Music.Theory.Duration.Sequence.Notate

Notation of a sequence of Rq values as annotated Duration values.

1. Separate input sequence into measures, adding tie annotations as required (see to_measures_ts). Ensure all Rq_Tied values can be notated as common music notation durations.
2. 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.
3. Simplify each measure (see m_simplify and default_rule). Coalesces tied durations where appropriate.
4. Notate measures (see m_notate or mm_notate).
5. Ascribe values to notated durations, see ascribe.

Lists

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

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
coalesce jn [1..5] == map sum [[1],[2,3],[4,5]]

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

Variant of coalesce with accumulation parameter.

coalesce_accum (\_ 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)
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]
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]

Variant of coalesce_accum that accumulates running sum.

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

Separate

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

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])

Variant of take_sum_by with id function.

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

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]]

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))

Split sequence l 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_split_sum :: Rq -> [Rq_Tied] -> Maybe ([Rq_Tied], [Rq_Tied])

Variant of split_sum that operates at Rq_Tied sequences.

t = True
f = False

r = Just ([(3,f),(2,t)],[(1,f)])
rqt_split_sum 5 [(3,f),(2,t),(1,f)] == r

r = Just ([(3,f),(1,t)],[(1,t),(1,f)])
rqt_split_sum 4 [(3,f),(2,t),(1,f)] == r

rqt_split_sum 4 [(5/2,False)] == Nothing

rqt_separate :: [Rq] -> [Rq_Tied] -> Either String [[Rq_Tied]]

Separate Rq_Tied 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.

t = True
f = False

d = [(2,f),(2,f),(2,f)]
r = [[(2,f),(1,t)],[(1,f),(2,f)]]
rqt_separate [3,3] d == Right r

d = [(5/8,f),(1,f),(3/8,f)]
r = [[(5/8,f),(3/8,t)],[(5/8,f),(3/8,f)]]
rqt_separate [1,1] d == Right r

d = [(4/7,t),(1/7,f),(1,f),(6/7,f),(3/7,f)]
r = [[(4/7,t),(1/7,f),(2/7,t)],[(5/7,f),(2/7,t)],[(4/7,f),(3/7,f)]]
rqt_separate [1,1,1] d == Right r

rqt_separate_m :: [Rq] -> [Rq_Tied] -> Maybe [[Rq_Tied]]

Maybe form ot rqt_separate

rqt_separate_tuplet :: Rq -> [Rq_Tied] -> Either String [[Rq_Tied]]

If the input Rq_Tied 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_Tied] -> [[Rq_Tied]]

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_Tied]] -> [[Rq_Tied]]

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_Tied] -> [Rq_Tied]

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)]

rqt_tuplet_subdivide_seq_sanity_ :: Rq -> [[Rq_Tied]] -> [[Rq_Tied]]

Divisions

to_measures_rq :: [Rq] -> [Rq] -> Either String [[Rq_Tied]]

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_untied_err :: [Rq] -> [Rq] -> [[Rq]]

Variant that is applicable only at sequence that do not require splitting and ties, else error.

to_measures_rq_cmn :: [Rq] -> [Rq] -> Either String [[Rq_Tied]]

Variant of to_measures_rq that ensures Rq_Tied 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_Tied]]

Variant of to_measures_rq with measures given by Time_Signature values. Does not ensure Rq_Tied 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]]

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_Tied] -> Either String [[Rq_Tied]]

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_Tied] -> Either String [[Rq_Tied]]

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_Tied]]]

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_Tied]]]

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_Tied] -> Maybe ((Integer, Integer), [Rq_Tied])

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_Tied] -> Either String [Duration_A]

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_Tied]] -> Either String [Duration_A]

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_Tied]]] -> Either String [[Duration_A]]

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))

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

type Simplify_P = Simplify_T -> Bool

Predicate function at Simplify_T.

type Simplify_M = ([Time_Signature], [Rq], [(Rq, Rq)])

Variant of Simplify_T allowing multiple rules.

meta_table_p :: Simplify_M -> Simplify_P

Transform Simplify_M to Simplify_P.

meta_table_t :: Simplify_M -> [Simplify_T]

Transform Simplify_M to set of Simplify_T.

default_table :: Simplify_P

The default table of simplifiers.

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

default_8_rule :: Simplify_P

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

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

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

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

Measure simplifier. Apply given Simplify_P.

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

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

p_simplify_rule :: Simplify_P

Pulse simplifier predicate, which is const True.

p_simplify :: [Duration_A] -> [Duration_A]

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]]

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]]

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)])

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)]

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)])

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)])

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)]

snd . m_ascribe.

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

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)]]

'mm_ascribe of notate.

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

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

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)]

Variant of ascribe that groups the rhs elements using group_chd and with the indicated chord function, then rejoins the resulting sequence.

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

Variant of mm_ascribe using group_chd