 676/675, 1287/1280
Mapping: {{mapping| 1 -4 4 19 23 -3 | 0 10 -3 -29 -35 12 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 176/175, 256/255, 273/272, 676/675
Mapping: {{mapping| 1 -4 4 19 23 -3 8 | 0 10 -3 -29 -35 12 -7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361
Mapping: {{mapping| 1 -4 4 19 23 -3 8 21 | 0 10 -3 -29 -35 12 -7 -30 }}

=== Cohemimabila
Subgroup: 2.3.5.7
Comma list: 3136/3125, 65536/64827
Mapping: {{mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1375/1372, 16384/16335
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 640/637, 676/675, 1375/1372
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 442/441, 640/637, 715/714
Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475
Mapping: {{mapping| 1 -4 4 7 11 -3 8 9 | 0 20 -6 -15 -27 24 -14 -17 }}

=== Hemimabila
Subgroup: 2.3.5.7
Comma list: 6144/6125, 117649/116640
Mapping: {{mapping|legend=1| 1 -14 7 -12 | 0 20 -6 19 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 67228/66825
Mapping: {{mapping| 1 -14 7 -12 -2 | 0 20 -6 19 7 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 196/195, 676/675
Mapping: {{mapping| 1 -14 7 -12 -2 -15 | 0 20 -6 19 7 24 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 176/175, 196/195, 676/675
Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 | 0 20 -6 19 7 24 -14 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360
Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 -9 | 0 20 -6 19 7 24 -14 17 }}

=== Trimabila
Subgroup: 2.3.5.7
Comma list: 1728/1715, 268435456/263671875
Mapping: {{mapping|legend=1| 3 -2 9 1 | 0 10 -3 11 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 805255/802816
Mapping: {{mapping| 3 -2 9 1 7 | 0 10 -3 11 5 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 540/539, 676/675, 1573/1568
Mapping: {{mapping| 3 -2 9 1 7 3 | 0 10 -3 11 5 12 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 540/539, 676/675, 715/714
Mapping: {{mapping| 3 -2 9 1 7 3 17 | 0 10 -3 11 5 12 -7 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539
Mapping: {{mapping| 3 -2 9 1 7 3 17 6 | 0 10 -3 11 5 12 -7 10 }}

=== References


= Keegic temperaments

=== Aurora
Subgroup: 2.3.5.7
Comma list: 1029/1000, 28672/28125
Mapping: [{{val|1 -3 5 7}}, {{val|0 12 -7 -11}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 1029/1000, 5632/5625
Mapping: [{{val|1 -3 5 7 5}}, {{val|0 12 -7 -11 -4}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 105/104, 512/507, 637/625
Mapping: [{{val|1 -3 5 7 5 6}}, {{val|0 12 -7 -11 -4 -6}}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 56/55, 105/104, 170/169, 221/220, 375/374
Mapping: [{{val|1 -3 5 7 5 6 6}}, {{val|0 12 -7 -11 -4 -6 -5}}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220
Mapping: [{{val|1 -3 5 7 5 6 6 5}}, {{val|0 12 -7 -11 -4 -6 -5 -2}}]

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220
Mapping: [{{val|1 -3 5 7 5 6 6 5 3}}, {{val|0 12 -7 -11 -4 -6 -5 -2 4}}]

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220
Mapping: [{{val|1 -3 5 7 5 6 6 5 3 6}}, {{val|0 12 -7 -11 -4 -6 -5 -2 4 -3}}]


= Triwellismic temperaments

=== Interaufo
Subgroup: 2.3.5.7
Comma list: 235298/234375, 33756345/33554432
Mapping: [{{val|1 15 -26 -28}}, {{val|0 -27 57 62}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 102487/102400, 235298/234375
Mapping: [{{val|1 15 -26 -28 -3}}, {{val|0 -27 57 62 13}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1001/1000, 6656/6655, 26411/26364
Mapping: [{{val|1 15 -26 -28 -3 -44}}, {{val|0 -27 57 62 13 96}}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 441/440, 833/832, 1001/1000, 1089/1088, 8624/8619
Mapping: [{{val|1 15 -26 -28 -3 -44 18}}, {{val|0 -27 57 62 13 96 -28}}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 441/440, 513/512, 833/832, 969/968, 1001/1000, 1521/1520
Mapping: [{{val|1 15 -26 -28 -3 -44 18 -36}}, {{val|0 -27 57 62 13 96 -28 81}}]

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 441/440, 513/512, 529/528, 833/832, 897/896, 969/968, 1001/1000
Mapping: [{{val|1 15 -26 -28 -3 -44 18 -36 8}}, {{val|0 -27 57 62 13 96 -28 81 -7}}]

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 441/440, 513/512, 529/528, 551/550, 609/608, 783/782, 833/832, 969/968
Mapping: [{{val|1 15 -26 -28 -3 -44 18 -36 8 -18}}, {{val|0 -27 57 62 13 96 -28 81 -7 46}}]


= Olympic clan

=== Olympian
Subgroup: 2.3.7.11
Comma list: 131072/130977
Mapping: {{mapping|legend=2| 1 0 0 17 | 0 1 0 -5 | 0 0 1 -2 }}

==== Overview to extensions

=== Orthoschismic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 32805/32768
Mapping: {{mapping|legend=1| 1 0 15 0 17 | 0 1 -8 0 -5 | 0 0 0 1 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 4096/4095
Mapping: {{mapping| 1 0 15 0 17 -3 | 0 1 -8 0 -5 6 | 0 0 0 1 -2 -1 }}

=== Baffin
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 131072/130977
Mapping: {{mapping|legend=1| 1 0 0 13 -9 | 0 2 0 -7 4 | 0 0 1 -2 4 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095
Mapping: {{mapping| 1 0 0 13 -9 1 | 0 2 0 -7 4 3 | 0 0 1 -2 4 1 }}

=== Sophia
Subgroup: 2.3.5.7.11
Comma list: 42875/42768, 131072/130977
Mapping: {{mapping|legend=1| 1 0 2 3 11 | 0 1 0 0 -5 | 0 0 5 -3 6 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4096/4095, 13720/13689
Mapping: {{mapping| 1 0 2 3 11 7 | 0 1 0 0 -5 -2 | 0 0 5 -3 6 -2 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 833/832, 1156/1155, 4096/4095
Mapping: {{mapping| 1 0 2 3 11 7 7 | 0 1 0 0 -5 -2 -2 | 0 0 5 -3 6 -2 4 }}

=== References


= Frameshift clan

===400 & 159
Subgroup: 2.3.5.7.11
Comma list: [[200704/200475]], [[160083/160000]], [[166698/166375]]
Mapping: [{{val|1 4 47 66 26}}, {{val|0 -6 -111 -157 -56}}]

===Brief
Subgroup: 2.3.5.7.11
Comma list: [[2401/2400]], [[131072/130977]], [[200704/200475]]
Mapping:

===118 & 400
Subgroup: 2.3.5.7.11
Comma list: [[5632/5625]], [[9801/9800]], [[200704/200475]]
Mapping: [{{val|2 5 8 23 24}}, {{val|0 -6 -11 -57 -56}}]


= Cartoonismic temperaments

=== Hydrogen
Subgroup: 2.3.5.7
Comma list: 165288374272/164794921875, 206244329553920/205891132094649
Mapping: [{{val|1 1 0 -1}}, {{val|0 65 258 423}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024,  422576/421875, 83886080000000/83881572334857
Mapping: [{{val|1 1 0 -1 3}}, {{val|0 65 258 423 51}}]

==== Deuterium
Subgroup: 2.3.5.7.11
Comma list: 200704/200475, 104162436/103984375, 246071287/246037500
Mapping: [{{val|1 1 0 -1 4}}, {{val|0 65 258 423 -60}}]


= Bronzismic temperaments

=== Reenactment
Subgroup: 2.3.5.7
Comma list: 2097152/2083725, {{monzo| 21 -24 -12 16 }}
Mapping: {{mapping|legend=1| 4 2 19 12 | 0 17 -38 -3 }}


= No-twos subgroup temperaments

== Overview by mapping of 5

== 3.5.7 subgroup temperaments

=== Arcturus
Subgroup: 3.5.7
Comma list: 15625/15309

==== Polturus
Subgroup: 3.5.7.11
Comma list: 15625/15309, 177147/171875
Mapping: [{{val|1 1 -1 5}}, {{val|0 1 6 -6}}]

=== BPS
Subgroup: 3.5.7
Comma list: 245/243

==== Mintra
Subgroup: 3.5.7.11
Comma list: 245/243, 1331/1323
Mapping: {{mapping|legend=2|1 5 0 1|0 -6 3 2}}

===== Tridecimal Mintra
Subgroup: 3.5.7.11.13
Comma list: 245/243, 275/273, 1575/1573
Mapping: {{mapping|legend=2|1 5 0 1 10|0 -6 3 2 -13}}

==== Dubhe
Subgroup: 3.5.7.17
Comma list: 245/243, 2025/2023
Mapping: {{mapping|legend=2|1 1 2 2|0 4 -2 5}}

=== Canopus
Subgroup: 3.5.7
Comma list: 16875/16807
Mapping: {{mapping|legend=2|1 3 3|0 -5 -4}}

==== Suhail
Subgroup: 3.5.7.11.13
Comma list: 1575/1573, 1625/1617, 4459/4455
Mapping: {{mapping|legend=2|3 4 5 6 7|0 5 4 7 0}}

=== Izar
Subgroup: 3.5.7
Comma list: 13841287201/13839609375
Mapping: {{mapping|legend=2|1 7 5|0 -12 -7}}

=== Nekkar
Subgroup: 3.5.7
Comma list: 35303692060125/33232930569601
Mapping: {{mapping|legend=2|1 8 3|0 -16 -3}}

==== 3.5.7.11 subgroup
Subgroup: 3.5.7.11
Comma list: 1331/1323, 120285/117649
Mapping: {{mapping|legend=2|1 8 3 3|0 -16 -3 -2}}

==== 3.5.7.11.13 subgroup
Subgroup: 3.5.7.11.13
Comma list: 169/165, 351/343, 11011/10935
Mapping: {{mapping|legend=2|1 8 3 3 6|0 -16 -3 -2 -9}}

=== Procyon
Subgroup: 3.5.7
Comma list: 823543/820125
Mapping: {{mapping|legend=2|1 2 2|0 -7 -3}}

==== Erigone
Subgroup: 3.5.7.11.13
Comma list: 847/845, 1575/1573, 4459/4455
Mapping: {{mapping|legend=2|1 9 5 9 7|0 -21 -9 -19 -13}}

===== Hemigone
Subgroup: 3.5.7.11.13.17.19
Comma list: 665/663, 847/845, 1575/1573, 1617/1615, 4459/4455
Mapping: {{mapping|legend=2|1 30 14 28 20 25 2|0 -42 -18 -38 -26 -33 1}}

===== (no-2s) 23-limit
Subgroup: 3.5.7.11.13.17.19.23
Comma list: 665/663, 847/845, 1575/1573, 1617/1615, 2277/2275, 4459/4455
Mapping: {{mapping|legend=2|1 30 14 28 20 25 2 64|0 -42 -18 -38 -26 -33 1 -90}}

=== Sirius
Subgroup: 3.5.7
Comma list: 3125/3087
Mapping: {{mapping|legend=2| 1 1 1 | 0 3 5 }}

==== Remus
Subgroup: 3.5.7.11.13
Comma list: 275/273, 1625/1617, 1575/1573
Mapping: {{mapping|legend=2|1 4 6 5 6|0 -9 -15 -10 -13}}

==== Mizar
Subgroup: 3.5.7.17
Comma list: 3125/3087, 2025/2023
Mapping: {{mapping|legend=2|1 -2 -4 2|0 6 10 1}}

===== Full no-twos 17-limit
Subgroup: 3.5.7.11.13.17
Comma list: 275/273, 459/455, 1625/1617, 2025/2023
Mapping: {{mapping|legend=2|1 -2 -4 12 11 2|0 6 10 -17 -15 1}}

=== Bohlenic
Subgroup: 3.5.7.11
Comma list: 245/243, 3125/3087
Mapping: {{mapping|legend=2| 13 19 23 0 | 0 0 0 1 }}

==== Full no-twos 13-limit
Subgroup: 3.5.7.11.13
Comma list: 245/243, 275/273, 847/845
Mapping: {{mapping|legend=2| 13 19 23 0 2 | 0 0 0 1 1 }}

=== Tuning diagrams

== 3.5.11 subgroup temperaments

=== Polaris
Subgroup: 3.5.11
Comma list: 177147/171875

=== Deneb
Subgroup: 3.5.11
Comma list: 6655/6561

==== Fomalhaut
Subgroup: 3.5.11.13
Comma list: 6655/6561, 274625/264627

===== 3.5.11.13.17
Subgroup: 3.5.11.13.17
Comma list: 1105/1089, 4225/4131, 6655/6561

===== 3.5.11.13.17.19
Subgroup: 3.5.11.13.17.19
Comma list: 247/243, 325/323, 1105/1089, 4675/4617

===== 3.5.11.13.17.19.23
Subgroup: 3.5.11.13.17.19.23
Comma list: 209/207, 247/243, 255/253, 325/323, 4675/4617

=== Alnilam
Subgroup: 3.5.11
Comma list: {{monzo|0 -35 9 0 10}}

== 3.7.11 subgroup temperaments

=== Mintaka
Subgroup: 3.7.11
Comma list: 1331/1323

==== Tridecimal Mintaka
Subgroup: 3.7.11.13
Comma list: 1331/1323, 218491/216513

==== Minalzidar
Subgroup: 3.7.11.13
Comma list: 1331/1323, 351/343

=== Mebsuta
Subgroup: 3.7.11
Comma list: 387420489/386683451

==== 3.7.11.19 subgroup
Subgroup: 3.7.11.19
Comma list: 3971/3969, 41553/41503

===== 3.5.7.11.19 subgroup
Subgroup: 3.5.7.11.19
Comma list: 3971/3969, 12005/11979, 41553/41503

==== Adhara
Subgroup: 3.7.11.13.17
Comma list: 14161/14157, 107811/107653, 1108809/1108723

===== 3.7.11.13.17.19 subgroup
Subgroup: 3.7.11.13.17.19
Comma list: 3213/3211, 3971/3969, 14161/14157, 41553/41503

===== 3.7.8.11.13.17.19 subgroup
Subgroup: 3.7.8.11.13.17.19
Comma list: 513/512, 729/728, 833/832, 969/968, 3971/3969

===== 3.5.7.8.11.13.17.19.23 subgroup
Subgroup: 3.5.7.8.11.13.17.19.23
Comma list: 361/360, 441/440, 513/512, 729/728, 833/832, 969/968, 1127/1125

== Other tritave-based subgroups

=== Aldebaran
Subgroup: 3.5.13
Comma list: 3159/3125

=== Keladic
Subgroup: 3.7.13
Comma list: 351/343

=== Sadalmelik
Subgroup: 3.13.17
Comma list: 85293/83521

== No-twos-or-threes subgroup temperaments

=== Antipyth
Subgroup: 5.7.11
Comma list: 859375/823543
Mapping: {{mapping|legend=2| 1 2 7 | 0 1 7 }}

=== Juggernaut
Subgroup: 5.7.11
Comma list: 125/121
Mapping: {{mapping|legend=2| 2 4 3 | 0 1 0 }}

==== Tridecimal juggernaut
Subgroup: 5.7.11.13
Comma list: 125/121, 637/625
Mapping: {{mapping|legend=2| 2 4 3 0 | 0 1 0 -2 }}

== Graphs

=== Projective tuning space diagrams


= Rastmic clan

=== Neutral
Subgroup: 2.3.11
Comma list: 243/242
Mapping: {{mapping|legend=2| 1 1 2 | 0 2 5 }}
Mapping: {{mapping|legend=3| 1 1 0 0 2 | 0 2 0 0 5 }}

==== Namo
Subgroup: 2.3.11.13
Comma list: 144/143, 243/242
Mapping: {{mapping|legend=2| 1 1 2 4 | 0 2 5 -1 }}
Mapping: {{mapping|legend=3| 1 1 0 0 2 4 | 0 2 0 0 5 -1 }}

=== Suhajira
Subgroup: 2.3.7.11
Comma list: 64/63, 243/242
Mapping: {{mapping|legend=2| 1 1 4 2 | 0 2 -4 5 }}
Mapping: {{mapping|legend=3| 1 1 0 4 2 | 0 2 0 -4 5 }}

==== 2.3.7.11.13 subgroup
Subgroup: 2.3.7.11.13
Comma list: 64/63, 78/77, 144/143
Mapping: {{mapping| 1 1 4 2 4 | 0 2 -4 5 -1 }}

=== Mohaha

==== 2.3.5.11 subgroup
Subgroup: 2.3.5.11
Comma list: 81/80, 121/120
Mapping: {{mapping|legend=2| 1 1 0 2 | 0 2 8 5 }}
Mapping: {{mapping|legend=3| 1 1 0 0 2 | 0 2 8 0 5 }}

===== Mohoho
Subgroup: 2.3.5.11.13
Comma list: 66/65, 81/80, 121/120
Mapping: {{mapping| 1 1 0 2 4| 0 2 8 5 -1 }}

==== Migration
Subgroup: 2.3.5.7.11
Comma list: 81/80, 121/120, 126/125
Mapping: {{mapping| 1 1 0 -3 2 | 0 2 8 20 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 81/80, 121/120, 126/125
Mapping: {{mapping| 1 1 0 -3 2 4 | 0 2 8 20 5 -1 }}

==== Ptolemy
Subgroup: 2.3.5.7.11
Comma list: 81/80, 121/120, 525/512
Mapping: {{mapping| 1 1 0 8 2 | 0 2 8 -18 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 81/80, 105/104, 121/120
Mapping: {{mapping| 1 1 0 8 2 6 | 0 2 8 -18 5 -8 }}

==== Neutrominant
Subgroup: 2.3.5.7.11
Comma list: 36/35, 64/63, 121/120
Mapping: {{mapping| 1 1 0 4 2 | 0 2 8 -4 5 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 64/63, 66/65, 121/120
Mapping: {{mapping| 1 1 0 4 2 4 | 0 2 8 -4 5 -1 }}

=== Semisema
Subgroup: 2.3.7.11
Comma list: 49/48, 243/242
Mapping: {{mapping|legend=2| 2 0 4 -1 | 0 2 1 5 }}
Mapping: {{mapping|legend=3| 2 0 0 4 -1 | 0 2 0 1 5 }}


= Bapbo clan

=== Bapbo
Subgroup: 2.5.7
Comma list: [[256/245]]

==== No-threes 11-limit
Subgroup: 2.5.7.11
Comma list: 80/77, 176/175

=== Summary of full 7-limit extensions


= Supermatertismic temperaments

=== Vydubychi
Subgroup: 2.3.5.7
Comma list: 52734375/52706752, 2199023255552/2197176384375
Mapping: [{{val|1 28 -53 -57}}, {{val|0 -53 111 120}}]

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 131072/130977, 151263/151250, 161280/161051
Mapping: [{{val|1 28 -53 -57 -9}}, {{val|0 -53 111 120 25}}]

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4096/4095, 91125/91091, 151263/151250
Mapping: [{{val|1 28 -53 -57 -9 66}}, {{val|0 -53 111 120 25 -125}}]

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2058/2057, 2080/2079, 2500/2499, 4096/4095, 11016/11011
Mapping: [{{val|1 28 -53 -57 -9 66 -124}}, {{val|0 -53 111 120 25 -125 257}}]

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 2058/2057, 2080/2079, 2432/2431, 2500/2499, 3136/3135, 11016/11011
Mapping: [{{val|1 28 -53 -57 -9 66 -124 -74}}, {{val|0 -53 111 120 25 -125 257 157}}]

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 2025/2024, 2058/2057, 2080/2079, 2432/2431, 2500/2499, 3060/3059, 3520/3519
Mapping: [{{val|1 28 -53 -57 -9 66 -124 -74 12}}, {{val|0 -53 111 120 25 -125 257 157 -15}}]


= Vavoom family

=== Vavoom
Subgroup: 2.3.5
Comma list: {{monzo| -68 18 17 }}
Mapping: {{mapping| 1 0 4 | 0 17 -18 }}

=== Raccoon
Subgroup: 2.3.5.7
Comma list: 225/224, 41943040/40353607
Mapping: {{mapping| 1 0 4 3 | 0 17 -18 -2 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1344/1331, 2420/2401
Mapping: {{mapping| 1 0 4 3 3 | 0 17 -18 -2 5 }}

=== Doubloon
Subgroup: 2.3.5.7
Comma list: 3136/3125, 33756345/33554432
Mapping: {{mapping| 1 0 4 7 | 0 17 -18 -45 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 35937/35840
Mapping: {{mapping| 1 0 4 7 7 | 0 17 -18 -45 -38 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1001/1000, 1188/1183, 3136/3125
Mapping: {{mapping| 1 0 4 7 7 1 | 0 17 -18 -45 -38 29 }}

=== Kaboom
Subgroup: 2.3.5.7
Comma list: 65625/65536, 4802000/4782969
Mapping: {{mapping| 1 0 4 -4 | 0 17 -18 73 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 12005/11979, 19712/19683
Mapping: {{mapping| 1 0 4 -4 -4 | 0 17 -18 73 80 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 4096/4095, 4459/4455
Mapping: {{mapping| 1 0 4 -4 -4 12 | 0 17 -18 73 80 -89 }}

=== Vacuum
Subgroup: 2.3.5.7
Comma list: 4375/4374, {{monzo| -68 18 17 }}
Mapping: {{mapping| 1 0 4 -15 | 0 17 -18 191 }}

==== Vortex
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 42592/42525, 805255/802816
Mapping: {{mapping| 1 0 4 -15 -4 | 0 17 -18 191 80 }}

==== Void
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 496125/495616, 806736/805255
Mapping: {{mapping| 1 0 4 -15 -15 | 0 17 -18 191 198 }}


= Garischismic family

=== Garischismic
Subgroup: 2.3.5.7
Comma list: 33554432/33480783
Mapping: {{mapping|legend=1| 1 0 0 25 | 0 1 0 -14 | 0 0 1 0 }}

=== Cassaschismic
Subgroup: 2.3.5.7.11
Comma list: 19712/19683, 41503/41472
Mapping: {{mapping|legend=1| 1 0 0 25 -33 | 0 1 0 -14 23 | 0 0 1 0 0 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4096/4095, 19712/19683
Mapping: {{mapping| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}

==== 2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079
Mapping: {{mapping| 1 0 0 25 -33 -13 -6 | 0 1 0 -14 23 12 5 | 0 0 1 0 0 -1 1 }}

=== Androschismic
Subgroup: 2.3.5.7.11
Comma list: 151263/151250, 200704/200475
Mapping: {{mapping|legend=1| 1 0 0 25 62 | 0 1 0 -14 -34 | 0 0 1 0 -2 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 43904/43875, 154880/154791
Mapping: {{mapping| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}


= Fendo family

=== Fendo
Subgroup: 2.3.13/5
Comma list: 40/39
Mapping:  {{mapping| 1 1 2 | 0 1 -1 }}

== Main extensions:

=== Fendo-18
Subgroup: 2.3.5.13
Comma list: 40/39, 832/729
Mapping: {{mapping| 1 1 -2 0 | 0 1 7 6 }}

=== Fendo-13
Subgroup: 2.3.5.13
Comma list: 40/39, 260/243
Mapping: {{mapping| 2 2 1 5 | 0 1 3 2 }}

=== Fendo-8
Subgroup: 2.3.5.13
Comma list: 40/39, 6656/6075
Mapping: {{mapping| 1 1 6 8 | 0 1 -6 -7 }}


= Buzzardsmic clan

== 2.3.7 subgroup

=== Buzzard
Subgroup: 2.3.7
Comma list: 65536/64827
Mapping: {{mapping|legend=1| 1 0 4 | 0 4 -3 }}

== Strong extensions

=== Septimal buzzard
Subgroup: 2.3.5.7
Comma list: 1728/1715, 5120/5103
Mapping: {{mapping|legend=1| 1 0 -6 4 | 0 4 21 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 5120/5103
Mapping: {{mapping| 1 0 -6 4 -12 | 0 4 21 -3 39 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539, 676/675
Mapping: {{mapping| 1 0 -6 4 -12 -7 | 0 4 21 -3 39 27 }}

===== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539
Mapping: {{mapping| 1 0 -6 4 -12 -7 14 | 0 4 21 -3 39 27 -25 }}

===== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539
Mapping: {{mapping| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}

==== Buteo
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 2200/2187
Mapping: {{mapping| 1 0 -6 4 9 | 0 4 21 -3 -14 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 275/273, 385/384, 572/567
Mapping: {{mapping| 1 0 -6 4 9 -7 | 0 4 21 -3 -14 27 }}

=== Subfourth
Subgroup: 2.3.5.7
Comma list: 10976/10935, 65536/64827
Mapping: {{mapping|legend=1| 1 0 17 4 | 0 4 -37 -3 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891, 12005/11979
Mapping: {{mapping| 1 0 17 4 11 | 0 4 -37 -3 -19 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 540/539, 676/675
Mapping: {{mapping| 1 0 17 4 11 16 | 0 4 -37 -3 -19 -31 }}

=== Lemongrass
Subgroup: 2.3.5.7
Comma list: 245/243, 65536/64827
Mapping: {{mapping|legend=1| 1 0 17 4 | 0 4 26 -3 }}

== Weak extensions

=== Demibuzzard

==== 7-limit
Subgroup: 2.3.5.7
Comma list: 225/224, 51200/50421
Mapping: {{mapping|legend=1| 1 -4 10 7 | 0 8 -11 -6 }}

===== 2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: 169/168, 225/224, 640/637
Mapping: {{mapping| 1 -4 10 7 3 | 0 8 -11 -6 1 }}

==== Submajor
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 6655/6561
Mapping: {{mapping| 1 -4 10 7 -14 | 0 8 -11 -6 25 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 275/273, 385/384
Mapping: {{mapping| 1 -4 10 7 -14 3 | 0 8 -11 -6 25 1 }}

==== Interpental
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 51200/50421
Mapping: {{mapping| 1 -4 10 7 23 | 0 8 -11 -6 -28 }}

===== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 169/168, 176/175, 640/637
Mapping: {{mapping| 1 -4 10 7 23 3 | 0 8 -11 -6 -28 1 }}

=== Thuja
Subgroup: 2.3.5.7
Comma list: 126/125, 65536/64827
Mapping: {{mapping|legend=1| 1 -4 0 7 | 0 12 5 -9 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 1344/1331
Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 176/175, 364/363
Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 144/143, 176/175, 221/220, 256/255
Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}

==== 23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}

==== 29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}

=== Subsedia
Subgroup: 2.3.5.7
Comma list: 16875/16807, 65536/64827
Mapping: {{mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 65536/64827
Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 676/675, 1375/1372
Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}

==== 19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}

=== Anthoine
Subgroup: 2.3.5.7
Comma list: 3125/3087, 65536/64827
Mapping: {{mapping|legend=1| 1 -12 3 13 | 0 20 -1 -15 }}


= No-thirteens subgroup temperaments

=== Superkleismic
Subgroup: 2.3.5.7.11.19
Comma list: 100/99, 133/132, 190/189, 385/384
Mapping: {{mapping|legend=2| 1 4 5 2 4 8 | 0 -9 -10 3 -2 -14}}


= Miscellaneous 7-limit temperaments

=== Breeze
Subgroup: 2.3.5.7
Comma list: 2460375/2458624
Mapping: {{mapping|legend=1| 1 0 -2 -4 | 0 1 1 3 | 0 0 4 3 }}

=== Metric
Subgroup: 2.3.5.7
Comma list: 703125/702464
Mapping: {{mapping|legend=1| 1 0 -1 -6 | 0 1 1 3 | 0 0 3 7 }}

=== Greenwoodmic
Subgroup: 2.3.5.7
Comma list: 405/392
Mapping: {{mapping|legend=1| 1 0 1 -1 | 0 1 0 2 | 0 0 2 1 }}

=== Avicennmic
Subgroup: 2.3.5.7
Comma list: 525/512
Mapping: {{mapping|legend=1| 1 0 0 9 | 0 1 0 -1 | 0 0 1 -2 }}

=== Varuna
Subgroup: 2.3.5.7
Comma list: 321489/320000
Mapping: {{mapping|legend=1| 2 0 0 9 | 0 1 0 -4 | 0 0 1 2 }}

=== Nuwell
Subgroup: 2.3.5.7
Comma list: 2430/2401
Mapping: {{mapping|legend=1| 1 0 -5 -1 | 0 1 3 2 | 0 0 4 1 }}

=== Schismean
Subgroup: 2.3.5.7
Comma list: 3645/3584
Mapping: {{mapping|legend=1| 1 0 0 -9 | 0 1 0 6 | 0 0 1 1 }}

=== Keegic
Subgroup: 2.3.5.7
Comma list: 1029/1000
Mapping: {{mapping|legend=1| 1 0 0 1 | 0 3 0 -1 | 0 0 1 1 }}

=== Uniwiz
Subgroup: 2.3.5.7
Comma list: 1500625/1492992
Mapping: {{mapping|legend=1| 2 1 0 7 | 0 2 0 3 | 0 0 1 -1 }}

=== Stearnsmic
Subgroup: 2.3.5.7
Comma list: 118098/117649
Mapping: {{mapping|legend=1| 2 1 0 2 | 0 3 0 5 | 0 0 1 0 }}

=== Mirwomo
Subgroup: 2.3.5.7
Comma list: 33075/32768
Mapping: {{mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }}

=== Decovulture
Subgroup: 2.3.5.7
Comma list: 67108864/66976875
Mapping: {{mapping|legend=1| 1 0 0 13 | 0 2 0 -7 | 0 0 1 -2 }}

=== Trimyna
Subgroup: 2.3.5.7
Comma list: 50421/50000
Mapping: {{mapping|legend=1| 1 -1 0 1 | 0 5 0 -1 | 0 0 1 1 }}

=== Squalentine
Subgroup: 2.3.5.7
Comma list: 64827/64000
Mapping: {{mapping|legend=1| 1 0 1 3 | 0 1 1 0 | 0 0 -4 -3 }}

=== Quasiorwellismic
Subgroup: 2.3.5.7
Comma list: 29360128/29296875
Mapping: {{mapping|legend=1| 1 0 0 -22 | 0 1 0 1 | 0 0 1 10 }}

=== Buzzardsmic
Subgroup: 2.3.5.7
Comma list: 65536/64827
Mapping: {{mapping|legend=1| 1 0 0 4 | 0 4 0 -3 | 0 0 1 0 }}

=== Tolerant
Subgroup: 2.3.5.7
Comma list: 179200/177147
Mapping: {{mapping|legend=1| 1 0 0 -10 | 0 1 0 11 | 0 0 1 -2 }}

=== History
Comma list: 257298363/256000000
Mapping: {{mapping|legend=1| 1 2 0 0 | 0 -6 0 7 | 0 0 1 1 }}

=== Sensibeta
Comma list: 1071875/1062882
Mapping: {{mapping|legend=1| 1 0 2 -3 | 0 1 0 4 | 0 0 3 -5 }}

=== Parahemif
Subgroup: 2.3.5.7
Comma list: 1605632/1594323
Mapping: {{mapping|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }}

=== Septimagic
Subgroup: 2.3.5.7
Comma list: 537824/531441
Mapping: {{mapping|legend=1| 1 0 0 -1 | 0 5 0 12 | 0 0 1 0 }}

=== Compass
Subgroup: 2.3.5.7
Comma list: 9765625/9680832
Mapping: {{mapping|legend=1| 1 2 0 -2 | 0 -5 0 2 | 0 0 1 2 }}

=== Linus
Subgroup: 2.3.5.7
Comma list: 578509309952/576650390625
Mapping: {{mapping|legend=1| 10 0 0 -11 | 0 1 0 1 | 0 0 1 1 }}

=== Naiad
Subgroup: 2.3.5.7
Comma list: 161414428/158203125
Mapping: {{mapping|legend=1| 1 5 0 2 | 0 -9 0 -4 | 0 0 1 1 }}


= Moctdelismic clan

=== Moctdelic
Subgroup: 2.5.7.11
Comma list: 1375/1372
Mapping: {{mapping|legend=2| 1 0 0 2 | 0 1 0 -3 | 0 0 1 3 }}

==== Overview to extensions

=== Mendel
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 5632/5625
Mapping: {{mapping|legend=1| 1 0 -1 -6 -13 | 0 1 1 3 6 | 0 0 3 7 12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 625/624, 1375/1372
Mapping: {{mapping| 1 0 -1 -6 -13 -8 | 0 1 1 3 6 3 | 0 0 3 7 12 12 }}

=== Compass
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4375/4356
Mapping: {{mapping|legend=1| 1 2 0 -2 -4 | 0 -5 0 2 6 | 0 0 1 2 3 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 625/624, 1375/1372
Mapping: {{mapping| 1 2 0 -2 -4 -6 | 0 -5 0 2 6 5 | 0 0 1 2 3 4 }}


= Wizardharry clan

=== Homalic
Subgroup: 2.3.5.11
Comma list: 4000/3993
Mapping: {{mapping|legend=2| 1 2 0 1 | 0 -3 0 1 | 0 0 1 1 }}

==== Overview to extensions

=== Marvelpine
Subgroup: 2.3.5.7.11
Comma list: 225/224, 4000/3993
Mapping: {{mapping|legend=1| 1 2 0 -1 1 | 0 -3 0 -6 1 | 0 0 1 2 1 }}

=== Moctpine
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4000/3993
Mapping: {{mapping|legend=1| 1 2 1 1 2 | 0 -3 -1 -1 0 | 0 0 3 4 3 }}

=== Naiad
Subgroup: 2.3.5.7.11
Comma list: 3773/3750, 4000/3993
Mapping: {{mapping|legend=1| 1 5 0 2 0 | 0 -9 0 -4 3 | 0 0 1 1 1 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 364/363, 1001/1000
Mapping: {{mapping| 1 5 0 2 0 1 | 0 -9 0 -4 3 1 | 0 0 1 1 1 1 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 196/195, 221/220, 364/363
Mapping: {{mapping| 1 5 0 2 0 1 1 | 0 -9 0 -4 3 1 2 | 0 0 1 1 1 1 1 }}


= Sensibeta temperaments

=== Elven
Subgroup: 2.3.5.7
Comma list: 1071875/1062882, 9765625/9680832
Mapping: {{mapping|legend=1| 11 2 7 0 | 0 5 6 10 }}

==== 11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4375/4356, 59290/59049
Mapping: {{mapping| 11 2 7 0 1 | 0 5 6 10 12 }}

==== 13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 1375/1372, 1575/1573, 2200/2197
Mapping: {{mapping| 11 2 7 0 1 16 | 0 5 6 10 12 8 }}

==== 17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 375/374, 595/594, 1275/1274, 2200/2197
Mapping: {{mapping| 11 2 7 0 1 16 11 | 0 5 6 10 12 8 11 }}