MusicXML: From DTD specification to Haskell implementation Samuel Silva [[email protected]] November 4, 2008 Contents 1 Introdution 1 2 Implementation 2 2.1 Attributes.........................................2 2.2 Barline........................................... 16 2.3 Common . 19 2.4 Container ......................................... 51 2.5 Direction ......................................... 53 2.6 Identity .......................................... 79 2.7 Layout........................................... 83 2.8 Link............................................ 90 2.9 MusicXML . 93 2.10Note............................................ 96 2.11Opus............................................ 137 2.12 Partwise . 139 2.13Score............................................ 141 2.14 Timewise . 154 2.15Util ............................................ 156 3 Test 164 4 Conclusion 166 1 Introdution This document contains Haskell[4, 3] code formatted with lhs2TeX tool. Type definition are conforming specification built by Recordare at second version of MusicXML DTDs, presented on figure 1. At moment of writing this library, Recordare was publishing unstable versions of MusicXML schemas after discussion made by MusicXML comunity to improve its specification[2]. This library are architecture presented on figure 2. Type definition wasn't use datatype, using type definitions to improve performance. To improve maintainability was built Util module, which contains elementary functions to reading and writing. To minimize code, at reading from MusicXML format is used State Monad. However writing to MusicXML format it is used functional way. This approach help us maintainability by close to MusicXML DTDs specification. Next sec- tion presents implementation using Haskell language of MusicXML DTD specification. Following section presents some use cases of this library into real examples of musicxml documents. 1 Figure 1: MusicXML architecture Figure 2: MusicXML modules 2 Implementation This implementation shows comments from MusicXML specification[5, 1] like this style. 2.1 Attributes -- j -- Maintainer : [email protected] -- Stability : experimental -- Portability: HaXML -- module Text:XML:MusicXML:Attributes where import Text:XML:MusicXML:Common hiding (Directive; read Directive; show Directive) import Text:XML:HaXml:Types (Content) import Control:Monad (MonadPlus (::)) import Prelude (Maybe (::); Show; Eq; Monad (::); (·); String; (++)) The attributes DTD module contains the attributes element and its children, such as key and time signatures. The attributes element contains musical information that typically changes on measure boundaries. This includes key and time signatures, clefs, transpositions, and staving. -- * Attributes -- j type Attributes = (Editorial; Maybe Divisions; [Key ]; [Time ]; Maybe Staves; Maybe Part Symbol; Maybe Instruments; [Clef ]; [Staff Details ]; Maybe Transpose; [Directive ]; [Measure Style ]) -- j 2 read Attributes :: Eq i ) STM Result [Content i ] Attributes read Attributes = do y read ELEMENT "attributes" read 12 read Editorial (read MAYBE read Divisions) (read LIST read Key)(read LIST read Time) (read MAYBE read Staves)(read MAYBE read Part Symbol) (read MAYBE read Instruments)(read LIST read Clef ) (read LIST read Staff Details)(read MAYBE read Transpose) (read LIST read Directive)(read LIST read Measure Style) (childs y) -- j show Attributes :: Attributes ! [Content ()] show Attributes (a; b; c; d; e; f ; g; h; i; j ; k; l) = show ELEMENT "attributes" [] (show Editorial a ++ show MAYBE show Divisions b ++ show LIST show Key c ++ show LIST show Time d ++ show MAYBE show Staves e ++ show MAYBE show Part Symbol f ++ show MAYBE show Instruments g ++ show LIST show Clef h ++ show LIST show Staff Details i ++ show MAYBE show Transpose j ++ show LIST show Directive k ++ show LIST show Measure Style l) Traditional key signatures are represented by the number of flats and sharps, plus an optional mode for major/ minor/mode distinctions. Negative numbers are used for flats and positive numbers for sharps, reflecting the key's placement within the circle of fifths (hence the element name). A cancel element indicates that the old key signature should be cancelled before the new one appears. This will always happen when changing to C major or A minor and need not be specified then. The cancel value matches the fifths value of the cancelled key signature (e.g., a cancel of -2 will provide an explicit cancellation for changing from B flat major to F major). The optional location attribute indicates whether the cancellation appears to the left or the right of the new key signature. It is left by default. Non-traditional key signatures can be represented using the Humdrum/Scot concept of a list of altered tones. The key-step and key-alter elements are represented the same way as the step and alter elements are in the pitch element in the note.mod file. The different element names indicate the different meaning of altering notes in a scale versus altering a sounding pitch. Valid mode values include major, minor, dorian, phrygian, lydian, mixolydian, aeolian, ionian, and locrian. The optional number attribute refers to staff numbers, from top to bottom on the system. If absent, the key signature applies to all staves in the part. The optional list of key-octave elements is used to specify in which octave each element of the key signature appears. The content specifies the octave value using the same values as the display-octave element. The number attribute is a positive integer that refers to the key signature element in left-to-right order. If the cancel attribute is set to yes, then this number refers to an element specified by the cancel element. It is no by default. -- ** Key -- j type Key = ((Maybe CDATA; Print Style; Print Object); (Key ; [Key Octave ])) -- j read Key :: Eq i ) STM Result [Content i ] Key read Key = do y read ELEMENT "key" y1 read 3 (read IMPLIED "number" read CDATA) read Print Style read Print Object (attributes y) y2 read 2 read Key (read LIST read Key Octave)(childs y) return (y1 ; y2 ) -- j show Key :: Key ! [Content ()] show Key ((a; b; c); (d; e)) = 3 show ELEMENT "key" (show IMPLIED "number" show CDATA a ++ show Print Style b ++ show Print Object c) (show Key d ++ show LIST show Key Octave e) -- j data Key = Key 1 (Maybe Cancel; Fifths; Maybe Mode) j Key 2 [(Key Step; Key Alter)] deriving (Eq; Show) -- j read Key :: Eq i ) STM Result [Content i ] Key read Key = (read Key aux1 >>= return · Key 1 ) `mplus` (read LIST read Key aux2 >>= return · Key 2 ) -- j show Key :: Key ! [Content ()] show Key (Key 1 (a; b; c)) = show MAYBE show Cancel a ++ show Fifths b ++ show MAYBE show Mode c show Key (Key 2 a) = show LIST show Key aux1 a -- j read Key aux1 :: Eq i ) STM Result [Content i ](Maybe Cancel; Fifths; Maybe Mode) read Key aux1 = do y1 read MAYBE read Cancel y2 read Fifths y3 read MAYBE read Mode return (y1 ; y2 ; y3 ) read Key aux2 :: Eq i ) STM Result [Content i ](Key Step; Key Alter) read Key aux2 = do y1 read Key Step y2 read Key Alter return (y1 ; y2 ) -- j show Key aux1 :: (Key Step; Key Alter) ! [Content ()] show Key aux1 (a; b) = show Key Step a ++ show Key Alter b -- j type Cancel = (Maybe Left Right; PCDATA) -- j read Cancel :: STM Result [Content i ] Cancel read Cancel = do y read ELEMENT "cancel" y1 read 1 (read IMPLIED "location" read Left Right)(attributes y) y2 read 1 read PCDATA (childs y) return (y1 ; y2 ) -- j show Cancel :: Cancel ! [Content ()] show Cancel (a; b) = show ELEMENT "cancel" (show IMPLIED "location" show Left Right a) (show PCDATA b) -- j type Fifths = PCDATA -- j read Fifths :: STM Result [Content i ] Fifths read Fifths = do y read ELEMENT "fifths" read 1 read PCDATA (childs y) -- j show Fifths :: Fifths ! [Content ()] show Fifths a = show ELEMENT "fifths" [](show PCDATA a) -- j type Mode = PCDATA 4 -- j read Mode :: STM Result [Content i ] Mode read Mode = do y read ELEMENT "mode" read 1 read PCDATA (childs y) -- j show Mode :: Mode ! [Content ()] show Mode a = show ELEMENT "mode" [](show PCDATA a) -- j type Key Step = PCDATA -- j read Key Step :: STM Result [Content i ] Key Step read Key Step = do y read ELEMENT "key-step" read 1 read PCDATA (childs y) -- j show Key Step :: Key Step ! [Content ()] show Key Step a = show ELEMENT "key-step" [](show PCDATA a) -- j type Key Alter = PCDATA -- j read Key Alter :: STM Result [Content i ] Key Alter read Key Alter = do y read ELEMENT "key-alter" read 1 read PCDATA (childs y) -- j show Key Alter :: Key Alter ! [Content ()] show Key Alter a = show ELEMENT "key-alter" [](show PCDATA a) -- j type Key Octave = ((CDATA; Maybe Yes No); PCDATA) -- j read Key Octave :: STM Result [Content i ] Key Octave read Key Octave = do y read ELEMENT "key-octave" y1 read 2 (read REQUIRED "number" read CDATA) (read IMPLIED "cancel" read Yes No)(attributes y) y2 read 1 read PCDATA (childs y) return (y1 ; y2 ) -- j show Key Octave :: Key Octave ! [Content ()] show Key Octave ((a; b); c) = show ELEMENT "key-octave" (show REQUIRED "number" show CDATA a ++ show IMPLIED "cancel" show Yes No b) (show PCDATA c) Musical notation duration is commonly represented as fractions. The divisions element indicates how many divisions per quarter note are used to indicate a note's duration. For example, if duration = 1 and divisions = 2, this is an eighth note duration. Duration and divisions are used directly for generating sound output, so they must be chosen to take tuplets into account. Using a divisions element lets us use just one number to represent a duration for each note in the score, while retaining the full power of a fractional representation. For maximum compatibility with Standard MIDI Files, the divisions value should not exceed 16383. -- ** Divisions -- j type Divisions = PCDATA -- j read Divisions :: STM Result [Content i ] Divisions read Divisions = do 5 y read ELEMENT "divisions" read 1 read PCDATA (childs y) -- j show Divisions :: Divisions ! [Content ()] show Divisions a = show ELEMENT "divisions" [](show PCDATA a) Time signatures are represented by two elements. The beats element indicates the number of beats, as found in the numerator of a time signature.