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zmVault/music-theory-as-code.md
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# Music Theory as Code
PowerShell module to assist in translating between banjo fingerings and concert notes,
as well as between [[lilypond]] and conventional notation.
```powershell
$Db4 = [Pitch]::FromLilyPond("des'")
[Note]::($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
```
```powershell
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
}
```
```mermaid
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
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