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Language  Haskell98 
Common music notation pitch values.
 type PitchClass = Int
 type Octave = Int
 type Octave_PitchClass i = (i, i)
 type OctPC = (Octave, PitchClass)
 data Pitch = Pitch {
 note :: Note_T
 alteration :: Alteration_T
 octave :: Octave
 data Pitch' = Pitch' Note_T Alteration_T' Octave
 pitch'_pp :: Pitch' > String
 pitch'_class_pp :: Pitch' > String
 pitch_clear_quarter_tone :: Pitch > Pitch
 pitch_to_octpc :: Integral i => Pitch > Octave_PitchClass i
 pitch_is_12et :: Pitch > Bool
 pitch_to_midi :: Integral i => Pitch > i
 pitch_to_fmidi :: Fractional n => Pitch > n
 pitch_to_pc :: Pitch > PitchClass
 pitch_compare :: Pitch > Pitch > Ordering
 octpc_to_pitch :: Integral i => Spelling i > Octave_PitchClass i > Pitch
 octpc_nrm :: Integral i => Octave_PitchClass i > Octave_PitchClass i
 octpc_trs :: Integral i => i > Octave_PitchClass i > Octave_PitchClass i
 octpc_to_midi :: Integral i => Octave_PitchClass i > i
 octpc_to_fmidi :: (Integral i, Num n) => Octave_PitchClass i > n
 midi_to_octpc :: Integral i => i > Octave_PitchClass i
 octpc_range :: (OctPC, OctPC) > [OctPC]
 midi_to_pitch :: Integral i => Spelling i > i > Pitch
 fmidi_to_pitch :: RealFrac n => Spelling Int > n > Pitch
 pitch_tranpose :: RealFrac n => Spelling Int > n > Pitch > Pitch
 pitch_in_octave_nearest :: Pitch > Pitch > Pitch
 pitch_note_raise :: Pitch > Pitch
 pitch_note_lower :: Pitch > Pitch
 pitch_rewrite_threequarter_alteration :: Pitch > Pitch
 pitch_edit_octave :: (Octave > Octave) > Pitch > Pitch
 midi_to_cps :: (Integral i, Floating f) => i > f
 fmidi_to_cps :: Floating a => a > a
 pitch_to_cps :: Floating n => Pitch > n
 cps_to_midi :: (Integral i, Floating f, RealFrac f) => f > i
 cps_to_fmidi :: Floating a => a > a
 type Midi_Detune = (Int, Double)
 cps_to_midi_detune :: Double > Midi_Detune
 midi_detune_to_cps :: Midi_Detune > Double
 octpc_to_cps :: (Integral i, Floating n) => Octave_PitchClass i > n
 cps_to_octpc :: (Floating f, RealFrac f, Integral i) => f > Octave_PitchClass i
 parse_iso_pitch_oct :: Octave > String > Maybe Pitch
 parse_iso_pitch :: String > Maybe Pitch
 pitch_pp :: Pitch > String
 pitch_class_pp :: Pitch > String
 pitch_class_names_12et :: Integral n => n > n > [String]
 pitch_pp_iso :: Pitch > String
 pitch_pp_hly :: Pitch > String
 pitch_pp_tonh :: Pitch > String
Documentation
type PitchClass = Int Source
Pitch classes are modulo twelve integers.
type Octave_PitchClass i = (i, i) Source
Octave
and PitchClass
duple.
type OctPC = (Octave, PitchClass) Source
Common music notation pitch value.
Pitch  

Generalised pitch, given by a generalised alteration.
pitch'_class_pp :: Pitch' > String Source
Pitch'
printed without octave.
pitch_clear_quarter_tone :: Pitch > Pitch Source
Simplify Pitch
to standard 12ET by deleting quarter tones.
let p = Pitch A QuarterToneSharp 4 in alteration (pitch_clear_quarter_tone p) == Sharp
pitch_to_octpc :: Integral i => Pitch > Octave_PitchClass i Source
Pitch
to Octave
and PitchClass
notation.
pitch_to_octpc (Pitch F Sharp 4) == (4,6)
pitch_is_12et :: Pitch > Bool Source
Is Pitch
12ET.
pitch_to_midi :: Integral i => Pitch > i Source
Pitch
to midi note number notation.
pitch_to_midi (Pitch A Natural 4) == 69
pitch_to_fmidi :: Fractional n => Pitch > n Source
Pitch
to fractional midi note number notation.
pitch_to_fmidi (Pitch A QuarterToneSharp 4) == 69.5
pitch_to_pc :: Pitch > PitchClass Source
Extract PitchClass
of Pitch
pitch_to_pc (Pitch A Natural 4) == 9 pitch_to_pc (Pitch F Sharp 4) == 6
pitch_compare :: Pitch > Pitch > Ordering Source
Pitch
comparison, implemented via pitch_to_fmidi
.
pitch_compare (Pitch A Natural 4) (Pitch A QuarterToneSharp 4) == LT
octpc_to_pitch :: Integral i => Spelling i > Octave_PitchClass i > Pitch Source
octpc_nrm :: Integral i => Octave_PitchClass i > Octave_PitchClass i Source
Normalise OctPC
value, ie. ensure PitchClass
is in (0,11).
octpc_nrm (4,16) == (5,4)
octpc_trs :: Integral i => i > Octave_PitchClass i > Octave_PitchClass i Source
Transpose OctPC
value.
octpc_trs 7 (4,9) == (5,4) octpc_trs (11) (4,9) == (3,10)
octpc_to_midi :: Integral i => Octave_PitchClass i > i Source
OctPC
value to integral midi note number.
octpc_to_midi (4,9) == 69
octpc_to_fmidi :: (Integral i, Num n) => Octave_PitchClass i > n Source
midi_to_octpc :: Integral i => i > Octave_PitchClass i Source
Inverse of octpc_to_midi
.
midi_to_octpc 69 == (4,9)
octpc_range :: (OctPC, OctPC) > [OctPC] Source
Enumerate range, inclusive.
octpc_range ((3,8),(4,1)) == [(3,8),(3,9),(3,10),(3,11),(4,0),(4,1)]
midi_to_pitch :: Integral i => Spelling i > i > Pitch Source
Midi note number to Pitch
.
let r = ["C4","E♭4","F♯4"] in map (pitch_pp . midi_to_pitch pc_spell_ks) [60,63,66] == r
fmidi_to_pitch :: RealFrac n => Spelling Int > n > Pitch Source
Fractional midi note number to Pitch
.
import Music.Theory.Pitch.Spelling pitch_pp (fmidi_to_pitch pc_spell_ks 65.5) == "F𝄲4" pitch_pp (fmidi_to_pitch pc_spell_ks 66.5) == "F𝄰4" pitch_pp (fmidi_to_pitch pc_spell_ks 67.5) == "A𝄭4" pitch_pp (fmidi_to_pitch pc_spell_ks 69.5) == "B𝄭4"
pitch_tranpose :: RealFrac n => Spelling Int > n > Pitch > Pitch Source
Composition of pitch_to_fmidi
and then fmidi_to_pitch
.
import Music.Theory.Pitch.Name as T import Music.Theory.Pitch.Spelling as T
pitch_tranpose T.pc_spell_ks 2 T.ees5 == T.f5
pitch_in_octave_nearest :: Pitch > Pitch > Pitch Source
Set octave of p2 so that it nearest to p1.
import Music.Theory.Pitch.Name as T
let {r = ["B1","C2","C#2"];f = pitch_in_octave_nearest T.cis2} in map (pitch_pp_iso . f) [T.b4,T.c4,T.cis4] == r
pitch_note_raise :: Pitch > Pitch Source
pitch_note_lower :: Pitch > Pitch Source
pitch_rewrite_threequarter_alteration :: Pitch > Pitch Source
Rewrite Pitch
to not use 3/4
tone alterations, ie. respell
to 1/4
alteration.
let {p = Pitch A ThreeQuarterToneFlat 4 ;q = Pitch G QuarterToneSharp 4} in pitch_rewrite_threequarter_alteration p == q
pitch_edit_octave :: (Octave > Octave) > Pitch > Pitch Source
Apply function to octave
of PitchClass
.
pitch_edit_octave (+ 1) (Pitch A Natural 4) == Pitch A Natural 5
Frequency (CPS)
midi_to_cps :: (Integral i, Floating f) => i > f Source
Midi note number to cycles per second.
map midi_to_cps [60,69] == [261.6255653005986,440.0]
fmidi_to_cps :: Floating a => a > a Source
Fractional midi note number to cycles per second.
map fmidi_to_cps [69,69.1] == [440.0,442.5488940698553]
pitch_to_cps :: Floating n => Pitch > n Source
cps_to_midi :: (Integral i, Floating f, RealFrac f) => f > i Source
Frequency (cycles per second) to midi note number, ie. round
of cps_to_fmidi
.
map cps_to_midi [261.6,440] == [60,69]
cps_to_fmidi :: Floating a => a > a Source
Frequency (cycles per second) to fractional midi note number.
cps_to_fmidi 440 == 69 cps_to_fmidi (fmidi_to_cps 60.25) == 60.25
type Midi_Detune = (Int, Double) Source
Midi note number with cents detune.
cps_to_midi_detune :: Double > Midi_Detune Source
Frequency (in hertz) to Midi_Detune
.
map (fmap round . cps_to_midi_detune) [440.00,508.35] == [(69,0),(71,50)]
midi_detune_to_cps :: Midi_Detune > Double Source
Inverse of cps_to_midi_detune
.
octpc_to_cps :: (Integral i, Floating n) => Octave_PitchClass i > n Source
octpc_to_cps (4,9) == 440
cps_to_octpc :: (Floating f, RealFrac f, Integral i) => f > Octave_PitchClass i Source
Parsers
parse_iso_pitch_oct :: Octave > String > Maybe Pitch Source
Slight generalisation of ISO pitch representation. Allows octave
to be elided, pitch names to be lower case, and double sharps
written as ##
.
See http://www.musiccog.ohiostate.edu/Humdrum/guide04.html
let r = [Pitch C Natural 4,Pitch A Flat 5,Pitch F DoubleSharp 6] in mapMaybe (parse_iso_pitch_oct 4) ["C","Ab5","f##6",""] == r
parse_iso_pitch :: String > Maybe Pitch Source
Variant of parse_iso_pitch_oct
requiring octave.
Pretty printers
pitch_pp :: Pitch > String Source
Pretty printer for Pitch
(unicode, see alteration_symbol
).
pitch_pp (Pitch E Flat 4) == "E♭4" pitch_pp (Pitch F QuarterToneSharp 3) == "F𝄲3"
pitch_class_pp :: Pitch > String Source
Pitch
printed without octave.
pitch_class_names_12et :: Integral n => n > n > [String] Source
Sequential list of n pitch class names starting from k.
pitch_class_names_12et 11 2 == ["B","C"]
pitch_pp_iso :: Pitch > String Source
Pretty printer for Pitch
(ISO, ASCII, see alteration_iso
).
pitch_pp_iso (Pitch E Flat 4) == "Eb4" pitch_pp_iso (Pitch F DoubleSharp 3) == "Fx3"
pitch_pp_hly :: Pitch > String Source
Pretty printer for Pitch
(ASCII, see alteration_tonh
).
pitch_pp_hly (Pitch E Flat 4) == "ees4" pitch_pp_hly (Pitch F QuarterToneSharp 3) == "fih3" pitch_pp_hly (Pitch B Natural 6) == "b6"
pitch_pp_tonh :: Pitch > String Source
Pretty printer for Pitch
(Tonhöhe, see alteration_tonh
).
pitch_pp_tonh (Pitch E Flat 4) == "Es4" pitch_pp_tonh (Pitch F QuarterToneSharp 3) == "Fih3" pitch_pp_tonh (Pitch B Natural 6) == "H6"