Documentation

Interval type or degree.

Interval quality.

Common music notation interval. An Ordering of LT indicates an ascending interval, GT a descending interval, and EQ a unison.

Interval type between Note_T values.

map (interval_ty C) [E,B] == [Third,Seventh]

Table of interval qualities. For each Interval_T gives directed semitone interval counts for each allowable Interval_Q. For lookup function see interval_q, for reverse lookup see interval_q_reverse.

Lookup Interval_Q for given Interval_T and semitone count.

interval_q Unison 11 == Just Diminished
interval_q Third 5 == Just Augmented
interval_q Fourth 5 == Just Perfect
interval_q Unison 3 == Nothing

Lookup semitone difference of Interval_T with Interval_Q.

interval_q_reverse Third Minor == Just 3
interval_q_reverse Unison Diminished == Just 11

Semitone difference of Interval.

interval_semitones (interval (Pitch C Sharp 4) (Pitch E Sharp 5)) == 16
interval_semitones (interval (Pitch C Natural 4) (Pitch D Sharp 3)) == -9

Inclusive set of Note_T within indicated interval. This is not equal to enumFromTo which is not circular.

note_span E B == [E,F,G,A,B]
note_span B D == [B,C,D]
enumFromTo B D == []

Invert Ordering, ie. GT becomes LT and vice versa.

map invert_ordering [LT,EQ,GT] == [GT,EQ,LT]

Determine Interval between two Pitches.

interval (Pitch C Sharp 4) (Pitch D Flat 4) == Interval Second Diminished EQ 0
interval (Pitch C Sharp 4) (Pitch E Sharp 5) == Interval Third Major LT 1

Apply invert_ordering to interval_direction of Interval.

invert_interval (Interval Third Major LT 1) == Interval Third Major GT 1

The signed difference in semitones between two Interval_Q values when applied to the same Interval_T. Can this be written correctly without knowing the Interval_T?

quality_difference_m Minor Augmented == Just 2
quality_difference_m Augmented Diminished == Just (-3)
quality_difference_m Major Perfect == Nothing

Erroring variant of quality_difference_m.

Transpose a Pitch by an Interval.

transpose (Interval Third Diminished LT 0) (Pitch C Sharp 4) == Pitch E Flat 4

Make leftwards (perfect fourth) and and rightwards (perfect fifth) circles from Pitch.

let c = circle_of_fifths (Pitch F Sharp 4)
in map pitch_to_pc (snd c) == [6,1,8,3,10,5,12,7,2,9,4,11]

Parse a positive integer into interval type and octave displacement.

mapMaybe parse_interval_type (map show [1 .. 15])

Parse interval quality notation.

mapMaybe parse_interval_quality "dmPMA" == [minBound .. maxBound]

Degree of interval type and octave displacement. Inverse of parse_interval_type.

map interval_type_degree [(Third,0),(Second,1),(Unison,2)] == [3,9,15]

Inverse of 'parse_interval_quality.

Parse standard common music interval notation.

let i = mapMaybe parse_interval (words "P1 d2 m2 M2 A3 P8 +M9 -M2")
in unwords (map interval_pp i) == "P1 d2 m2 M2 A3 P8 M9 -M2"

mapMaybe (fmap interval_octave . parse_interval) (words "d1 d8 d15") == [-1,0,1]

Pretty printer for intervals, inverse of parse_interval.

Standard names for the intervals within the octave, divided into perfect, major and minor at the left, and diminished and augmented at the right.

let {bimap f (p,q) = (f p,f q)
    ;f = mapMaybe (fmap interval_semitones . parse_interval)}
in bimap f std_interval_names