At 11:53 AM -0700 7/4/10, Michael Mossey wrote:
Wondering if I could get some suggestions for coding this problem.
A musical document (or "score") consists primarily of a list of measures. A measure consists primarily of lists of "items". We'll consider only one kind of item: a note. Items have a location within the measure. A note's location indicates both where it goes on the page (i.e. a visual representation of the score) and what moment in time it begins sounding (i.e. rendering the score in sound). My concern here is sound.
data Doc = [Measure]
data Loc = ... (represents a location within the musical document including measure number)
data Measure = Measure [(Loc,Item)] -- In the Meausre, we can assume (Loc,Item) are in -- ascending order
Notes also have an end, when indicates when in time they stop sounding. See the 'end' field below. Also note the 'soundedEnd' 'tieStart' and 'tieStop' fields which I will explain.
data Item = Note { pitch :: Pitch , end :: Loc , soundedEnd :: Maybe Loc , tieNext :: Bool , tiePrior :: Bool }
There is a concept of "tied notes". When two notes are tied together, their durations are summed and they are sounded continuously as if one note. Ties have several uses, but one important one is to make a sound that begins in one measure and ends in a later measure, by tying notes across measures.
The 'tieNext' field indicates if a note is tied to the following note (that is, the next note of the same pitch). 'tiePrior' indicates if tied to immediately prior note of same pitch.
A chain of notes can be tied. Notes in the middle with have both tieNext and tiePrior set.
In the event a note is within a chain of ties, its 'soundedEnd' field needs to be computed as Just e where e is the end of the last note in the chain. This information is useful when rendering the document as sound.
My problem is:
- given a Doc in which all fields have been set EXCEPT soundedEnd (all soundedEnd's are given a default value of Nothing) - update those notes in the Doc which need to have soundedEnd set. This involves chasing down the chain of ties.
I can solve a simpler problem which is
-- Given a note with tieNext set, and a list of notes, find -- the end Loc of the last note in the chain. Only notes -- with the same pitch as 'firstNote' are considered when looking -- for the chain of notes. computeSoundedEnd :: Item -> [Item] -> Loc computeSoundedEnd firstNote notes = compSndEnd (pitch firstNote) notes
compSndEnd :: Pitch -> [Item] -> Loc compSndEnd _ [] = error "tie chain doesn't come to completion" compSndEnd p (n:ns) = if pitch n == p then if tieNext n then if tiePrior n then compSndEnd p ns else error "illegal tie chain" else if tiePrior n then end n else error "illegal tie chain" else compSndEnd p ns
The thing that is hard for me to understand is how, in a functional paradigm, to update the entire Doc by chasing down every tie and making all necessary updates.
Thanks, Mike
[Sorry to be coming so late to this thread. I'm catching up on old Haskell e-mail.] I agree with some of the earlier posters that your representation is probably more complicated than needed. (BTW, a graph especially seems like overkill.) Nevertheless, given your representation, `soundedEnd` can be computed idiomatically and efficiently in Haskell. As you showed, computing `soundedEnd` for one item depends only on the item and those that follow it. In an imperative language, we would compute the `soundedEnd` values from the end to the beginning, storing the results as we go. In Haskell, we can simply use a "foldr" pattern and let lazy evaluation take care of the rest. (Unfortunately, in this case the "foldr" is not quite so simple, due to the two levels of lists--measures and items.) I simplify the computation of `soundedEnd` by letting it be defined always: For a note whose `tieNext` is `False`, the `soundedEnd` value equals the `end` value. With this approach, `soundedEnd` has type `Loc`. (In fact, its value could be computed (i.e., the thunk to evaluate it could be installed) when the item is originally created, thanks again to lazy evaluation.) Also, I eliminate `tiePrior` because it's not needed for this demonstration. Dean import Ratio type Duration = Rational -- Whole note has duration 1. type Loc = (Int, Duration) type Pitch = Char -- for simplicity data Item = Note { pitch :: Pitch , end :: Loc , soundedEnd :: Loc , tieNext :: Bool } deriving (Show, Read) data Measure = Measure [(Loc, Item)] deriving (Show, Read) type Doc = [Measure] computeSoundedEnd :: Doc -> Doc computeSoundedEnd measures = foldr eachMeasure [] measures where eachMeasure (Measure litems) remainingMeasures = Measure (foldr eachLItem [] litems) : remainingMeasures where eachLItem (loc, item) remainingLItems = (loc, item') : remainingLItems where item' = item{ soundedEnd = soundedEndFor item' remainingLItems remainingMeasures } soundedEndFor :: Item -> [(Loc, Item)] -> [Measure] -> Loc soundedEndFor item litems measures | tieNext item = case filter ((pitch item ==) . pitch . snd) (litems ++ concatMap unMeasure measures) of [] -> error "illegal tie chain" (_, item') : _ -> soundedEnd item' | otherwise = end item unMeasure :: Measure -> [(Loc, Item)] unMeasure (Measure litems) = litems measureLength = 4%4 -- for simplicity plus :: Loc -> Duration -> Loc (m, o) `plus` d = let o' = (o + d) / measureLength md = floor o' od = o' - fromIntegral md in (m + md, od) li tied start pitch dur = (start, Note pitch (start `plus` dur) (error "undefined soundedEnd") tied) ni start pitch dur = li False start pitch dur ti start pitch dur = li True start pitch dur [a,b,c,d,e,f,g] = ['a'..'g'] -- In the following graphical representation: -- * Each character position represents an eighth note. -- * A capitalized note is tied to its successor. -- * Note that the "B" line is musically dubious. -- | | | g.| -- | | | Ff. | -- | E.|E.......|E.e | -- | D.d. | | | -- |c. c. | | | -- | B.| |b.......| -- | |A.A.A.a.| | doc1 = [Measure [ni (0,0%4) c (1%4), ti (0,1%4) d (1%4), ni (0,2%4) c (1%4), ni (0,2%4) d (1%4), ti (0,3%4) b (1%4), ti (0,3%4) e (1%4)], Measure [ti (1,0%4) a (1%4), ti (1,0%4) e (1%1), ti (1,1%4) a (1%4), ti (1,2%4) a (1%4), ni (1,3%4) a (1%4)], Measure [ti (2,0%4) e (1%4), ni (2,0%4) b (1%1), ni (2,1%4) e (1%8), ti (2,3%8) f (1%8), ni (2,2%4) f (1%4), ni (2,3%4) g (1%4)]] main = print (computeSoundedEnd doc1)