Music.Theory.Interval

Common music notation intervals.

Documentation

data Interval_T

Interval type or degree.

Constructors

Unison

Second

Third

Fourth

Fifth

Sixth

Seventh

Instances

Bounded Interval_T

Enum Interval_T

Eq Interval_T

Ord Interval_T

Show Interval_T

data Interval_Q

Interval quality.

Constructors

Diminished

Minor

Perfect

Major

Augmented

Instances

Bounded Interval_Q

Enum Interval_Q

Eq Interval_Q

Ord Interval_Q

Show Interval_Q

data Interval

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

Constructors

Interval

Fields

interval_type :: Interval_T

interval_quality :: Interval_Q

interval_direction :: Ordering

interval_octave :: Octave

Instances

Eq Interval

Show Interval

interval_ty :: Note_T -> Note_T -> Interval_T

Interval type between Note_T values.

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

interval_q_tbl :: Integral n => [(Interval_T, [(n, Interval_Q)])]

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.

interval_q :: Interval_T -> Int -> Maybe Interval_Q

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

interval_q_reverse :: Interval_T -> Interval_Q -> Maybe Integer

Lookup semitone difference of Interval_T with Interval_Q.

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

interval_semitones :: Interval -> Integer

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

note_span :: Note_T -> Note_T -> [Note_T]

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 :: Ordering -> Ordering

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

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

interval :: Pitch -> Pitch -> Interval

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

invert_interval :: Interval -> Interval

Apply invert_ordering to interval_direction of Interval.

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

quality_difference_m :: Interval_Q -> Interval_Q -> Maybe Int

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

quality_difference :: Interval_Q -> Interval_Q -> Int

Erroring variant of quality_difference_m.

transpose :: Interval -> Pitch -> Pitch

Transpose a Pitch by an Interval.

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

circle_of_fifths :: Pitch -> ([Pitch], [Pitch])

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]