I've continued on my (hopefully) short-term fascination with music+math (it's fun, but really bad for productivity). So I found this great library for generating music in Python called Pyknon. And it can be installed using pip: pip install pyknon.
I wrote a little python script just to help me understand some concepts in music theory like intervals and chords. It is meant to be read top to bottom (which is why I intersperse functions and variables throughout). It is NOT written in good modular form (in general, I don't recommend writing python like this). This code can also be used as an intro to the pyknon library.
Behold:
from pyknon.genmidi import Midi
from pyknon.music import NoteSeq, Note, Rest
####### First we'll generate all piano notes
# Pyknon dubs C5 as the value 0, so Note(0) give you C5
# (C in the 5th octave). So we have to move 51 keys to the
# left to get the far left key on a piano.
first_note = Note("A,,,,,") # The far-left key on the piano
def key_number(n):
return n.octave * 12 + n.value - first_note.value
def note_from_key_number(k):
return Note(k - 51)
def intervals(notes):
interval = []
for n in range(len(notes)-1):
interval.append(notes[n+1] - notes[n])
return interval
piano_notes = map(note_from_key_number, range(88))
midi = Midi(1, tempo=80)
midi.seq_notes(piano_notes, track=0)
midi.write("piano_keys.mid")
####### Next we'll examine a major and minor scale, and look at the intervals between
####### each of their notes
middle_c = Note("C,") # key_number=39
note_nums = map(key_number, piano_notes)
print "All piano notes:", note_nums
print "Middle C key number:", key_number(middle_c)
# A, means drop the octave, C' means raise the octave.
# Also, in a NoteSeq, Pyknon stays in the same octave unless explicitly
# changed by using either , or '.
C_major = NoteSeq("C D E F G A B C'' ")
A_minor = NoteSeq("A, B C' D E F G A")
# Note, when defining a NoteSeq, all notes are by default in the same
# octave as the starting note.
print "C major (staring with middle C):", map(key_number, NoteSeq("C, D E F G A B"))
print "C major:", map(key_number, C_major)
print "Intervals for C major:", intervals(map(key_number, C_major))
print "A minor:", map(key_number, A_minor)
print "Intervals A minor:", intervals(map(key_number, A_minor))
####### Last we'll generate some chords in a major and minor keys.
def major_chord(root):
root_key_num = key_number(root)
return map(note_from_key_number, [root_key_num, root_key_num+4, root_key_num+7])
def minor_chord(root):
root_key_num = key_number(root)
return map(note_from_key_number, [root_key_num, root_key_num+3, root_key_num+7])
def dim_chord(root):
root_key_num = key_number(root)
return map(note_from_key_number, [root_key_num, root_key_num+3, root_key_num+6])
# Chord qualities: M m m M M m d (M)
major_chord_progression = [major_chord, minor_chord, minor_chord, major_chord, \
major_chord, minor_chord, dim_chord]
# Chord qualities: m d M m m M M (m)
minor_chord_progression = [minor_chord, dim_chord, major_chord, minor_chord, \
minor_chord, major_chord, major_chord]
####### Generate C major chords ###
C_maj_chords = []
for i in range(len(major_chord_progression)):
C_maj_chords.append(major_chord_progression[i](C_major[i]))
# Throw a "mistake" in there to hear the difference
C_maj_chords.append([Note("C"), Note("F#"), Note("Bb")])
print "C major chords:", C_maj_chords
midi = Midi(1, tempo=80)
midi.seq_chords(map(NoteSeq, C_maj_chords))
midi.write("c_major_chords.mid")
####### Generate G minor chords ###
G_minor = NoteSeq("G, A Bb C' D Eb F")
G_min_chords = []
for i in range(len(minor_chord_progression)):
G_min_chords.append(minor_chord_progression[i](G_minor[i]))
print "G minor chords:", G_min_chords
midi = Midi(1, tempo=80)
midi.seq_chords(map(NoteSeq, G_min_chords))
midi.write("g_minor_chords.mid")
And here is the output (excluding the MIDI files it writes):
localhost:music caleb$ python piano_notes.py
All piano notes: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43,
44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87]
Middle C key number: 39
C major (staring with middle C): [39, 41, 43, 44, 46, 48, 50]
C major: [51, 53, 55, 56, 58, 60, 62, 63]
Intervals for C major: [2, 2, 1, 2, 2, 2, 1]
A minor: [48, 50, 51, 53, 55, 56, 58, 60]
Intervals A minor: [2, 1, 2, 2, 1, 2, 2]
C major chords: [[<c>, <e>, <g>], [<d>, <f>, <a>], [<e>, <g>, <b>], [<f>, <a>, <c>],
[<g>, <b>, <d>], [<a>, <c>, <e>], [<b>, <d>, <f>], [<c>, <F#>, <A#>]]
G minor chords: [[<g>, <A#>, <d>], [<a>, <c>, <D#>], [<A#>, <d>, <f>], [<c>, <D#>, <g>],
[<d>, <f>, <a>], [<D#>, <g>, <A#>], [<f>, <a>, <c>]]