Music.Pitch

A pitch represents a specific frequency of sound with a letter name, octave, and accidental. E.g. the pitch "B♭4".

type alias Pitch =

Pitch

Helpers

transposeUp : Interval -> Pitch -> Pitch

Transpose a pitch upward by an interval.

transposeUp Interval.perfectFifth c4 == g4

transposeDown : Interval -> Pitch -> Pitch

Transpose a pitch downward by an interval.

transposeDown Interval.perfectFifth c4 == f3

intervalBetween : Pitch -> Pitch -> Interval

Get the interval between two pitches:

intervalBetween c4 g4 == Interval.perfectFifth

areEnharmonicEquivalents : Pitch -> Pitch -> Bool

Check whether two pitches are enharmonic equivalents of each other. Enharmonic equivalents are two pitches with different names but the same sound:

areEnharmonicEquivalents cSharp4 dFlat4 == True

octave : Pitch -> Int

Get the octave of a pitch:

octave c4 == 4

Generating

chromaticRun : Pitch -> Pitch -> List Pitch

Generate a section of the ascending or descending chromatic scale between two pitches:

chromaticRun a4 d5
    == [ a4
       , aSharp4
       , b4
       , c5
       , cSharp5
       , d5
       ]

Ascending runs use sharps; descending runs use flats:

chromaticRun d5 a4
    == [ d5
       , dFlat5
       , c5
       , b4
       , bFlat4
       , a4
       ]

Conversion

semitones : Pitch -> Int

Distance in semitones from C0. Useful for sorting.

semitones c4 == 48

toMIDINoteNumber : Pitch -> Int

Convert a pitch to a MIDI number:

toMIDINoteNumber c4 == 60

toFrequency : Pitch -> Float

Convert a pitch to a frequency in Hertz:

toFrequency c4 == 261.6255653005986

toString : Pitch -> String

A pitch's letter name, accidental, and octave number:

toString cSharp4 == "C♯4"

fromPitchClassInOctave : Int -> PitchClass -> Pitch

Create a pitch from a pitch class and octave number:

fromPitchClassInOctave 4 c == c4

Respelling

Equivalent pitches can be spelled multiple ways. These functions help with respelling pitches for certain circumstances.

normalize : Pitch -> Pitch

Respell a pitch with at most two accidentals:

bTripleSharp4 =
    bSharp4
        |> transposeUp Interval.augmentedUnison
        |> transposeUp Interval.augmentedUnison


normalize bTripleSharp4
    == d5

Pitches with three or more accidentals are theoretically possible, but extremely unlikely in practice; most notation software will not support them. This function is a helpful pre-export step if you plan to use pitch data with software in which three or more accidentals are not representable.

simplify : Pitch -> Pitch

Respell a pitch with as few accidentals as possible:

simplify fFlat4
    == e4

This is helpful in musical idioms like jazz, where simple spellings are preferred.

Constructors

c0 : Pitch

c1 : Pitch

c2 : Pitch

c3 : Pitch

c4 : Pitch

c5 : Pitch

c6 : Pitch

c7 : Pitch

c8 : Pitch

cSharp0 : Pitch

cSharp1 : Pitch

cSharp2 : Pitch

cSharp3 : Pitch

cSharp4 : Pitch

cSharp5 : Pitch

cSharp6 : Pitch

cSharp7 : Pitch

cSharp8 : Pitch

d0 : Pitch

d1 : Pitch

d2 : Pitch

d3 : Pitch

d4 : Pitch

d5 : Pitch

d6 : Pitch

d7 : Pitch

d8 : Pitch

dFlat0 : Pitch

dFlat1 : Pitch

dFlat2 : Pitch

dFlat3 : Pitch

dFlat4 : Pitch

dFlat5 : Pitch

dFlat6 : Pitch

dFlat7 : Pitch

dFlat8 : Pitch

dSharp0 : Pitch

dSharp1 : Pitch

dSharp2 : Pitch

dSharp3 : Pitch

dSharp4 : Pitch

dSharp5 : Pitch

dSharp6 : Pitch

dSharp7 : Pitch

dSharp8 : Pitch

e0 : Pitch

e1 : Pitch

e2 : Pitch

e3 : Pitch

e4 : Pitch

e5 : Pitch

e6 : Pitch

e7 : Pitch

e8 : Pitch

eFlat0 : Pitch

eFlat1 : Pitch

eFlat2 : Pitch

eFlat3 : Pitch

eFlat4 : Pitch

eFlat5 : Pitch

eFlat6 : Pitch

eFlat7 : Pitch

eFlat8 : Pitch

f0 : Pitch

f1 : Pitch

f2 : Pitch

f3 : Pitch

f4 : Pitch

f5 : Pitch

f6 : Pitch

f7 : Pitch

f8 : Pitch

fSharp0 : Pitch

fSharp1 : Pitch

fSharp2 : Pitch

fSharp3 : Pitch

fSharp4 : Pitch

fSharp5 : Pitch

fSharp6 : Pitch

fSharp7 : Pitch

fSharp8 : Pitch

g0 : Pitch

g1 : Pitch

g2 : Pitch

g3 : Pitch

g4 : Pitch

g5 : Pitch

g6 : Pitch

g7 : Pitch

g8 : Pitch

gFlat0 : Pitch

gFlat1 : Pitch

gFlat2 : Pitch

gFlat3 : Pitch

gFlat4 : Pitch

gFlat5 : Pitch

gFlat6 : Pitch

gFlat7 : Pitch

gFlat8 : Pitch

gSharp0 : Pitch

gSharp1 : Pitch

gSharp2 : Pitch

gSharp3 : Pitch

gSharp4 : Pitch

gSharp5 : Pitch

gSharp6 : Pitch

gSharp7 : Pitch

gSharp8 : Pitch

a0 : Pitch

a1 : Pitch

a2 : Pitch

a3 : Pitch

a4 : Pitch

a5 : Pitch

a6 : Pitch

a7 : Pitch

a8 : Pitch

aFlat0 : Pitch

aFlat1 : Pitch

aFlat2 : Pitch

aFlat3 : Pitch

aFlat4 : Pitch

aFlat5 : Pitch

aFlat6 : Pitch

aFlat7 : Pitch

aFlat8 : Pitch

aSharp0 : Pitch

aSharp1 : Pitch

aSharp2 : Pitch

aSharp3 : Pitch

aSharp4 : Pitch

aSharp5 : Pitch

aSharp6 : Pitch

aSharp7 : Pitch

aSharp8 : Pitch

b0 : Pitch

b1 : Pitch

b2 : Pitch

b3 : Pitch

b4 : Pitch

b5 : Pitch

b6 : Pitch

b7 : Pitch

b8 : Pitch

bFlat0 : Pitch

bFlat1 : Pitch

bFlat2 : Pitch

bFlat3 : Pitch

bFlat4 : Pitch

bFlat5 : Pitch

bFlat6 : Pitch

bFlat7 : Pitch

bFlat8 : Pitch

Less common pitches

These are used less frequently in music. Most likely you want a pitch from the previous section.

Enharmonic equivalents of natural notes

cFlat1 : Pitch

cFlat2 : Pitch

cFlat3 : Pitch

cFlat4 : Pitch

cFlat5 : Pitch

cFlat6 : Pitch

cFlat7 : Pitch

cFlat8 : Pitch

eSharp0 : Pitch

eSharp1 : Pitch

eSharp2 : Pitch

eSharp3 : Pitch

eSharp4 : Pitch

eSharp5 : Pitch

eSharp6 : Pitch

eSharp7 : Pitch

eSharp8 : Pitch

fFlat0 : Pitch

fFlat1 : Pitch

fFlat2 : Pitch

fFlat3 : Pitch

fFlat4 : Pitch

fFlat5 : Pitch

fFlat6 : Pitch

fFlat7 : Pitch

fFlat8 : Pitch

bSharp0 : Pitch

bSharp1 : Pitch

bSharp2 : Pitch

bSharp3 : Pitch

bSharp4 : Pitch

bSharp5 : Pitch

bSharp6 : Pitch

bSharp7 : Pitch

bSharp8 : Pitch

duncanmalashock/elm-music-theory/1.0.0