Music.Theory.Duration

Common music notation duration model.

Documentation

type Division = Integer

type Dots = Int

data Duration

Common music notation durational model

Constructors

Duration

Fields

• division :: Division

  division of whole note

• dots :: Int

  number of dots

• multiplier :: Rational

  tuplet modifier

Instances

Show Duration

Defined in Music.Theory.Duration

Methods

showsPrec :: Int -> Duration -> ShowS

show :: Duration -> String

showList :: [Duration] -> ShowS

Eq Duration

Defined in Music.Theory.Duration

Methods

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

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

Ord Duration

Ord instance in terms of duration_compare_meq_err.

Defined in Music.Theory.Duration

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

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 :: Rational -> (Division, Division) -> Maybe Duration

Sum undotted divisions, input is required to be sorted.

sum_dur_dotted :: Rational -> (Division, Dots, Division, Dots) -> Maybe Duration

Sum dotted divisions, input is required to be sorted.

sum_dur_dotted 1 (4,1,4,1) == Just (Duration 2 1 1)
sum_dur_dotted 1 (4,0,2,1) == Just (Duration 1 0 1)
sum_dur_dotted 1 (8,1,4,0) == Just (Duration 4 2 1)
sum_dur_dotted 1 (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
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_std_set :: [Division]

Standard divisions (from 1 to 256). MusicXml allows 0 for breve and -1 for long. Negative divisors can represent any number of longer durations, -2 be a breve, -4 a long, -8 a maximus, &etc.

divisions_musicxml_set :: [Division]

duration_set :: Dots -> [Duration]

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

beam_count_tbl :: [(Division, Int)]

Table of number of beams at notated division.

whole_note_division_to_beam_count :: Division -> Maybe Int

Lookup beam_count_tbl.

whole_note_division_to_beam_count 32 == Just 3

duration_beam_count :: Duration -> Int

Calculate number of beams at Duration.

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

MusicXml

division_musicxml_tbl :: [(Division, String)]

Table giving MusicXml types for divisions.

whole_note_division_to_musicxml_type :: Division -> 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 :: Division -> 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]
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)]
map duration_recip_pp d == ["3.","4.","6."]

Letter

whole_note_division_name_tbl :: [(Division, String)]

Names for note divisions. Starting from 1/32 these names haev uniqe initial letters that can be used for concise notation.

whole_note_division_name :: Division -> Maybe String

whole_note_division_letter_tbl :: [(Division, Char)]

whole_note_division_letter_pp :: Division -> Maybe Char

duration_letter_pp :: Duration -> Maybe String