A general schematic for an asynchronous timer on the Arduino. (Untested conceptual sketch)

arduino_timer.ino

// constants won't change. They're used here to set pin numbers:
const int motorPin = 4;

// int high_in_millisecond = 50;  // how long 5V is sent (in ms)
// int low_in_millisecond = 500; // how long 0V is sent (in ms)

// variables will change:
// int motorState = LOW;
//int ledState = HIGH;
int switchPin = 8;
int data = 1;
int val = 0;

const motor_on_duration = 500; //ms, independent of heartbeat period

// beat FREQUENCY (v) is 1.333 beats per second. You want beat PERIOD, 1/v = 750ms

// Inverting beat frequency: (frequency would be 80/60, but we're taking the reciprocal so the whole thing is flipped)
//   60 seconds         1 minute
//  ----		  x   ----         = .75 seconds = 750 ms
//    1 minute         80 beats

const beat_frequency = 80;	  // beats per minute
const beat_frequency_seconds = beat_frequency / 60;
const heartbeat_period = 1 / beat_frequency_seconds; // ms; i.e 1 / 1.333s = 0.75s = 750ms

// Stores 'timestamps'
unsigned long current_millis = 0;
unsigned long heartbeat_started = 0;
unsigned long motor_started = 0;

void setup() {

  Serial.begin(9600);
  pinMode(motorPin, OUTPUT);
  pinMode(switchPin, INPUT);

}

void loop() {
  // millis() gives a 'timestamp', the number of milliseconds since the processor was started
  current_millis = millis();

  if(current_millis - heartbeat_started >= heartbeat_period){
  	// Time to beat the heart, so to speak

  	// turn the motor on and start the motor timer
  	motor_started = current_millis;
  	digitalWrite(motorPin, HIGH);

  	heartbeat_started = current_millis; // reset the timer
  }

  if(current_millis - motor_started >= motor_on_duration){
  	// turn the motor off
  	digitalWrite(motorPin, LOW);
  }

  // val = digitalRead(switchPin);   // read the input pin
  // Serial.println (val);
}