Music.Pitch.Common.Semitones

Provides semitone, octave and step representaiton of intervals.

Types

Octaves

data Octaves

An interval represented as a number of octaves, including negative intervals.

 octaves a = semitones a `div` 12
 steps   a = semitones a `mod` 12

Instances

Enum Octaves

Eq Octaves

Integral Octaves

Num Octaves

Ord Octaves

Real Octaves

Show Octaves

Steps

data Steps

An interval represented as a number of steps in the range 0 ≤ x < 12.

 octaves a = semitones a `div` 12
 steps   a = semitones a `mod` 12

Instances

Enum Steps

Eq Steps

Integral Steps

Num Steps

Ord Steps

Real Steps

Show Steps

Semitones

data Semitones

An interval represented as a number of semitones, including negative intervals, as well as intervals larger than one octave. This representation does not take spelling into account, so for example a major third and a diminished fourth can not be distinguished.

Intervals that name a number of semitones (i.e. semitone, tritone) does not have an unequivocal spelling. To convert these to an interval, a Spelling must be provided as in:

 spell sharps tritone == augmented fourth
 spell flats  tritone == diminished fifth

Instances

Enum Semitones

Eq Semitones

Integral Semitones

Num Semitones

Ord Semitones

Real Semitones

Show Semitones

HasSemitones Semitones

class HasSemitones a where

Class of intervals that can be converted to a number of Semitones.

Methods

semitones :: a -> Semitones

Returns the number of semitones spanned by an interval.

The number of semitones is negative if and only if the interval is negative.

Examples:

 semitones (perfect unison)  =  0
 semitones tritone           =  6
 semitones d5                =  6
 semitones (-_P8)            =  -12

Instances

HasSemitones Semitones

HasSemitones Interval

semitone :: Semitones

Precisely one semitone.

tone :: Semitones

Precisely one whole tone, or two semitones.

ditone :: Semitones

Precisely two whole tones, or four semitones.

tritone :: Semitones

Precisely three whole tones, or six semitones.

isSemitone :: HasSemitones a => a -> Bool

Returns true iff the given interval spans one semitone.

isTone :: HasSemitones a => a -> Bool

Returns true iff the given interval spans one whole tone (two semitones).

isTritone :: HasSemitones a => a -> Bool

Returns true iff the given interval spans three whole tones (six semitones).

Enharmonic equivalence

(=:=) :: HasSemitones a => a -> a -> Bool

Enharmonic equivalence.

(/:=) :: HasSemitones a => a -> a -> Bool

Enharmonic non-equivalence.