zmVault/music-theory-as-code.md

Music Theory as Code

PowerShell module to assist in translating between banjo fingerings and concert notes, as well as between lilypond and conventional notation.

$Db4 = [Pitch]::FromLilyPond("des'")
[Note]::($Db4,1/4).PlayInTime(120)

$str1 = [FrettedStringTuning]::FromOpen([Pitch]::FromLilyPond("d,,,"))
$str1c2 = $str1.Capo(2)

$openGtuning = [FrettedStringInstrumentTuning]::FromStringTunings(@(
    [FrettedStringTuning]::FromOpen([Pitch]::FromLilyPond("d,,,")),
    [FrettedStringTuning]::FromOpen([Pitch]::FromLilyPond("b,,")),
    [FrettedStringTuning]::FromOpen([Pitch]::FromLilyPond("g,")),
    [FrettedStringTuning]::FromOpen([Pitch]::FromLilyPond("d")),
    [FrettedStringTuning]::FromOpen([Pitch]::FromLilyPond("g'")),
    # note: the notation used above is concert octave,
    # banjo is transposed up one octave.
))
[Note]::($openGc2tuning.GetPitchFromFingering(4,11)/4).PlayInTime(120) # play Db4

$openGc2tuning = $openGtuning.Capo(2)
[Note]::($openGc2tuning.GetPitchFromFingering(4,9),1/4).PlayInTime(120) # play Db4

# TODO: class iFrettedStringInstrument
# class Banjo implements iFrettedStringInstrument

class Pitch {
    [Pitch] TransposeOctave([Note]$note1,[Note]$note2) {}
    [Pitch] TransposeOctave([int]$modifier) {}
}

class Duration {
    # 1/4, 1/8, etc.
    # does not encode timing.
}

class Note {
    [Pitch]$_pitch
    [Duration]$_duration
}

classDiagram
    %% simple score definition, does not support polyphony
    class Score {
        List~Note~ notes
        float beatsPerMinute
        +Beep() void
    }

    Score *-- Note
    class Note {
        Pitch pitch
        float beats
        +BeepInTime(int bpm)
    }

    Note *-- Pitch
    class Pitch {
        +Transpose(Pitch from, Pitch to) Pitch
        +TransposeOctave(int modifier) Pitch
        +FromLilyPond(string text) Pitch
        +GetFrequency() float
        +Beep(int milliseconds) void
    }

    class Banjo {
        +FromNamedTuning(string tuningName) Banjo
    }

    Banjo <|.. iFrettedStringInstrument
    class iFrettedStringInstrument {
        -FrettedStringInstrumentTuning tuning
        +GetPitchFromFingering(int string,int fret) Pitch
        +GetFingeringsFromPitch(Pitch pitch) todo
    }

    iFrettedStringInstrument *-- FrettedStringInstrumentTuning
    class FrettedStringInstrumentTuning {
        -List~FrettedStringTuning~ stringTunings
        +GetPitchFromFingering(int string,int fret) Pitch
        +GetFingeringsFromPitch(Pitch pitch) todo
        +Capo(int fret) FrettedStringInstrumentTuning
    }

    FrettedStringInstrumentTuning *-- FrettedStringTuning
    class FrettedStringTuning {
        Pitch openPitch
        int fretOffset
        +GetPitchFromFret(int fret) Pitch
        +SetOffset(int fret) FrettedStringTuning
    }

music-theory

midi	tone	mod12	concert-octave
0	C	0	-1
1	C♯/D♭	1	-1
2	D	2	-1
3	D♯/E♭	3	-1
4	E	4	-1
5	F	5	-1
6	F♯/G♭	6	-1
7	G	7	-1
8	G♯/A♭	8	-1
9	A	9	-1
10	A♯/B♭	10	-1
11	B	11	-1
12	C	0	0
13	C♯/D♭	1	0
14	D	2	0
15	D♯/E♭	3	0
16	E	4	0
17	F	5	0
18	F♯/G♭	6	0
19	G	7	0
20	G♯/A♭	8	0
21	A	9	0
22	A♯/B♭	10	0
23	B	11	0
24	C	0	1
25	C♯/D♭	1	1
26	D	2	1
27	D♯/E♭	3	1
28	E	4	1
29	F	5	1
30	F♯/G♭	6	1
31	G	7	1
32	G♯/A♭	8	1
33	A	9	1
34	A♯/B♭	10	1
35	B	11	1
36	C	0	2
37	C♯/D♭	1	2
38	D	2	2
39	D♯/E♭	3	2
40	E	4	2
41	F	5	2
42	F♯/G♭	6	2
43	G	7	2
44	G♯/A♭	8	2
45	A	9	2
46	A♯/B♭	10	2
47	B	11	2
48	C	0	3
49	C♯/D♭	1	3
50	D	2	3
51	D♯/E♭	3	3
52	E	4	3
53	F	5	3
54	F♯/G♭	6	3
55	G	7	3
56	G♯/A♭	8	3
57	A	9	3
58	A♯/B♭	10	3
59	B	11	3
60	C	0	4
61	C♯/D♭	1	4
62	D	2	4
63	D♯/E♭	3	4
64	E	4	4
65	F	5	4
66	F♯/G♭	6	4
67	G	7	4
68	G♯/A♭	8	4
69	A	9	4
70	A♯/B♭	10	4
71	B	11	4
72	C	0	5
73	C♯/D♭	1	5
74	D	2	5
75	D♯/E♭	3	5
76	E	4	5
77	F	5	5
78	F♯/G♭	6	5
79	G	7	5
80	G♯/A♭	8	5
81	A	9	5
82	A♯/B♭	10	5
83	B	11	5
84	C	0	6
85	C♯/D♭	1	6
86	D	2	6
87	D♯/E♭	3	6
88	E	4	6
89	F	5	6
90	F♯/G♭	6	6
91	G	7	6
92	G♯/A♭	8	6
93	A	9	6
94	A♯/B♭	10	6
95	B	11	6
96	C	0	7
97	C♯/D♭	1	7
98	D	2	7
99	D♯/E♭	3	7
100	E	4	7
101	F	5	7
102	F♯/G♭	6	7
103	G	7	7
104	G♯/A♭	8	7
105	A	9	7
106	A♯/B♭	10	7
107	B	11	7
108	C	0	8
109	C♯/D♭	1	8
110	D	2	8
111	D♯/E♭	3	8
112	E	4	8
113	F	5	8
114	F♯/G♭	6	8
115	G	7	8
116	G♯/A♭	8	8
117	A	9	8
118	A♯/B♭	10	8
119	B	11	8
120	C	0	9
121	C♯/D♭	1	9
122	D	2	9
123	D♯/E♭	3	9
124	E	4	9
125	F	5	9
126	F♯/G♭	6	9
127	G	7	9

spelling	mod7	mod12
C	0	0
C♯	0	1
D♭	1	1
D	1	2
D♯	1	3
E♭	2	3
E	2	4
F	3	5
F♯	3	6
G♭	4	6
G	4	7
G♯	4	8
A♭	5	8
A	5	9
A♯	5	10
B♭	6	10
B	6	11

difMod7	genericInterval
0	Unison

mod12 pitch class mod7 staff position class