Music.Theory.Duration.RQ

Rational quarter-note notation for durations.

Documentation

type RQ = Rational

Rational Quarter-Note

rq_to_duration :: RQ -> Maybe Duration

Rational quarter note to duration value. It is a mistake to hope this could handle tuplets directly since, for instance, a 3:2 dotted note will be of the same duration as a plain undotted note.

rq_to_duration (3/4) == Just dotted_eighth_note

rq_is_cmn :: RQ -> Bool

Is RQ a cmn duration.

map rq_is_cmn [1/4,1/5,1/8,3/32] == [True,False,True,False]

rq_to_duration_err :: Show a => a -> RQ -> Duration

Variant of rq_to_duration with error message.

whole_note_division_to_rq :: Integer -> RQ

Convert a whole note division integer to an RQ value.

map whole_note_division_to_rq [1,2,4,8] == [4,2,1,1/2]

rq_apply_dots :: RQ -> Integer -> RQ

Apply dots to an RQ duration.

map (rq_apply_dots 1) [1,2] == [3/2,7/4]

duration_to_rq :: Duration -> RQ

Convert Duration to RQ value, see rq_to_duration for partial inverse.

let d = [half_note,dotted_quarter_note,dotted_whole_note]
in map duration_to_rq d == [2,3/2,6]

duration_compare_rq :: Duration -> Duration -> Ordering

compare function for Duration via duration_to_rq.

half_note `duration_compare_rq` quarter_note == GT

rq_mod :: RQ -> RQ -> RQ

RQ modulo.

map (rq_mod (5/2)) [3/2,3/4,5/2] == [1,1/4,0]

rq_divisible_by :: RQ -> RQ -> Bool

Is p divisible by q, ie. is the denominator of p/q == 1.

map (rq_divisible_by (3%2)) [1%2,1%3] == [True,False]

rq_is_integral :: RQ -> Bool

Is RQ a whole number (ie. is denominator == 1.

map rq_is_integral [1,3/2,2] == [True,False,True]

rq_integral :: RQ -> Maybe Integer

Return numerator of RQ if denominator == 1.

map rq_integral [1,3/2,2] == [Just 1,Nothing,Just 2]

rq_derive_tuplet_plain :: [RQ] -> Maybe (Integer, Integer)

Derive the tuplet structure of a set of RQ values.

rq_derive_tuplet_plain [1/2] == Nothing
rq_derive_tuplet_plain [1/2,1/2] == Nothing
rq_derive_tuplet_plain [1/4,1/4] == Nothing
rq_derive_tuplet_plain [1/3,2/3] == Just (3,2)
rq_derive_tuplet_plain [1/2,1/3,1/6] == Just (6,4)
rq_derive_tuplet_plain [1/3,1/6] == Just (6,4)
rq_derive_tuplet_plain [2/5,3/5] == Just (5,4)
rq_derive_tuplet_plain [1/3,1/6,2/5,1/10] == Just (30,16)

map rq_derive_tuplet_plain [[1/3,1/6],[2/5,1/10]] == [Just (6,4)
                                                     ,Just (10,8)]

rq_derive_tuplet :: [RQ] -> Maybe (Integer, Integer)

Derive the tuplet structure of a set of RQ values.

rq_derive_tuplet [1/4,1/8,1/8] == Nothing
rq_derive_tuplet [1/3,2/3] == Just (3,2)
rq_derive_tuplet [1/2,1/3,1/6] == Just (3,2)
rq_derive_tuplet [2/5,3/5] == Just (5,4)
rq_derive_tuplet [1/3,1/6,2/5,1/10] == Just (15,8)

rq_un_tuplet :: (Integer, Integer) -> RQ -> RQ

Remove tuplet multiplier from value, ie. to give notated duration. This seems odd but is neccessary to avoid ambiguity. Ie. is 1 a quarter note or a 3:2 tuplet dotted-quarter-note etc.

map (rq_un_tuplet (3,2)) [1,2/3,1/2,1/3] == [3/2,1,3/4,1/2]

rq_to_cmn :: RQ -> Maybe (RQ, RQ)

If an RQ duration is un-representable by a single cmn duration, give tied notation.

catMaybes (map rq_to_cmn [1..9]) == [(4,1),(4,3),(8,1)]

map rq_to_cmn [5/4,5/8] == [Just (1,1/4),Just (1/2,1/8)]

rq_can_notate :: [RQ] -> Bool

Predicate to determine if a segment can be notated either without a tuplet or with a single tuplet.

rq_can_notate [1/2,1/4,1/4] == True
rq_can_notate [1/3,1/6] == True
rq_can_notate [2/5,1/10] == True
rq_can_notate [1/3,1/6,2/5,1/10] == False
rq_can_notate [4/7,1/7,6/7,3/7] == True
rq_can_notate [4/7,1/7,2/7] == True