Here's Looking at Euclid...

heres_looking_at_euclid.py

# Licensed under the Apache License Version 2.0: http://www.apache.org/licenses/LICENSE-2.0.txt
# Here's Looking at Euclid. Giles R. Greenway, March 2015.
# Euclidian poly-rhythms...

import itertools

# http://www.pygame.org/docs/ref/midi.html
import pygame
from pygame import midi
from pygame import time

# http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf
def euclid_rhythm(n,k):
    if k > n:
        n,k = k,n    
    seq = [ [True] for i in range(k) ] + [ [False] for j in range(n-k) ] 

    while seq[-1] == seq[-2]: # Are there multiple copies of the same sequence at the end?
        last = seq[-1]
        for item in seq:
            if item == last:
                break # Run out of things to tack the sequence on to...
            else:
                if seq[-1] == last:
                    item += seq.pop()
                else:
                    break # Run out of copies of the sequence.
    return [ i for i in itertools.chain(*seq) ]

# Phase rhythms in and out according to a three-bit Grey code.
gray = [ [0,0,1], [0,1,1], [0,1,0], [1,1,0], [1,1,1], [1,0,1], [1,0,0] ]

# Return the ith Gray code for j beats.
def masker(i,j): 
    for t in range(j):
        yield gray[i]
        
# Three rhythms, as the Korg Volca Keys has three voices. It's amusing to ring-mod them together.
# 4, 9 & 25 are the lowest triplet of relatively prime intergers, the first three primes squared.
pairs = [ (4,9), (9,25), (4,25) ]

# Lengths of each rhythm.
lengths = [ max(i) + abs(i[0]-i[1]) for i in pairs ]

# Number of beats given to each combination of rhythms given by the number of rhythms present, 
# multiplied by the sum of their lengths.
dur = [ sum(gray[j]) * sum([ lengths[i] for i in gray[j] ]) for j in range(7) ]

# Iterate over the combination of rhythms at each beat.
masks = itertools.chain(*[ masker(i,dur[i]) for i in range(7) ])

# Three iterators to cycle through each rhythm.
voices = [ itertools.cycle(euclid_rhythm(*v)) for v in pairs ]

freqs = [ 30, 60, 120 ]
intervals = [ 4, 2, 1 ]
counts = [ 0, 0, 0 ]

pygame.init()
midi.init()
# Gratuitously hard-coded MIDI channel...
midi_out = midi.Output(2) 

for mask in masks:
    
    beats = [ v.next() for v in voices ]
    # Each note is the base pitch for each rhythm, plus the time since the last beat multiplied by an interval.        
    notes = [ (freqs[i] + intervals[i] * counts[i]) & 127 for i in range(3) if beats[i] and mask[i] ]

    for i in range(3):
        if beats[i]:
            counts[i] = 0
        else:
            counts[i] += 1
             
    for i in notes:
        midi_out.note_on(i,127)
                
    time.delay(200)
    
    for i in notes:
        midi_out.note_off(i,127)

midi_out.close()