1 -- Basic Semantics V2 for a Reactive Music Cellular Automaton.
2 -- Inspired by the reacTogon.
3 -- Written by Henrik Nilsson, 2016-05-27
4 -- Based on an earlier version.
6 -- This gives the semantics of a single RMCA layer. The output is
7 -- a high-level representation of notes for each beat. This is to be
8 -- translated to low-level MIDI message by a subsequent translator
9 -- responsible for merging notes from different layers, ensuring that
10 -- a note off message corresponding to each note on message is always
11 -- emitted after the appropriate time, rendering any embellismnets
12 -- such as slides (while not generating too much MIDI data), etc.
15 -- * Add boolean flag to change direction to indicate start tile
17 -- * Change main routine to generate start play heads from board
19 -- * Add an optional restart facility: Maybe Int, restart every n
22 -- * Interpret a negative repeat as repeat indefinitely.
24 -- * Interpret a non-positve duration as mute: don't emit any note.
26 -- * Eliminate Ignore as now almost the same as Absorb with duration 0?
27 -- The only difference is that Absorb mostly overrides the repeat count.
28 -- Absorb = Stop {duration 0, repeat 1}
29 -- And as absorb might be a common case, it might be useful to have
30 -- a distinct graphical representation?
31 -- DECIDED AGAINST FOR NOW
33 module RMCA.Semantics where
36 import Data.List (intercalate, nub)
37 import Data.Maybe (catMaybes)
41 ------------------------------------------------------------------------------
42 -- Basic Type Synonyms
43 ------------------------------------------------------------------------------
45 -- Unipolar control value; [0, 1]
48 -- Bipolar control value; [-1, 1]
51 -- Unipolar control values are usually between 0 and 127.
52 toUCtrl :: Int -> UCtrl
53 toUCtrl x = fromIntegral x / 127
55 fromUCtrl :: UCtrl -> Int
56 fromUCtrl x = floor $ bound (0,1) x * 127
58 -- Bipolar control values are usually between -127 and 127.
59 toBCtrl :: Int -> BCtrl
62 fromBCtrl :: BCtrl -> Int
65 ------------------------------------------------------------------------------
67 ------------------------------------------------------------------------------
71 -- LTempo designates a layer tempo. Useful for not transforming twice
75 ------------------------------------------------------------------------------
77 ------------------------------------------------------------------------------
79 -- The assumption is that the automaton is clocked by a beat clock and
80 -- thus advances one step per beat. For an automaton working in real time,
81 -- the beat clock would be defined externally, synchronized with other
82 -- layers and possibly external MIDI, and account for tempo, any swing, etc.
86 -- Beats per Bar: number of beats per bar in the time signature of a layer.
88 type BeatsPerBar = Int
90 -- The beat number in the time signature of the layer. The first beat is 1.
93 nextBeatNo :: BeatsPerBar -> BeatNo -> BeatNo
94 nextBeatNo bpb bn = bn `mod` bpb + 1
98 -- Not needed for individual layers (at present)
105 ------------------------------------------------------------------------------
107 ------------------------------------------------------------------------------
109 -- This semantics mainly works with a high-level represemntation of notes.
110 -- But it is convenient to express some of the high-level aspects directly
111 -- in the corresponding MIDI terms to facilitate the translation.
113 -- MIDI note number; [0,127]
117 -- Assume MIDI convetion: 60 = "Middle C" = C4
124 -- MIDI velocity; [0,127]
128 -- MIDI Program Change: Program Number; [0,127]
132 -- MIDI Control Change: Control Number and Control Value; [0,127]
136 -- MIDICVRnd gives the option to pick a control value at random.
137 -- (Handled through subsequent translation to low-level MIDI events.)
138 data MIDICVRnd = MIDICV MIDICV | MIDICVRnd deriving (Eq, Show, Read)
141 ------------------------------------------------------------------------------
143 ------------------------------------------------------------------------------
147 -- We chose to represent pitch by MIDI note number
148 newtype Pitch = Pitch MIDINN deriving Eq
150 pitchToMNN :: Pitch -> MIDINN
151 pitchToMNN (Pitch nn) = nn
153 instance Show Pitch where
154 show (Pitch nn) = names !! note ++ show oct
158 oct = nn' `div` 12 + middleCOct
159 names = ["C", "C#", "D", "D#", "E", "F",
160 "F#", "G", "G#", "A", "A#", "B"]
162 -- Relative pitch in semi tones. Used for e.g. transposition.
168 -- Each layer has a setting that indicate how strongly the notes
169 -- should normally be played as a percentage of full strength.
170 -- (In the real application, this settig can be set to a fixed value
171 -- or set to be derived from teh last input note, "as played").
172 -- Individual notes can tehn be accented (played more strongly),
173 -- either unconditionally or as a function of the beat count.
175 type Strength = UCtrl
177 -- This could of course be generalised, e.g. a list of beat numbers to
178 -- accentuate. But this is simple and accounts for the most common patterns.
179 data Articulation = NoAccent
185 deriving (Eq, Show, Read, Enum)
187 accentStrength :: Strength
190 -- Articulated strength
191 articStrength :: Strength -> BeatNo -> Articulation -> Strength
192 articStrength st bn art
193 | accentedBeat = st * accentStrength
198 (_, NoAccent) -> False
201 (1, Accent13) -> True
202 (3, Accent13) -> True
203 (1, Accent14) -> True
204 (4, Accent14) -> True
205 (1, Accent24) -> True
206 (4, Accent24) -> True
212 -- Duration in terms of a whole note at the *system* tempo. (Each layer
213 -- is clocked at a layer beat that is a fraction/multiple of the system
214 -- tempo). Note that notes are played a little shorter than their nominal
215 -- duration. This is taken care of by the translation into low-level
216 -- MIDI events. (One might consider adding indications of staccato or
219 -- A non-positive duration is interpreted as mute: no note emitted.
220 type Duration = Rational
225 -- Notes can be ornamented. Traditionnally, ornamenting refers to modifications
226 -- of the pitch, such as a trill or a grace note. Here we use the term in
227 -- a generalised sense.
228 -- * A MIDI program change (to be sent before the note).
229 -- * A MIDI Continuous Controler Change (to be sent before the note).
231 -- One might also consider adding trills, grace notes, MIDI after touch ...
233 data Ornaments = Ornaments {
234 ornPC :: Maybe MIDIPN,
235 ornCC :: [(MIDICN, MIDICVRnd)],
236 ornSlide :: SlideType
237 } deriving (Show,Read,Eq)
239 data SlideType = NoSlide | SlideUp | SlideDn deriving (Eq, Show, Enum, Read)
242 noOrn = Ornaments { ornPC = Nothing
249 -- Attributes needed to generate a note.
250 -- * The pitch of a note is given by the position on the board
251 -- * The strength is given by the layer strength, beat no., and articulation
252 -- * Duratio and Ornamentatio are stored
253 data NoteAttr = NoteAttr {
254 naArt :: Articulation,
257 } deriving (Show,Read,Eq)
260 -- High level note representation emitted form a layer
269 ------------------------------------------------------------------------------
271 ------------------------------------------------------------------------------
273 -- Numbering; row number inside tile, column number below:
284 -- Angle measured in multiples of 60 degrees.
287 data Dir = N | NE | SE | S | SW | NW deriving (Enum, Bounded, Eq, Show, Read)
289 predDir :: Dir -> Dir
290 predDir d | d == minBound = maxBound
293 nextDir :: Dir -> Dir
294 nextDir d | d == maxBound = minBound
297 turn :: Dir -> Angle -> Dir
298 turn d a = toEnum ((fromEnum d + a) `mod` 6)
301 type Pos = (Int, Int)
303 -- Position of neighbour in given direction
304 neighbor :: Dir -> Pos -> Pos
305 neighbor N (x,y) = (x, y + 1)
306 neighbor NE (x,y) = (x + 1, y + 1 - x `mod` 2)
307 neighbor SE (x,y) = (x + 1, y - x `mod` 2)
308 neighbor S (x,y) = (x, y - 1)
309 neighbor SW (x,y) = (x - 1, y - x `mod` 2)
310 neighbor NW (x,y) = (x - 1, y + 1 - x `mod` 2)
313 -- Position and transposition to pitch:
314 -- * Harmonic Table" layout: N = +7; NE = +4; SE = -3
315 -- * (0,0) assumed to be "Middle C"
316 posToPitch :: Pos -> RelPitch -> Pitch
317 posToPitch (x,y) tr =
318 Pitch (y * 7 + x `div` 2 - 3 * (x `mod` 2) + middleC + tr)
322 -- A ChDir counter is optionally a start counter if the Boolean flag is
324 -- Any counter can be made silent by setting the note duration to a
325 -- non-positive number.
327 data Action = Inert -- No action, play heads move through.
328 | Absorb -- Remove play head silently.
329 | Stop NoteAttr -- Play note then remove play head.
330 | ChDir Bool NoteAttr Dir -- Play note then change direction.
331 | Split NoteAttr -- Play note then split head into five.
332 deriving (Show,Read,Eq)
336 -- A cell stores an action and a repetition number.
337 -- 0: the cell is completely bypassed, as if it wasn't there.
338 -- 1: the action is carried out once (default)
339 -- n > 1: any note output of the action is repeated (n-1) times before the
340 -- action is carried out.
341 -- n < 0: any note output of the action is repeated indefinitely (oo).
343 type Cell = (Action, Int)
346 -- Make a cell with a default repeat count of 1.
347 mkCell :: Action -> Cell
348 mkCell a = mkCellRpt a 1
351 -- Make a cell with a non-default repeition number.
352 mkCellRpt :: Action -> Int -> Cell
353 mkCellRpt a n = (a, n)
356 -- Board extent: south-west corner and north-east corner.
357 -- This covers most of the MIDI range: A#-1 (10) to G7 (103).
363 -- Test if a position is on the board as defined by swc and nec.
364 -- The assumption is that odd columns contain one more cell, as per the
365 -- picture above. Of course, one could opt for a "zig-zag" layout
366 -- with each column having the same number of cells which would be slightly
368 onBoard :: Pos -> Bool
369 onBoard (x,y) = xMin <= x && x <= xMax
377 (xMax, yMax) = case nec of
378 (x, y) | even x -> (x, y + 1)
379 | otherwise -> (x, y)
382 type Board = Array Pos Cell
385 -- Build a board from a list specifying the non-empty cells.
386 makeBoard :: [(Pos, Cell)] -> Board
389 ([(p, if onBoard p then mkCell Inert else mkCell Absorb)
390 | p <- range (swc, nec')]
391 ++ [(p,c) | (p, c) <- pcs, onBoard p])
393 -- This is to ensure (neighbor NW nec) is included on the board,
394 -- regardless of whether the column of nec is even or odd.
395 -- Otherwise, due to the "jagged" upper edge, the top row would
396 -- be missing, but every other cell of that *is* on the board.
397 -- The "superfluous" cells are set to Absorb above.
398 nec' = neighbor N nec
402 lookupCell :: Board -> Pos -> Cell
403 lookupCell b p = if onBoard p then b ! p else (Absorb, 1)
406 ------------------------------------------------------------------------------
408 ------------------------------------------------------------------------------
410 -- A play head is characterised by:
411 -- * Current position
412 -- * Number of beats before moving
413 -- * Direction of travel
414 -- If an action involves playing a note, this is repeated once for
415 -- each beat the play head is staying, with the rest of the action
416 -- carried out at the last beat.
427 ------------------------------------------------------------------------------
429 ------------------------------------------------------------------------------
431 startHeads :: Board -> [PlayHead]
438 | (p, (ChDir True _ d, n)) <- assocs bd ]
441 ------------------------------------------------------------------------------
443 ------------------------------------------------------------------------------
445 -- Advance the state of a single play head.
447 -- The result is a list of heads to be actioned at the *next* beat
448 -- later) and possibly a note to be played at *this* beat.
450 advanceHead :: Board -> BeatNo -> RelPitch -> Strength -> PlayHead
451 -> ([PlayHead], Maybe Note)
452 advanceHead bd bn tr st ph = ahAux (moveHead bd ph)
454 ahAux ph@PlayHead {phPos = p, phBTM = btm, phDir = d} =
455 case fst (lookupCell bd p) of
456 Inert -> ([ph], Nothing)
457 Absorb -> ([], Nothing) -- No point waiting until BTM=0
458 Stop na -> (newPHs [], mkNote p bn tr st na)
459 ChDir _ na d' -> (newPHs [ph {phDir = d'}],
460 mkNote p bn tr st na)
461 Split na -> (newPHs [ PlayHead {
469 mkNote p bn tr st na)
471 newPHs phs = if btm == 0 then phs else [ph]
474 -- Moves a play head if the BTM counter has reached 0, otherwise decrement BTM.
475 -- Any encountered cells where the repeat count is < 1 are skipped.
476 moveHead :: Board -> PlayHead -> PlayHead
477 moveHead bd (ph@PlayHead {phPos = p, phBTM = btm, phDir = d})
480 btm' = snd (lookupCell bd p')
482 moveHead bd (ph {phPos = p', phBTM = btm'})
483 | btm > 0 = ph {phBTM = btm - 1}
484 | otherwise = ph -- Repeat indefinitely
486 mkNote :: Pos -> BeatNo -> RelPitch -> Strength -> NoteAttr -> Maybe Note
487 mkNote p bn tr st na@NoteAttr {naDur = d}
488 | d <= 0 = Nothing -- Notes of non-positive length are silent.
491 notePch = posToPitch p tr,
492 noteStr = articStrength st bn (naArt na),
498 -- Advance a list of heads, collecting all resulting heads and notes.
499 -- Any duplicate play heads are eliminated (or their number may uselessly
500 -- grow very quickly), and a cap (50, arbitrary, but should be plenty,
501 -- expecially given the board size) on the number of simultaneous playheads
502 -- per layer is imposed.
503 advanceHeads :: Board -> BeatNo -> RelPitch -> Strength -> [PlayHead]
504 -> ([PlayHead], [Note])
505 advanceHeads bd bn tr st phs =
507 (phss, mns) = unzip (map (advanceHead bd bn tr st) phs)
509 (take 50 (nub (concat phss)), catMaybes mns)
512 -- Given a board with start counters, run a board indefinitely, optionally
513 -- restarting every ri bars.
517 -- (2) Beats Per Bar (bpb); > 0
518 -- (3) Optioal repeat Interval (mri); In bars.
519 -- (4) Transposition (tr)
523 -- Stream of notes played at each beat.
525 -- In the real implementation:
526 -- * A layer beat clock would be derived from the system beat (as a
527 -- fraction/multiple, adding any swing) and each clock event be tagged
528 -- with the beat number.
529 -- * The board (bd) would not necessarily be a constant input. (One might
530 -- consider allowing editing a layer while the machine is running)
531 -- * The time signature, and thus the beats per par (bpb), along with
532 -- repeat interval (ri) would likely be static (only changeable while
533 -- automaton is stopped).
534 -- * The transposition (tr) would be dynamic, the sum of a per layer
535 -- transposition that can be set through the user interface and the
536 -- difference between the MIDI note number of the last external
537 -- note received for the layer and middle C (say).
538 -- * The strength (st) would be dynamic, configurable as either the strength
539 -- set through the user interface or the strength of the last external
540 -- note received for the layer (derived from its MIDI velocity).
542 runRMCA :: Board -> BeatsPerBar -> Maybe Int -> RelPitch -> Strength
544 runRMCA bd bpb mri tr st
549 | ri > 0 -> cycle (take (ri * bpb) nss)
550 | otherwise -> error "The repeat interval must be at \
552 | otherwise = error "The number of beats per bar must be at least 1."
554 nss = runAux 1 (startHeads bd)
556 runAux bn phs = ns : runAux (nextBeatNo bpb bn) phs'
558 (phs', ns) = advanceHeads bd bn tr st phs
561 -- Print played notes in a time-stamped (bar, beat), easy-to-read format.
563 ppNotes :: BeatsPerBar -> [[Note]] -> IO ()
564 ppNotes bpb nss = ppnAux (zip [(br,bn) | br <- [1..], bn <- [1..bpb]] nss)
565 where ppnAux :: [((Int,BeatsPerBar),[Note])] -> IO ()
566 ppnAux [] = return ()
567 ppnAux ((_, []) : tnss) = ppnAux tnss
568 ppnAux ((t, ns) : tnss) = do
569 putStrLn (leftJustify 10 (show t) ++ ": "
570 ++ intercalate ", " (map show ns))
574 leftJustify :: Int -> String -> String
575 leftJustify w s = replicate (w - length s) ' ' ++ s
578 ------------------------------------------------------------------------------
580 ------------------------------------------------------------------------------
583 makeBoard [((0,0), mkCell (ChDir True na1 N)),
584 ((0,1), mkCell (ChDir False na1 SE)),
585 ((1,1), mkCell (Split na1)),
586 ((1,-1), mkCell (Split na1)),
587 ((-1,0), mkCell (ChDir False na2 NE))]
590 makeBoard [((0,0), mkCell (ChDir False na1 N)),
591 ((0,1), mkCell (ChDir False na1 SE)),
592 ((1,1), mkCell (Split na1)),
593 ((1,-1), mkCell (Split na1)),
594 ((-1,0), mkCell (ChDir False na2 NE))]
597 makeBoard [((0,0), mkCell (ChDir True na1 N)),
598 ((0,2), mkCellRpt (ChDir False na2 SE) 3),
599 ((2,1), mkCell (ChDir False na1 SW)),
600 ((1,1), mkCellRpt (ChDir False na1 N) 0) {- Skipped! -},
601 ((0,4), mkCellRpt (ChDir True na1 N) (-1)) {- Rpt indef. -},
602 ((0, -6), mkCell (ChDir True na1 N)),
603 ((0, -2), mkCell (ChDir False na3 S) {- Silent -})]
606 makeBoard [((0,0), mkCell (ChDir True na1 N))]
611 naOrn = Ornaments Nothing [] NoSlide
617 naOrn = Ornaments Nothing [(10, MIDICVRnd)] SlideUp
623 naOrn = Ornaments Nothing [] NoSlide
630 main = ppNotes bpb (take 50 (runRMCA testBoard3 bpb (Just 2) 0 0.8))