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Basic Music Theory in ~200 Lines of Python
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# The code for my article with the same name. You can find it at the URL below: | |
# https://www.mvanga.com/blog/basic-music-theory-in-200-lines-of-python | |
# MIT License | |
# | |
# Copyright (c) 2021 Manohar Vanga | |
# | |
# Permission is hereby granted, free of charge, to any person obtaining a copy | |
# of this software and associated documentation files (the "Software"), to deal | |
# in the Software without restriction, including without limitation the rights | |
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
# copies of the Software, and to permit persons to whom the Software is | |
# furnished to do so, subject to the following conditions: | |
# | |
# The above copyright notice and this permission notice shall be included in all | |
# copies or substantial portions of the Software. | |
# | |
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | |
# SOFTWARE. | |
import pprint | |
import re | |
# The musical alphabet consists of seven letter from A through G | |
alphabet = ['C', 'D', 'E', 'F', 'G', 'A', 'B'] | |
# The twelve notes in Western music, along with their enharmonic equivalents | |
notes = [ | |
['B#', 'C', 'Dbb'], | |
['B##', 'C#', 'Db'], | |
['C##', 'D', 'Ebb'], | |
['D#', 'Eb', 'Fbb'], | |
['D##', 'E', 'Fb'], | |
['E#', 'F', 'Gbb'], | |
['E##', 'F#', 'Gb'], | |
['F##', 'G', 'Abb'], | |
['G#', 'Ab'], | |
['G##', 'A', 'Bbb'], | |
['A#', 'Bb', 'Cbb'], | |
['A##', 'B', 'Cb'], | |
] | |
def find_note_index(scale, search_note): | |
''' Given a scale, find the index of a particular note ''' | |
for i, note in enumerate(scale): | |
# Deal with situations where we have a list of enharmonic | |
# equivalents, as well as just a single note as and str. | |
if type(note) == list: | |
if search_note in note: | |
return i | |
elif type(note) == str: | |
if search_note == note: | |
return i | |
def rotate(scale, n): | |
''' Left-rotate a scale by n positions. ''' | |
return scale[n:] + scale[:n] | |
def chromatic(key): | |
''' Generate a chromatic scale in a given key. ''' | |
# Figure out how much to rotate the notes list by and return | |
# the rotated version. | |
num_rotations = find_note_index(notes, key) | |
return rotate(notes, num_rotations) | |
# Interval names that specify the distance between two notes | |
intervals = [ | |
['P1', 'd2'], # Perfect unison Diminished second | |
['m2', 'A1'], # Minor second Augmented unison | |
['M2', 'd3'], # Major second Diminished third | |
['m3', 'A2'], # Minor third Augmented second | |
['M3', 'd4'], # Major third Diminished fourth | |
['P4', 'A3'], # Perfect fourth Augmented third | |
['d5', 'A4'], # Diminished fifth Augmented fourth | |
['P5', 'd6'], # Perfect fifth Diminished sixth | |
['m6', 'A5'], # Minor sixth Augmented fifth | |
['M6', 'd7'], # Major sixth Diminished seventh | |
['m7', 'A6'], # Minor seventh Augmented sixth | |
['M7', 'd8'], # Major seventh Diminished octave | |
['P8', 'A7'], # Perfect octave Augmented seventh | |
] | |
# Interval names based off the notes of the major scale | |
intervals_major = [ | |
[ '1', 'bb2'], | |
['b2', '#1'], | |
[ '2', 'bb3', '9'], | |
['b3', '#2'], | |
[ '3', 'b4'], | |
[ '4', '#3', '11'], | |
['b5', '#4', '#11'], | |
[ '5', 'bb6'], | |
['b6', '#5'], | |
[ '6', 'bb7', '13'], | |
['b7', '#6'], | |
[ '7', 'b8'], | |
[ '8', '#7'], | |
] | |
def find_note_by_root(notes, root): | |
''' | |
Given a list of notes, find it's alphabet. Useful for figuring out which | |
enharmonic equivalent we must use in a particular scale. | |
''' | |
for note in notes: | |
if note[0] == root: | |
return note | |
def make_intervals(root): | |
labeled = {} | |
c = chromatic(root) | |
start_index = find_note_index(alphabet, root[0]) | |
for i, interval in enumerate(intervals): | |
for interval_name in interval: | |
interval_index = int(interval_name[1]) - 1 | |
note = c[i % len(c)] | |
note_root = alphabet[(start_index + interval_index) % len(alphabet)] | |
if note_root is not None: | |
labeled[interval_name] = find_note_by_root(note, note_root) | |
return labeled | |
def make_intervals_major(root): | |
labeled = {} | |
c = chromatic(root) | |
start_index = find_note_index(alphabet, root[0]) | |
for i, interval in enumerate(intervals_major): | |
for interval_name in interval: | |
interval_index = int(re.sub('[b#]', '', interval_name)) - 1 | |
note = c[i % len(c)] | |
note_root = alphabet[(start_index + interval_index) % len(alphabet)] | |
if note_root is not None: | |
labeled[interval_name] = find_note_by_root(note, note_root) | |
return labeled | |
def make_formula(formula, labeled): | |
''' | |
Given a comma-separated interval formula, and a set of labeled | |
notes in a key, return the notes of the formula. | |
''' | |
return [labeled[x] for x in formula.split(',')] | |
intervs = make_intervals('C') | |
print('Major :', ','.join(make_formula('P1,M2,M3,P4,P5,M6,M7,P8', intervs))) # Major | |
print('Minor :', ','.join(make_formula('P1,M2,m3,P4,P5,m6,m7,P8', intervs))) # Natural Minor | |
print('Mel. Minor:', ','.join(make_formula('P1,M2,m3,P4,P5,M6,M7,P8', intervs))) # Melodic Minor | |
print('Har. Minor:', ','.join(make_formula('P1,M2,m3,P4,P5,m6,M7,P8', intervs))) # Harmonic Minor | |
print('Major :', ','.join(make_formula('1,2,3,4,5,6,7', intervs))) # Major | |
formulas = { | |
# Scale formulas | |
'scales': { | |
# Basic chromatic scale | |
'chromatic': '1,b2,2,b3,3,4,b5,5,b6,6,b7,7', | |
# Major scale, its modes, and minor scale | |
'major': '1,2,3,4,5,6,7', | |
'minor': '1,2,b3,4,5,b6,b7', | |
# Melodic minor and its modes | |
'melodic_minor': '1,2,b3,4,5,6,7', | |
# Harmonic minor and its modes | |
'harmonic_minor': '1,2,b3,4,5,b6,7', | |
# Blues scales | |
'major_blues': '1,2,b3,3,5,6', | |
'minor_blues': '1,b3,4,b5,5,b7', | |
# Penatatonic scales | |
'pentatonic_major': '1,2,3,5,6', | |
'pentatonic_minor': '1,b3,4,5,b7', | |
'pentatonic_blues': '1,b3,4,b5,5,b7', | |
}, | |
'chords': { | |
# Major | |
'major': '1,3,5', | |
'major_6': '1,3,5,6', | |
'major_6_9': '1,3,5,6,9', | |
'major_7': '1,3,5,7', | |
'major_9': '1,3,5,7,9', | |
'major_13': '1,3,5,7,9,11,13', | |
'major_7_#11': '1,3,5,7,#11', | |
# Minor | |
'minor': '1,b3,5', | |
'minor_6': '1,b3,5,6', | |
'minor_6_9': '1,b3,5,6,9', | |
'minor_7': '1,b3,5,b7', | |
'minor_9': '1,b3,5,b7,9', | |
'minor_11': '1,b3,5,b7,9,11', | |
'minor_7_b5': '1,b3,b5,b7', | |
# Dominant | |
'dominant_7': '1,3,5,b7', | |
'dominant_9': '1,3,5,b7,9', | |
'dominant_11': '1,3,5,b7,9,11', | |
'dominant_13': '1,3,5,b7,9,11,13', | |
'dominant_7_#11': '1,3,5,b7,#11', | |
# Diminished | |
'diminished': '1,b3,b5', | |
'diminished_7': '1,b3,b5,bb7', | |
'diminished_7_half': '1,b3,b5,b7', | |
# Augmented | |
'augmented': '1,3,#5', | |
# Suspended | |
'sus2': '1,2,5', | |
'sus4': '1,4,5', | |
'7sus2': '1,2,5,b7', | |
'7sus4': '1,4,5,b7', | |
}, | |
} | |
def dump(scale, separator=' '): | |
''' | |
Pretty-print the notes of a scale. Replaces b and # characters | |
for unicode flat and sharp symbols. | |
''' | |
return separator.join(['{:<3s}'.format(x) for x in scale]) \ | |
.replace('b', '\u266d') \ | |
.replace('#', '\u266f') | |
intervs = make_intervals_major('C') | |
for key in formulas: | |
print(key) | |
for name, formula in formulas[key].items(): | |
v = make_formula(formula, intervs) | |
print('\t', name, ':', dump(v)) | |
major_mode_rotations = { | |
'Ionian': 0, | |
'Dorian': 1, | |
'Phrygian': 2, | |
'Lydian': 3, | |
'Mixolydian': 4, | |
'Aeolian': 5, | |
'Locrian': 6, | |
} | |
def mode(scale, degree): | |
return rotate(scale, degree) | |
intervs = make_intervals_major('C') | |
v = make_formula(formulas['scales']['major_I'], intervs) | |
print(dump(mode(v, major_mode_rotations['Phrygian']))) | |
print(find_note_index(notes, 'A')) | |
print(find_note_index(alphabet, 'A')) | |
def make_intervals(key, interval_type='standard'): | |
# Our labeled set of notes mapping interval names to notes | |
labels = {} | |
# Step 1: Generate a chromatic scale in our desired key | |
chromatic_scale = chromatic(key) | |
# The alphabets starting at provided key | |
alphabet_key = rotate(alphabet, find_note_index(alphabet, key[0])) | |
intervs = intervals if interval_type == 'standard' else intervals_major | |
# Iterate through all intervals (list of lists) | |
for index, interval_list in enumerate(intervs): | |
# Step 2: Find the notes to search through based on degree | |
notes_to_search = chromatic_scale[index % len(chromatic_scale)] | |
for interval_name in interval_list: | |
# Get the interval degree | |
if interval_type == 'standard': | |
degree = int(interval_name[1]) - 1 # e.g. M3 --> 2, m7 --> 6 | |
elif interval_type == 'major': | |
degree = int(re.sub('[b#]', '', interval_name)) - 1 | |
# Get the alphabet to look for | |
alphabet_to_search = alphabet_key[degree % len(alphabet_key)] | |
print('Interval {}, degree {}: looking for alphabet {} in notes {}'.format(interval_name, degree, alphabet_to_search, notes_to_search)) | |
try: | |
note = [x for x in notes_to_search if x[0] == alphabet_to_search][0] | |
except: | |
note = notes_to_search[0] | |
labels[interval_name] = note | |
return labels | |
intervs = make_intervals('B#', 'major') | |
pprint.pprint(make_intervals_standard('C'), sort_dicts=False) | |
formula = 'P1,M2,M3,P4,P5,M6,M7,P8' | |
for key in alphabet: | |
print(key, make_formula(formula, make_intervals_standard(key))) | |
for key in alphabet: | |
scale = make_formula(formula, make_intervals_standard(key)) | |
print('{}: {}'.format(key, dump(scale))) | |
intervs = make_intervals('C', 'major') | |
for ftype in formulas: | |
print(ftype) | |
for name, formula in formulas[ftype].items(): | |
v = make_formula(formula, intervs) | |
print('\t{}: {}'.format(name, dump(v))) | |
print('\n\n') | |
intervs = make_intervals('C', 'major') | |
c_major_scale = make_formula(formulas['scales']['major'], intervs) | |
for m in major_mode_rotations: | |
v = mode(c_major_scale, major_mode_rotations[m]) | |
print('{} {}: {}'.format(dump([v[0]]), m, dump(v))) | |
keys = [ | |
'B#', 'C', 'C#', 'Db', 'D', 'D#', 'Eb', 'E', 'Fb', 'E#', 'F', | |
'F#', 'Gb', 'G', 'G#', 'Ab', 'A', 'A#', 'Bb', 'B', 'Cb', | |
] | |
modes = {} | |
for key in keys: | |
print(key) | |
intervs = make_intervals(key, 'major') | |
c_major_scale = make_formula(formulas['scales']['major'], intervs) | |
for m in major_mode_rotations: | |
v = mode(c_major_scale, major_mode_rotations[m]) | |
if v[0] not in modes: | |
modes[v[0]] = {} | |
modes[v[0]][m] = v | |
pprint.pprint(modes['C']) |
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