Distance of pitch class to key tonic with respect to dissonance

key_distance.py

# https://github.com/bzamecnik/ideas/blob/master/key_coloring.md

import numpy as np

def key_distance(pitch_class, key):
  """
  Distance between a pitch class and tonic of a key
  which roughly approximates dissonance.
  
  Eg. in key of C the pitch classes sorted from most consonant
  to most dissonant:
  ['C', 'G', 'D', 'A', 'E', 'B', 'F', 'Bb', 'Eb', 'Ab', 'Db', 'Gb']
  
  Note that first there is an inner pentatonic (C G D A E),
  then border tones (B, F), then outer pentatonic (Bb Eb Ab Db Gb).
  
  pitch_class - range: [0; 11]
  key - range: [0; 11]
  returns: distance in range [0; 11]
  """
  i = ((pitch_class - key + 12) * 7) % 12
  return i if i < 6 else 12 - 1 + 6 - i

def test_key_distance():
  assert np.allclose(
    [key_distance(tone, 0) for tone in range(12)],
    [0, 10, 2, 8, 4, 6, 11, 1, 9, 3, 7, 5])
  assert np.allclose(
    [key_distance(tone, 1) for tone in range(12)],
    [5, 0, 10, 2, 8, 4, 6, 11, 1, 9, 3, 7])
    
 assert [name for pc, name in sorted(zip(
    [key_distance(tone, 0) for tone in range(12)],
    ['C', 'Db', 'D', 'Eb', 'E', 'F', 'Gb', 'G', 'Ab', 'A', 'Bb', 'B']
))] == ['C', 'G', 'D', 'A', 'E', 'B', 'F', 'Bb', 'Eb', 'Ab', 'Db', 'Gb']