List intervals in various edo/edX scales that are close to each other

edo_confluence.py

from collections import defaultdict
from dataclasses import dataclass
from fractions import Fraction
from itertools import pairwise
from typing import Final, Sequence

@dataclass
class EdIntervals:
    ed_fractions: list[Fraction]
    sources: dict[Fraction, list[int]]

def sorted_intervals(ed_sizes: Sequence[int]) -> EdIntervals:
    # generate a single period without 0\N and N\N because trivial
    ed_fractions = set()
    sources = defaultdict(list)
    for ed_size in ed_sizes:
        for step_count in range(1, ed_size):
            x = Fraction(step_count, ed_size)
            ed_fractions.add(x)
            sources[x].append(ed_size)
    return EdIntervals(list(sorted(ed_fractions)), sources)

def print_confluences(data: EdIntervals, max_error: Fraction) -> None:
    def cents(x: Fraction) -> str:
        return f'{x * 1200 :.2f}¢'

    def in_ed(x: Fraction, ed_size: int) -> str:
        return f'{x * ed_size}\\{ed_size}'

    def full_info(x: Fraction) -> str:
        return f'{cents(x)} [{", ".join(in_ed(x, n)
                                        for n in data.sources[x])}]'

    for x1, x2 in pairwise(data.ed_fractions):
        if (delta := x2 - x1) >= max_error:
            continue
        print(f'{full_info(x1)} is {cents(delta)} away from {full_info(x2)}')

def main() -> None:
    CENT: Final = Fraction(1, 1200)
    intervals = sorted_intervals([12, 17, 22, 24])
    print_confluences(intervals, 10 * CENT)

if __name__ == '__main__':
    main()

This is at least Python 3.10 because walrus was used. Can downgrade the version even more.

With these settings, the output is:

50.00¢ [1\24] is 4.55¢ away from 54.55¢ [1\22]
100.00¢ [1\12, 2\24] is 9.09¢ away from 109.09¢ [2\22]
141.18¢ [2\17] is 8.82¢ away from 150.00¢ [3\24]
211.76¢ [3\17] is 6.42¢ away from 218.18¢ [4\22]
272.73¢ [5\22] is 9.63¢ away from 282.35¢ [4\17]
350.00¢ [7\24] is 2.94¢ away from 352.94¢ [5\17]
490.91¢ [9\22] is 3.21¢ away from 494.12¢ [7\17]
494.12¢ [7\17] is 5.88¢ away from 500.00¢ [5\12, 10\24]
545.45¢ [10\22] is 4.55¢ away from 550.00¢ [11\24]
650.00¢ [13\24] is 4.55¢ away from 654.55¢ [12\22]
700.00¢ [7\12, 14\24] is 5.88¢ away from 705.88¢ [10\17]
705.88¢ [10\17] is 3.21¢ away from 709.09¢ [13\22]
847.06¢ [12\17] is 2.94¢ away from 850.00¢ [17\24]
917.65¢ [13\17] is 9.63¢ away from 927.27¢ [17\22]
981.82¢ [18\22] is 6.42¢ away from 988.24¢ [14\17]
1050.00¢ [21\24] is 8.82¢ away from 1058.82¢ [15\17]
1090.91¢ [20\22] is 9.09¢ away from 1100.00¢ [11\12, 22\24]
1145.45¢ [21\22] is 4.55¢ away from 1150.00¢ [23\24]

Basically don’t specify an MedX if an (M×N)edX is already present (like 12 is superfluous here with 24 already present) and the output will be cleaner.

P. S. Sorry this is all lies, this is all edX for X = 2 only because the cents are calculated with this in mind. Sorry I forgot.