Safe Haskell | Safe |
---|---|

Language | Haskell98 |

Notation of a sequence of `RQ`

values as annotated `Duration`

values.

- Separate input sequence into measures, adding tie annotations as
required (see
`to_measures_ts`

). Ensure all`RQ_T`

values can be notated as*common music notation*durations. - Separate each measure into pulses (see
`m_divisions_ts`

). Further subdivides pulses to ensure*cmn*tuplet notation. See`to_divisions_ts`

for a composition of`to_measures_ts`

and`m_divisions_ts`

. - Simplify each measure (see
`m_simplify`

and`default_rule`

). Coalesces tied durations where appropriate. - Notate measures (see
`m_notate`

or`mm_notate`

). - Ascribe values to notated durations, see
`ascribe`

.

- all_just :: [Maybe a] -> Maybe [a]
- all_right :: [Either a b] -> Either a [b]
- coalesce :: (a -> a -> Maybe a) -> [a] -> [a]
- coalesce_accum :: (b -> a -> a -> Either a b) -> b -> [a] -> [(b, a)]
- coalesce_sum :: (b -> a -> b) -> b -> (b -> a -> a -> Maybe a) -> [a] -> [a]
- either_to_maybe :: Either a b -> Maybe b
- take_sum_by :: (Ord n, Num n) => (a -> n) -> n -> [a] -> ([a], n, [a])
- take_sum :: (Ord a, Num a) => a -> [a] -> ([a], a, [a])
- take_sum_by_eq :: (Ord n, Num n) => (a -> n) -> n -> [a] -> Maybe ([a], [a])
- split_sum_by_eq :: (Ord n, Num n) => (a -> n) -> [n] -> [a] -> Maybe [[a]]
- split_sum :: (Ord a, Num a) => a -> [a] -> Maybe ([a], [a], Maybe (a, a))
- _t :: Bool
- _f :: Bool
- rqt_split_sum :: RQ -> [RQ_T] -> Maybe ([RQ_T], [RQ_T])
- rqt_separate :: [RQ] -> [RQ_T] -> Either String [[RQ_T]]
- rqt_separate_m :: [RQ] -> [RQ_T] -> Maybe [[RQ_T]]
- rqt_separate_tuplet :: RQ -> [RQ_T] -> Either String [[RQ_T]]
- rqt_tuplet_subdivide :: RQ -> [RQ_T] -> [[RQ_T]]
- rqt_tuplet_subdivide_seq :: RQ -> [[RQ_T]] -> [[RQ_T]]
- rqt_tuplet_sanity_ :: [RQ_T] -> [RQ_T]
- rqt_tuplet_subdivide_seq_sanity_ :: RQ -> [[RQ_T]] -> [[RQ_T]]
- to_measures_rq :: [RQ] -> [RQ] -> Either String [[RQ_T]]
- to_measures_rq_cmn :: [RQ] -> [RQ] -> Either String [[RQ_T]]
- to_measures_ts :: [Time_Signature] -> [RQ] -> Either String [[RQ_T]]
- to_measures_ts_by_eq :: (a -> RQ) -> [Time_Signature] -> [a] -> Maybe [[a]]
- m_divisions_rq :: [RQ] -> [RQ_T] -> Either String [[RQ_T]]
- m_divisions_ts :: Time_Signature -> [RQ_T] -> Either String [[RQ_T]]
- to_divisions_rq :: [[RQ]] -> [RQ] -> Either String [[[RQ_T]]]
- to_divisions_ts :: [Time_Signature] -> [RQ] -> Either String [[[RQ_T]]]
- p_tuplet_rqt :: [RQ_T] -> Maybe ((Integer, Integer), [RQ_T])
- p_notate :: Bool -> [RQ_T] -> Either String [Duration_A]
- m_notate :: Bool -> [[RQ_T]] -> Either String [Duration_A]
- mm_notate :: [[[RQ_T]]] -> Either String [[Duration_A]]
- type Simplify_T = (Time_Signature, RQ, (RQ, RQ))
- type Simplify_P = Simplify_T -> Bool
- type Simplify_M = ([Time_Signature], [RQ], [(RQ, RQ)])
- meta_table_p :: Simplify_M -> Simplify_P
- meta_table_t :: Simplify_M -> [Simplify_T]
- default_table :: Simplify_P
- default_8_rule :: Simplify_P
- default_4_rule :: Simplify_P
- default_rule :: [Simplify_T] -> Simplify_P
- m_simplify :: Simplify_P -> Time_Signature -> [Duration_A] -> [Duration_A]
- m_simplify_fix :: Int -> Simplify_P -> Time_Signature -> [Duration_A] -> [Duration_A]
- p_simplify_rule :: Simplify_P
- p_simplify :: [Duration_A] -> [Duration_A]
- notate_rqp :: Int -> Simplify_P -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> Either String [[Duration_A]]
- notate :: Int -> Simplify_P -> [Time_Signature] -> [RQ] -> Either String [[Duration_A]]
- zip_hold_lhs :: (Show t, Show x) => (x -> Bool) -> [x] -> [t] -> ([t], [(x, t)])
- zip_hold_lhs_err :: (Show t, Show x) => (x -> Bool) -> [x] -> [t] -> [(x, t)]
- zip_hold :: (Show t, Show x) => (x -> Bool) -> (t -> Bool) -> [x] -> [t] -> ([t], [(x, t)])
- m_ascribe :: Show x => [Duration_A] -> [x] -> ([x], [(Duration_A, x)])
- ascribe :: Show x => [Duration_A] -> [x] -> [(Duration_A, x)]
- mm_ascribe :: Show x => [[Duration_A]] -> [x] -> [[(Duration_A, x)]]
- notate_mm_ascribe :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] -> Either String [[(Duration_A, a)]]
- notate_mm_ascribe_err :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] -> [[(Duration_A, a)]]
- group_chd :: (x -> Bool) -> [x] -> [[x]]
- ascribe_chd :: Show x => (x -> Bool) -> [Duration_A] -> [x] -> [(Duration_A, x)]
- mm_ascribe_chd :: Show x => (x -> Bool) -> [[Duration_A]] -> [x] -> [[(Duration_A, x)]]

# Lists

coalesce :: (a -> a -> Maybe a) -> [a] -> [a] Source #

Applies a *join* function to the first two elements of the list.
If the *join* function succeeds the joined element is considered
for further coalescing.

coalesce (\p q -> Just (p + q)) [1..5] == [15]

let jn p q = if even p then Just (p + q) else Nothing in coalesce jn [1..5] == map sum [[1],[2,3],[4,5]]

coalesce_accum :: (b -> a -> a -> Either a b) -> b -> [a] -> [(b, a)] Source #

Variant of `coalesce`

with accumulation parameter.

coalesce_accum (\i p q -> Left (p + q)) 0 [1..5] == [(0,15)]

let jn i p q = if even p then Left (p + q) else Right (p + i) in coalesce_accum jn 0 [1..7] == [(0,1),(1,5),(6,9),(15,13)]

let jn i p q = if even p then Left (p + q) else Right [p,q] in coalesce_accum jn [] [1..5] == [([],1),([1,2],5),([5,4],9)]

coalesce_sum :: (b -> a -> b) -> b -> (b -> a -> a -> Maybe a) -> [a] -> [a] Source #

Variant of `coalesce_accum`

that accumulates running sum.

let f i p q = if i == 1 then Just (p + q) else Nothing in coalesce_sum (+) 0 f [1,1/2,1/4,1/4] == [1,1]

# Either

# Separate

take_sum_by :: (Ord n, Num n) => (a -> n) -> n -> [a] -> ([a], n, [a]) Source #

Take elements while the sum of the prefix is less than or equal to the indicated value. Returns also the difference between the prefix sum and the requested sum. Note that zero elements are kept left.

take_sum_by id 3 [2,1] == ([2,1],0,[]) take_sum_by id 3 [2,2] == ([2],1,[2]) take_sum_by id 3 [2,1,0,1] == ([2,1,0],0,[1]) take_sum_by id 3 [4] == ([],3,[4]) take_sum_by id 0 [1..5] == ([],0,[1..5])

take_sum :: (Ord a, Num a) => a -> [a] -> ([a], a, [a]) Source #

Variant of `take_sum_by`

with `id`

function.

take_sum_by_eq :: (Ord n, Num n) => (a -> n) -> n -> [a] -> Maybe ([a], [a]) Source #

Variant of `take_sum`

that requires the prefix to sum to value.

take_sum_by_eq id 3 [2,1,0,1] == Just ([2,1,0],[1]) take_sum_by_eq id 3 [2,2] == Nothing

split_sum_by_eq :: (Ord n, Num n) => (a -> n) -> [n] -> [a] -> Maybe [[a]] Source #

Recursive variant of `take_sum_by_eq`

.

split_sum_by_eq id [3,3] [2,1,0,3] == Just [[2,1,0],[3]] split_sum_by_eq id [3,3] [2,2,2] == Nothing

split_sum :: (Ord a, Num a) => a -> [a] -> Maybe ([a], [a], Maybe (a, a)) Source #

Split sequence such that the prefix sums to precisely *m*. The
third element of the result indicates if it was required to divide
an element. Note that zero elements are kept left. If the required
sum is non positive, or the input list does not sum to at least the
required sum, gives nothing.

split_sum 5 [2,3,1] == Just ([2,3],[1],Nothing) split_sum 5 [2,1,3] == Just ([2,1,2],[1],Just (2,1)) split_sum 2 [3/2,3/2,3/2] == Just ([3/2,1/2],[1,3/2],Just (1/2,1)) split_sum 6 [1..10] == Just ([1..3],[4..10],Nothing) fmap (\(a,_,c)->(a,c)) (split_sum 5 [1..]) == Just ([1,2,2],Just (2,1)) split_sum 0 [1..] == Nothing split_sum 3 [1,1] == Nothing split_sum 3 [2,1,0] == Just ([2,1,0],[],Nothing) split_sum 3 [2,1,0,1] == Just ([2,1,0],[1],Nothing)

rqt_separate :: [RQ] -> [RQ_T] -> Either String [[RQ_T]] Source #

Separate `RQ_T`

values in sequences summing to `RQ`

values. This
is a recursive variant of `rqt_split_sum`

. Note that is does not
ensure *cmn* notation of values.

let d = [(2,_f),(2,_f),(2,_f)] in rqt_separate [3,3] d == Right [[(2,_f),(1,_t)] ,[(1,_f),(2,_f)]]

let d = [(5/8,_f),(1,_f),(3/8,_f)] in rqt_separate [1,1] d == Right [[(5/8,_f),(3/8,_t)] ,[(5/8,_f),(3/8,_f)]]

let d = [(4/7,_t),(1/7,_f),(1,_f),(6/7,_f),(3/7,_f)] in rqt_separate [1,1,1] d == Right [[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(5/7,_f),(2/7,_t)] ,[(4/7,_f),(3/7,_f)]]

rqt_separate_tuplet :: RQ -> [RQ_T] -> Either String [[RQ_T]] Source #

If the input `RQ_T`

sequence cannot be notated (see
`rqt_can_notate`

) separate into equal parts, so long as each part
is not less than *i*.

rqt_separate_tuplet undefined [(1/3,_f),(1/6,_f)] rqt_separate_tuplet undefined [(4/7,_t),(1/7,_f),(2/7,_f)]

let d = map rq_rqt [1/3,1/6,2/5,1/10] in rqt_separate_tuplet (1/8) d == Right [[(1/3,_f),(1/6,_f)] ,[(2/5,_f),(1/10,_f)]]

let d = [(1/5,True),(1/20,False),(1/2,False),(1/4,True)] in rqt_separate_tuplet (1/16) d

let d = [(2/5,_f),(1/5,_f),(1/5,_f),(1/5,_t),(1/2,_f),(1/2,_f)] in rqt_separate_tuplet (1/2) d

let d = [(4/10,True),(1/10,False),(1/2,True)] in rqt_separate_tuplet (1/2) d

rqt_tuplet_subdivide :: RQ -> [RQ_T] -> [[RQ_T]] Source #

Recursive variant of `rqt_separate_tuplet`

.

let d = map rq_rqt [1,1/3,1/6,2/5,1/10] in rqt_tuplet_subdivide (1/8) d == [[(1/1,_f)] ,[(1/3,_f),(1/6,_f)] ,[(2/5,_f),(1/10,_f)]]

rqt_tuplet_subdivide_seq :: RQ -> [[RQ_T]] -> [[RQ_T]] Source #

Sequence variant of `rqt_tuplet_subdivide`

.

let d = [(1/5,True),(1/20,False),(1/2,False),(1/4,True)] in rqt_tuplet_subdivide_seq (1/2) [d]

rqt_tuplet_sanity_ :: [RQ_T] -> [RQ_T] Source #

If a tuplet is all tied, it ought to be a plain value?!

rqt_tuplet_sanity_ [(4/10,_t),(1/10,_f)] == [(1/2,_f)]

# Divisions

to_measures_rq :: [RQ] -> [RQ] -> Either String [[RQ_T]] Source #

Separate `RQ`

sequence into measures given by `RQ`

length.

to_measures_rq [3,3] [2,2,2] == Right [[(2,_f),(1,_t)],[(1,_f),(2,_f)]] to_measures_rq [3,3] [6] == Right [[(3,_t)],[(3,_f)]] to_measures_rq [1,1,1] [3] == Right [[(1,_t)],[(1,_t)],[(1,_f)]] to_measures_rq [3,3] [2,2,1] to_measures_rq [3,2] [2,2,2]

let d = [4/7,33/28,9/20,4/5] in to_measures_rq [3] d == Right [[(4/7,_f),(33/28,_f),(9/20,_f),(4/5,_f)]]

to_measures_rq_cmn :: [RQ] -> [RQ] -> Either String [[RQ_T]] Source #

Variant of `to_measures_rq`

that ensures `RQ_T`

are *cmn*
durations. This is not a good composition.

to_measures_rq_cmn [6,6] [5,5,2] == Right [[(4,_t),(1,_f),(1,_t)] ,[(4,_f),(2,_f)]]

let r = [[(4/7,_t),(1/7,_f),(1,_f),(6/7,_f),(3/7,_f)]] in to_measures_rq_cmn [3] [5/7,1,6/7,3/7] == Right r

to_measures_rq_cmn [1,1,1] [5/7,1,6/7,3/7] == Right [[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(4/7,_f),(3/7,_f)]]

to_measures_ts :: [Time_Signature] -> [RQ] -> Either String [[RQ_T]] Source #

Variant of `to_measures_rq`

with measures given by
`Time_Signature`

values. Does not ensure `RQ_T`

are *cmn*
durations.

to_measures_ts [(1,4)] [5/8,3/8] /= Right [[(1/2,_t),(1/8,_f),(3/8,_f)]] to_measures_ts [(1,4)] [5/7,2/7] /= Right [[(4/7,_t),(1/7,_f),(2/7,_f)]]

let {m = replicate 18 (1,4) ;x = [3/4,2,5/4,9/4,1/4,3/2,1/2,7/4,1,5/2,11/4,3/2]} in to_measures_ts m x == Right [[(3/4,_f),(1/4,_t)],[(1/1,_t)] ,[(3/4,_f),(1/4,_t)],[(1/1,_f)] ,[(1/1,_t)],[(1/1,_t)] ,[(1/4,_f),(1/4,_f),(1/2,_t)],[(1/1,_f)] ,[(1/2,_f),(1/2,_t)],[(1/1,_t)] ,[(1/4,_f),(3/4,_t)],[(1/4,_f),(3/4,_t)] ,[(1/1,_t)],[(3/4,_f),(1/4,_t)] ,[(1/1,_t)],[(1/1,_t)] ,[(1/2,_f),(1/2,_t)],[(1/1,_f)]]

to_measures_ts [(3,4)] [4/7,33/28,9/20,4/5] to_measures_ts (replicate 3 (1,4)) [4/7,33/28,9/20,4/5]

to_measures_ts_by_eq :: (a -> RQ) -> [Time_Signature] -> [a] -> Maybe [[a]] Source #

Variant of `to_measures_ts`

that allows for duration field
operation but requires that measures be well formed. This is
useful for re-grouping measures after notation and ascription.

m_divisions_rq :: [RQ] -> [RQ_T] -> Either String [[RQ_T]] Source #

Divide measure into pulses of indicated `RQ`

durations. Measure
must be of correct length but need not contain only *cmn*
durations. Pulses are further subdivided if required to notate
tuplets correctly, see `rqt_tuplet_subdivide_seq`

.

let d = [(1/4,_f),(1/4,_f),(2/3,_t),(1/6,_f),(16/15,_f),(1/5,_f) ,(1/5,_f),(2/5,_t),(1/20,_f),(1/2,_f),(1/4,_t)] in m_divisions_rq [1,1,1,1] d

m_divisions_rq [1,1,1] [(4/7,_f),(33/28,_f),(9/20,_f),(4/5,_f)]

m_divisions_ts :: Time_Signature -> [RQ_T] -> Either String [[RQ_T]] Source #

Variant of `m_divisions_rq`

that determines pulse divisions from
`Time_Signature`

.

let d = [(4/7,_t),(1/7,_f),(2/7,_f)] in m_divisions_ts (1,4) d == Just [d]

let d = map rq_rqt [1/3,1/6,2/5,1/10] in m_divisions_ts (1,4) d == Just [[(1/3,_f),(1/6,_f)] ,[(2/5,_f),(1/10,_f)]]

let d = map rq_rqt [4/7,33/28,9/20,4/5] in m_divisions_ts (3,4) d == Just [[(4/7,_f),(3/7,_t)] ,[(3/4,_f),(1/4,_t)] ,[(1/5,_f),(4/5,_f)]]

to_divisions_rq :: [[RQ]] -> [RQ] -> Either String [[[RQ_T]]] Source #

Composition of `to_measures_rq`

and `m_divisions_rq`

, where
measures are initially given as sets of divisions.

let m = [[1,1,1],[1,1,1]] in to_divisions_rq m [2,2,2] == Right [[[(1,_t)],[(1,_f)],[(1,_t)]] ,[[(1,_f)],[(1,_t)],[(1,_f)]]]

let d = [2/7,1/7,4/7,5/7,8/7,1,1/7] in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,_f),(1/7,_f),(4/7,_f)] ,[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(6/7,_f),(1/7,_t)] ,[(6/7,_f),(1/7,_f)]]]

let d = [5/7,1,6/7,3/7] in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(4/7,_f),(3/7,_f)]]]

let d = [2/7,1/7,4/7,5/7,1,6/7,3/7] in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,_f),(1/7,_f),(4/7,_f)] ,[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(4/7,_t),(1/7,_f),(2/7,_t)] ,[(4/7,_f),(3/7,_f)]]]

let d = [4/7,33/28,9/20,4/5] in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,_f),(3/7,_t)] ,[(3/4,_f),(1/4,_t)] ,[(1/5,_f),(4/5,_f)]]]

let {p = [[1/2,1,1/2],[1/2,1]] ;d = map (/6) [1,1,1,1,1,1,4,1,2,1,1,2,1,3]} in to_divisions_rq p d == Right [[[(1/6,_f),(1/6,_f),(1/6,_f)] ,[(1/6,_f),(1/6,_f),(1/6,_f),(1/2,True)] ,[(1/6,_f),(1/6,_f),(1/6,True)]] ,[[(1/6,_f),(1/6,_f),(1/6,_f)] ,[(1/3,_f),(1/6,_f),(1/2,_f)]]]

to_divisions_ts :: [Time_Signature] -> [RQ] -> Either String [[[RQ_T]]] Source #

Variant of `to_divisions_rq`

with measures given as set of
`Time_Signature`

.

let d = [3/5,2/5,1/3,1/6,7/10,17/15,1/2,1/6] in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)] ,[(1/3,_f),(1/6,_f),(1/2,_t)] ,[(1/5,_f),(4/5,_t)] ,[(1/3,_f),(1/2,_f),(1/6,_f)]]]

let d = [3/5,2/5,1/3,1/6,7/10,29/30,1/2,1/3] in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)] ,[(1/3,_f),(1/6,_f),(1/2,_t)] ,[(1/5,_f),(4/5,_t)] ,[(1/6,_f),(1/2,_f),(1/3,_f)]]]

let d = [3/5,2/5,1/3,1/6,7/10,4/5,1/2,1/2] in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)] ,[(1/3,_f),(1/6,_f),(1/2,_t)] ,[(1/5,_f),(4/5,_f)] ,[(1/2,_f),(1/2,_f)]]]

let d = [4/7,33/28,9/20,4/5] in to_divisions_ts [(3,4)] d == Just [[[(4/7,_f),(3/7,_t)] ,[(3/4,_f),(1/4,_t)] ,[(1/5,_f),(4/5,_f)]]]

# Durations

p_tuplet_rqt :: [RQ_T] -> Maybe ((Integer, Integer), [RQ_T]) Source #

Pulse tuplet derivation.

p_tuplet_rqt [(2/3,_f),(1/3,_t)] == Just ((3,2),[(1,_f),(1/2,_t)]) p_tuplet_rqt (map rq_rqt [1/3,1/6]) == Just ((3,2),[(1/2,_f),(1/4,_f)]) p_tuplet_rqt (map rq_rqt [2/5,1/10]) == Just ((5,4),[(1/2,_f),(1/8,_f)]) p_tuplet_rqt (map rq_rqt [1/3,1/6,2/5,1/10])

p_notate :: Bool -> [RQ_T] -> Either String [Duration_A] Source #

Notate pulse, ie. derive tuplet if neccesary. The flag indicates if the initial value is tied left.

p_notate False [(2/3,_f),(1/3,_t)] p_notate False [(2/5,_f),(1/10,_t)] p_notate False [(1/4,_t),(1/8,_f),(1/8,_f)] p_notate False (map rq_rqt [1/3,1/6]) p_notate False (map rq_rqt [2/5,1/10]) p_notate False (map rq_rqt [1/3,1/6,2/5,1/10]) == Nothing

m_notate :: Bool -> [[RQ_T]] -> Either String [Duration_A] Source #

Notate measure.

m_notate True [[(2/3,_f),(1/3,_t)],[(1,_t)],[(1,_f)]]

let f = m_notate False . concat

fmap f (to_divisions_ts [(4,4)] [3/5,2/5,1/3,1/6,7/10,17/15,1/2,1/6]) fmap f (to_divisions_ts [(4,4)] [3/5,2/5,1/3,1/6,7/10,29/30,1/2,1/3])

mm_notate :: [[[RQ_T]]] -> Either String [[Duration_A]] Source #

Multiple measure notation.

let d = [2/7,1/7,4/7,5/7,8/7,1,1/7] in fmap mm_notate (to_divisions_ts [(4,4)] d)

let d = [2/7,1/7,4/7,5/7,1,6/7,3/7] in fmap mm_notate (to_divisions_ts [(4,4)] d)

let d = [3/5,2/5,1/3,1/6,7/10,4/5,1/2,1/2] in fmap mm_notate (to_divisions_ts [(4,4)] d)

let {p = [[1/2,1,1/2],[1/2,1]] ;d = map (/6) [1,1,1,1,1,1,4,1,2,1,1,2,1,3]} in fmap mm_notate (to_divisions_rq p d)

# Simplifications

type Simplify_T = (Time_Signature, RQ, (RQ, RQ)) Source #

Structure given to `Simplify_P`

to decide simplification. The
structure is *(ts,start-rq,(left-rq,right-rq))*.

type Simplify_P = Simplify_T -> Bool Source #

Predicate function at `Simplify_T`

.

type Simplify_M = ([Time_Signature], [RQ], [(RQ, RQ)]) Source #

Variant of `Simplify_T`

allowing multiple rules.

meta_table_p :: Simplify_M -> Simplify_P Source #

Transform `Simplify_M`

to `Simplify_P`

.

meta_table_t :: Simplify_M -> [Simplify_T] Source #

Transform `Simplify_M`

to set of `Simplify_T`

.

default_table :: Simplify_P Source #

The default table of simplifiers.

default_table ((3,4),1,(1,1)) == True

default_8_rule :: Simplify_P Source #

The default eighth-note pulse simplifier rule.

default_8_rule ((3,8),0,(1/2,1/2)) == True default_8_rule ((3,8),1/2,(1/2,1/2)) == True default_8_rule ((3,8),1,(1/2,1/2)) == True default_8_rule ((2,8),0,(1/2,1/2)) == True default_8_rule ((5,8),0,(1,1/2)) == True default_8_rule ((5,8),0,(2,1/2)) == True

default_4_rule :: Simplify_P Source #

The default quarter note pulse simplifier rule.

default_4_rule ((3,4),0,(1,1/2)) == True default_4_rule ((3,4),0,(1,3/4)) == True default_4_rule ((4,4),1,(1,1)) == False default_4_rule ((4,4),2,(1,1)) == True default_4_rule ((4,4),2,(1,2)) == True default_4_rule ((4,4),0,(2,1)) == True default_4_rule ((3,4),1,(1,1)) == False

default_rule :: [Simplify_T] -> Simplify_P Source #

The default simplifier rule. To extend provide a list of
`Simplify_T`

.

m_simplify :: Simplify_P -> Time_Signature -> [Duration_A] -> [Duration_A] Source #

Measure simplifier. Apply given `Simplify_P`

.

m_simplify_fix :: Int -> Simplify_P -> Time_Signature -> [Duration_A] -> [Duration_A] Source #

Run simplifier until it reaches a fix-point, or for at most `limit`

passes.

p_simplify :: [Duration_A] -> [Duration_A] Source #

Pulse simplifier.

import Music.Theory.Duration.Name.Abbreviation p_simplify [(q,[Tie_Right]),(e,[Tie_Left])] == [(q',[])] p_simplify [(e,[Tie_Right]),(q,[Tie_Left])] == [(q',[])] p_simplify [(q,[Tie_Right]),(e',[Tie_Left])] == [(q'',[])] p_simplify [(q'',[Tie_Right]),(s,[Tie_Left])] == [(h,[])] p_simplify [(e,[Tie_Right]),(s,[Tie_Left]),(e',[])] == [(e',[]),(e',[])]

let f = rqt_to_duration_a False in p_simplify (f [(1/8,_t),(1/4,_t),(1/8,_f)]) == f [(1/2,_f)]

# Notate

notate_rqp :: Int -> Simplify_P -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> Either String [[Duration_A]] Source #

Notate RQ duration sequence. Derive pulse divisions from
`Time_Signature`

if not given directly. Composition of
`to_divisions_ts`

, `mm_notate`

`m_simplify`

.

let ts = [(4,8),(3,8)] ts_p = [[1/2,1,1/2],[1/2,1]] rq = map (/6) [1,1,1,1,1,1,4,1,2,1,1,2,1,3] sr x = T.default_rule [] x in T.notate_rqp 4 sr ts (Just ts_p) rq

notate :: Int -> Simplify_P -> [Time_Signature] -> [RQ] -> Either String [[Duration_A]] Source #

Variant of `notate_rqp`

without pulse divisions (derive).

notate 4 (default_rule [((3,2),0,(2,2)),((3,2),0,(4,2))]) [(3,2)] [6]

# Ascribe

zip_hold_lhs :: (Show t, Show x) => (x -> Bool) -> [x] -> [t] -> ([t], [(x, t)]) Source #

Variant of `zip`

that retains elements of the right hand (rhs)
list where elements of the left hand (lhs) list meet the given lhs
predicate. If the right hand side is longer the remaining elements
to be processed are given. It is an error for the right hand side
to be short.

zip_hold_lhs even [1..5] "abc" == ([],zip [1..6] "abbcc") zip_hold_lhs odd [1..6] "abc" == ([],zip [1..6] "aabbcc") zip_hold_lhs even [1] "ab" == ("b",[(1,'a')]) zip_hold_lhs even [1,2] "a" == undefined

zip_hold_lhs_err :: (Show t, Show x) => (x -> Bool) -> [x] -> [t] -> [(x, t)] Source #

Variant of `zip_hold`

that requires the right hand side to be
precisely the required length.

zip_hold_lhs_err even [1..5] "abc" == zip [1..6] "abbcc" zip_hold_lhs_err odd [1..6] "abc" == zip [1..6] "aabbcc" zip_hold_lhs_err id [False,False] "a" == undefined zip_hold_lhs_err id [False] "ab" == undefined

zip_hold :: (Show t, Show x) => (x -> Bool) -> (t -> Bool) -> [x] -> [t] -> ([t], [(x, t)]) Source #

Variant of `zip`

that retains elements of the right hand (rhs)
list where elements of the left hand (lhs) list meet the given lhs
predicate, and elements of the lhs list where elements of the rhs
meet the rhs predicate. If the right hand side is longer the
remaining elements to be processed are given. It is an error for
the right hand side to be short.

zip_hold even (const False) [1..5] "abc" == ([],zip [1..6] "abbcc") zip_hold odd (const False) [1..6] "abc" == ([],zip [1..6] "aabbcc") zip_hold even (const False) [1] "ab" == ("b",[(1,'a')]) zip_hold even (const False) [1,2] "a" == undefined

zip_hold odd even [1,2,6] [1..5] == ([4,5],[(1,1),(2,1),(6,2),(6,3)])

m_ascribe :: Show x => [Duration_A] -> [x] -> ([x], [(Duration_A, x)]) Source #

Zip a list of `Duration_A`

elements duplicating elements of the
right hand sequence for tied durations.

let {Just d = to_divisions_ts [(4,4),(4,4)] [3,3,2] ;f = map snd . snd . flip m_ascribe "xyz"} in fmap f (notate d) == Just "xxxyyyzz"

ascribe :: Show x => [Duration_A] -> [x] -> [(Duration_A, x)] Source #

mm_ascribe :: Show x => [[Duration_A]] -> [x] -> [[(Duration_A, x)]] Source #

Variant of `m_ascribe`

for a set of measures.

notate_mm_ascribe :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] -> Either String [[(Duration_A, a)]] Source #

'mm_ascribe of `notate`

.

notate_mm_ascribe_err :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] -> [[(Duration_A, a)]] Source #

group_chd :: (x -> Bool) -> [x] -> [[x]] Source #

Group elements as *chords* where a chord element is indicated by
the given predicate.

group_chd even [1,2,3,4,4,5,7,8] == [[1,2],[3,4,4],[5],[7,8]]

ascribe_chd :: Show x => (x -> Bool) -> [Duration_A] -> [x] -> [(Duration_A, x)] Source #

mm_ascribe_chd :: Show x => (x -> Bool) -> [[Duration_A]] -> [x] -> [[(Duration_A, x)]] Source #

Variant of `mm_ascribe`

using `group_chd`