Music.Theory.Duration

Common music notation duration model.

Documentation

data Duration

Common music notation durational model

Constructors

Duration

Fields

• division :: Integer

  division of whole note

• dots :: Integer

  number of dots

• multiplier :: Rational

  tuplet modifier

Instances

Eq Duration

Methods

(==) :: Duration -> Duration -> Bool

(/=) :: Duration -> Duration -> Bool

Ord Duration

Ord instance in terms of duration_compare_meq_err.

Methods

compare :: Duration -> Duration -> Ordering

(<) :: Duration -> Duration -> Bool

(<=) :: Duration -> Duration -> Bool

(>) :: Duration -> Duration -> Bool

(>=) :: Duration -> Duration -> Bool

max :: Duration -> Duration -> Duration

min :: Duration -> Duration -> Duration

Show Duration

Methods

showsPrec :: Int -> Duration -> ShowS

show :: Duration -> String

showList :: [Duration] -> ShowS

duration_meq :: Duration -> Duration -> Bool

Are multipliers equal?

duration_m1 :: Duration -> Bool

Is multiplier the identity (ie. 1)?

duration_compare_meq :: Duration -> Duration -> Maybe Ordering

Compare durations with equal multipliers.

duration_compare_meq_err :: Duration -> Duration -> Ordering

Erroring variant of duration_compare_meq.

no_dots :: (Duration, Duration) -> Bool

True if neither duration is dotted.

sum_dur_undotted :: (Integer, Integer) -> Maybe Duration

Sum undotted divisions, input is required to be sorted.

sum_dur_dotted :: (Integer, Integer, Integer, Integer) -> Maybe Duration

Sum dotted divisions, input is required to be sorted.

sum_dur_dotted (4,1,4,1) == Just (Duration 2 1 1)
sum_dur_dotted (4,0,2,1) == Just (Duration 1 0 1)
sum_dur_dotted (8,1,4,0) == Just (Duration 4 2 1)
sum_dur_dotted (16,0,4,2) == Just (Duration 2 0 1)

sum_dur :: Duration -> Duration -> Maybe Duration

Sum durations. Not all durations can be summed, and the present algorithm is not exhaustive.

import Music.Theory.Duration.Name
sum_dur quarter_note eighth_note == Just dotted_quarter_note
sum_dur dotted_quarter_note eighth_note == Just half_note
sum_dur quarter_note dotted_eighth_note == Just double_dotted_quarter_note

sum_dur_err :: Duration -> Duration -> Duration

Erroring variant of sum_dur.

divisions_set :: [Integer]

Standard divisions (from 0 to 256). MusicXML allows -1 as a division (for long).

duration_set :: Integer -> [Duration]

Durations set derived from divisions_set with up to k dots. Multiplier of 1.

beam_count_tbl :: [(Integer, Integer)]

Table of number of beams at notated division.

whole_note_division_to_beam_count :: Integer -> Maybe Integer

Lookup beam_count_tbl.

whole_note_division_to_beam_count 32 == Just 3

duration_beam_count :: Duration -> Integer

Calculate number of beams at Duration.

map duration_beam_count [Duration 2 0 1,Duration 16 0 1] == [0,2]

MusicXML

division_musicxml_tbl :: [(Integer, String)]

Table giving MusicXML types for divisions.

whole_note_division_to_musicxml_type :: Integer -> String

Lookup division_musicxml_tbl.

map whole_note_division_to_musicxml_type [2,4] == ["half","quarter"]

duration_to_musicxml_type :: Duration -> String

Variant of whole_note_division_to_musicxml_type extracting division from Duration, dots & multipler are ignored.

duration_to_musicxml_type (Duration 4 0 1) == "quarter"

Unicode

division_unicode_tbl :: [(Integer, Char)]

Table giving Unicode symbols for divisions.

whole_note_division_to_unicode_symbol :: Integer -> Char

Lookup division_unicode_tbl.

map whole_note_division_to_unicode_symbol [1,2,4,8] == "𝅝𝅗𝅥𝅘𝅥𝅘𝅥𝅮"

duration_to_unicode :: Duration -> String

Give Unicode string for Duration. The duration multiplier is not written.

map duration_to_unicode [Duration 1 2 1,Duration 4 1 1] == ["𝅝𝅭𝅭","𝅘𝅥𝅭"]

Lilypond

duration_to_lilypond_type :: Duration -> String

Give Lilypond notation for Duration. Note that the duration multiplier is not written.

map duration_to_lilypond_type [Duration 2 0 1,Duration 4 1 1] == ["2","4."]

Humdrum

duration_recip_pp :: Duration -> String

Duration to **recip notation.

http://humdrum.org/Humdrum/representations/recip.rep.html

let d = map (\z -> Duration z 0 1) [0,1,2,4,8,16,32]
in map duration_recip_pp d == ["0","1","2","4","8","16","32"]

let d = [Duration 1 1 (1/3),Duration 4 1 1,Duration 4 1 (2/3)]
in map duration_recip_pp d == ["3.","4.","6."]

Letter

whole_note_division_letter_pp :: Integer -> Maybe Char

duration_letter_pp :: Duration -> Maybe String