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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.
5 --
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.
13
14 -- ToDo:
15 -- * Add boolean flag to change direction to indicate start tile
16 -- DONE!
17 -- * Change main routine to generate start play heads from board
18 -- DONE!
19 -- * Add an optional restart facility: Maybe Int, restart every n
20 -- bars.
21 -- DONE!
22 -- * Interpret a negative repeat as repeat indefinitely.
23 -- DONE!
24 -- * Interpret a non-positve duration as mute: don't emit any note.
25 -- DONE!
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
32
33 module RMCA.Semantics where
34
35 import Data.Array
36 import Data.List (intercalate, nub)
37 import Data.Maybe (catMaybes)
38 import RMCA.Auxiliary
39
40
41 ------------------------------------------------------------------------------
42 -- Basic Type Synonyms
43 ------------------------------------------------------------------------------
44
45 type InstrumentNo = Int
46
47 -- Unipolar control value; [0, 1]
48 type UCtrl = Double
49
50 -- Bipolar control value; [-1, 1]
51 type BCtrl = Double
52
53 -- Unipolar control values are usually between 0 and 127.
54 toUCtrl :: Int -> UCtrl
55 toUCtrl x = fromIntegral x / 127
56
57 fromUCtrl :: UCtrl -> Int
58 fromUCtrl x = floor $ bound (0,1) x * 127
59
60 -- Bipolar control values are usually between -127 and 127.
61 toBCtrl :: Int -> BCtrl
62 toBCtrl = toUCtrl
63
64 fromBCtrl :: BCtrl -> Int
65 fromBCtrl = fromUCtrl
66
67 ------------------------------------------------------------------------------
68 -- Tempo
69 ------------------------------------------------------------------------------
70
71 type Tempo = Int
72
73 -- LTempo designates a layer tempo. Useful for not transforming twice
74 -- a tempo.
75 type LTempo = Tempo
76
77 ------------------------------------------------------------------------------
78 -- Time and Beats
79 ------------------------------------------------------------------------------
80
81 -- The assumption is that the automaton is clocked by a beat clock and
82 -- thus advances one step per beat. For an automaton working in real time,
83 -- the beat clock would be defined externally, synchronized with other
84 -- layers and possibly external MIDI, and account for tempo, any swing, etc.
85
86 -- Beats and Bars
87
88 -- Beats per Bar: number of beats per bar in the time signature of a layer.
89 -- Non-negative.
90 type BeatsPerBar = Int
91
92 -- The beat number in the time signature of the layer. The first beat is 1.
93 type BeatNo = Int
94
95 nextBeatNo :: BeatsPerBar -> BeatNo -> BeatNo
96 nextBeatNo bpb bn = bn `mod` bpb + 1
97
98
99 {-
100 -- Not needed for individual layers (at present)
101
102 -- Time; [0,+inf)
103 type Time = Double
104 -}
105
106
107 ------------------------------------------------------------------------------
108 -- MIDI
109 ------------------------------------------------------------------------------
110
111 -- This semantics mainly works with a high-level represemntation of notes.
112 -- But it is convenient to express some of the high-level aspects directly
113 -- in the corresponding MIDI terms to facilitate the translation.
114
115 -- MIDI note number; [0,127]
116 type MIDINN = Int
117
118
119 -- Assume MIDI convetion: 60 = "Middle C" = C4
120 middleC :: Int
121 middleC = 60
122 middleCOct :: MIDINN
123 middleCOct = 4
124
125
126 -- MIDI velocity; [0,127]
127 type MIDIVel = Int
128
129
130 -- MIDI Program Change: Program Number; [0,127]
131 type MIDIPN = Int
132
133
134 -- MIDI Control Change: Control Number and Control Value; [0,127]
135 type MIDICN = Int
136 type MIDICV = Int
137
138 -- MIDICVRnd gives the option to pick a control value at random.
139 -- (Handled through subsequent translation to low-level MIDI events.)
140 data MIDICVRnd = MIDICV MIDICV | MIDICVRnd deriving (Eq, Show, Read)
141
142 --
143 ------------------------------------------------------------------------------
144 -- Notes
145 ------------------------------------------------------------------------------
146
147 -- Pitch
148
149 -- We chose to represent pitch by MIDI note number
150 newtype Pitch = Pitch MIDINN deriving Eq
151
152 pitchToMNN :: Pitch -> MIDINN
153 pitchToMNN (Pitch nn) = nn
154
155 instance Show Pitch where
156 show (Pitch nn) = names !! note ++ show oct
157 where
158 nn' = nn - middleC
159 note = nn' `mod` 12
160 oct = nn' `div` 12 + middleCOct
161 names = ["C", "C#", "D", "D#", "E", "F",
162 "F#", "G", "G#", "A", "A#", "B"]
163
164 -- Relative pitch in semi tones. Used for e.g. transposition.
165 type RelPitch = Int
166
167
168 -- Articulation
169
170 -- Each layer has a setting that indicate how strongly the notes
171 -- should normally be played as a percentage of full strength.
172 -- (In the real application, this settig can be set to a fixed value
173 -- or set to be derived from teh last input note, "as played").
174 -- Individual notes can tehn be accented (played more strongly),
175 -- either unconditionally or as a function of the beat count.
176
177 type Strength = UCtrl
178
179 -- This could of course be generalised, e.g. a list of beat numbers to
180 -- accentuate. But this is simple and accounts for the most common patterns.
181 data Articulation = NoAccent
182 | Accent
183 | Accent1
184 | Accent13
185 | Accent14
186 | Accent24
187 deriving (Eq, Show, Read, Enum)
188
189 accentStrength :: Strength
190 accentStrength = 1.2
191
192 -- Articulated strength
193 articStrength :: Strength -> BeatNo -> Articulation -> Strength
194 articStrength st bn art
195 | accentedBeat = st * accentStrength
196 | otherwise = st
197 where
198 accentedBeat =
199 case (bn, art) of
200 (_, NoAccent) -> False
201 (_, Accent) -> True
202 (1, Accent1) -> True
203 (1, Accent13) -> True
204 (3, Accent13) -> True
205 (1, Accent14) -> True
206 (4, Accent14) -> True
207 (1, Accent24) -> True
208 (4, Accent24) -> True
209 _ -> False
210
211
212 -- Duration
213
214 -- Duration in terms of a whole note at the *system* tempo. (Each layer
215 -- is clocked at a layer beat that is a fraction/multiple of the system
216 -- tempo). Note that notes are played a little shorter than their nominal
217 -- duration. This is taken care of by the translation into low-level
218 -- MIDI events. (One might consider adding indications of staccato or
219 -- tenuto.)
220 --
221 -- A non-positive duration is interpreted as mute: no note emitted.
222 type Duration = Rational
223
224
225 -- Ornamentation
226
227 -- Notes can be ornamented. Traditionnally, ornamenting refers to modifications
228 -- of the pitch, such as a trill or a grace note. Here we use the term in
229 -- a generalised sense.
230 -- * A MIDI program change (to be sent before the note).
231 -- * A MIDI Continuous Controler Change (to be sent before the note).
232 -- * A Slide
233 -- One might also consider adding trills, grace notes, MIDI after touch ...
234
235 data Ornaments = Ornaments {
236 ornPC :: Maybe MIDIPN,
237 ornCC :: [(MIDICN, MIDICVRnd)],
238 ornSlide :: SlideType
239 } deriving (Show,Read,Eq)
240
241 data SlideType = NoSlide | SlideUp | SlideDn deriving (Eq, Show, Enum, Read)
242
243 noOrn :: Ornaments
244 noOrn = Ornaments { ornPC = Nothing
245 , ornCC = []
246 , ornSlide = NoSlide
247 }
248
249 -- Notes
250
251 -- Attributes needed to generate a note.
252 -- * The pitch of a note is given by the position on the board
253 -- * The strength is given by the layer strength, beat no., and articulation
254 -- * Duratio and Ornamentatio are stored
255 data NoteAttr = NoteAttr {
256 naArt :: Articulation,
257 naDur :: Duration,
258 naOrn :: Ornaments
259 } deriving (Show,Read,Eq)
260
261
262 -- High level note representation emitted form a layer
263 data Note = Note {
264 notePch :: Pitch,
265 noteStr :: Strength,
266 noteDur :: Duration,
267 noteOrn :: Ornaments
268 } deriving (Show,Eq)
269
270
271 ------------------------------------------------------------------------------
272 -- Board
273 ------------------------------------------------------------------------------
274
275 -- Numbering; row number inside tile, column number below:
276 -- _ _
277 -- _/2\_/2\_
278 -- / \_/1\_/1\
279 -- \_/1\_/1\_/
280 -- / \_/0\_/0\
281 -- \_/0\_/0\_/
282 -- \_/ \_/
283 -- -1 0 1 2
284
285
286 -- Angle measured in multiples of 60 degrees.
287 type Angle = Int
288
289 data Dir = N | NE | SE | S | SW | NW deriving (Enum, Bounded, Eq, Show, Read)
290
291 predDir :: Dir -> Dir
292 predDir d | d == minBound = maxBound
293 | otherwise = pred d
294
295 nextDir :: Dir -> Dir
296 nextDir d | d == maxBound = minBound
297 | otherwise = succ d
298
299 turn :: Dir -> Angle -> Dir
300 turn d a = toEnum ((fromEnum d + a) `mod` 6)
301
302
303 type Pos = (Int, Int)
304
305 -- Position of neighbour in given direction
306 neighbor :: Dir -> Pos -> Pos
307 neighbor N (x,y) = (x, y + 1)
308 neighbor NE (x,y) = (x + 1, y + 1 - x `mod` 2)
309 neighbor SE (x,y) = (x + 1, y - x `mod` 2)
310 neighbor S (x,y) = (x, y - 1)
311 neighbor SW (x,y) = (x - 1, y - x `mod` 2)
312 neighbor NW (x,y) = (x - 1, y + 1 - x `mod` 2)
313
314
315 -- Position and transposition to pitch:
316 -- * Harmonic Table" layout: N = +7; NE = +4; SE = -3
317 -- * (0,0) assumed to be "Middle C"
318 posToPitch :: Pos -> RelPitch -> Pitch
319 posToPitch (x,y) tr =
320 Pitch (y * 7 + x `div` 2 - 3 * (x `mod` 2) + middleC + tr)
321
322
323 -- Actions
324 -- A ChDir counter is optionally a start counter if the Boolean flag is
325 -- set to true.
326 -- Any counter can be made silent by setting the note duration to a
327 -- non-positive number.
328
329 data Action = Inert -- No action, play heads move through.
330 | Absorb -- Remove play head silently.
331 | Stop NoteAttr -- Play note then remove play head.
332 | ChDir Bool NoteAttr Dir -- Play note then change direction.
333 | Split NoteAttr -- Play note then split head into five.
334 deriving (Show,Read,Eq)
335
336
337 -- Cells
338 -- A cell stores an action and a repetition number.
339 -- 0: the cell is completely bypassed, as if it wasn't there.
340 -- 1: the action is carried out once (default)
341 -- n > 1: any note output of the action is repeated (n-1) times before the
342 -- action is carried out.
343 -- n < 0: any note output of the action is repeated indefinitely (oo).
344
345 type Cell = (Action, Int)
346
347
348 -- Make a cell with a default repeat count of 1.
349 mkCell :: Action -> Cell
350 mkCell a = mkCellRpt a 1
351
352
353 -- Make a cell with a non-default repeition number.
354 mkCellRpt :: Action -> Int -> Cell
355 mkCellRpt a n = (a, n)
356
357
358 -- Board extent: south-west corner and north-east corner.
359 -- This covers most of the MIDI range: A#-1 (10) to G7 (103).
360 swc, nec :: Pos
361 swc = (-9, -6)
362 nec = (9, 6)
363
364
365 -- Test if a position is on the board as defined by swc and nec.
366 -- The assumption is that odd columns contain one more cell, as per the
367 -- picture above. Of course, one could opt for a "zig-zag" layout
368 -- with each column having the same number of cells which would be slightly
369 -- simpler.
370 onBoard :: Pos -> Bool
371 onBoard (x,y) = xMin <= x && x <= xMax
372 && yMin <= y
373 && (if even x then
374 y < yMax
375 else
376 y <= yMax)
377 where
378 (xMin, yMin) = swc
379 (xMax, yMax) = case nec of
380 (x, y) | even x -> (x, y + 1)
381 | otherwise -> (x, y)
382
383
384 type Board = Array Pos Cell
385
386
387 -- Build a board from a list specifying the non-empty cells.
388 makeBoard :: [(Pos, Cell)] -> Board
389 makeBoard pcs =
390 array (swc,nec')
391 ([(p, if onBoard p then mkCell Inert else mkCell Absorb)
392 | p <- range (swc, nec')]
393 ++ [(p,c) | (p, c) <- pcs, onBoard p])
394 where
395 -- This is to ensure (neighbor NW nec) is included on the board,
396 -- regardless of whether the column of nec is even or odd.
397 -- Otherwise, due to the "jagged" upper edge, the top row would
398 -- be missing, but every other cell of that *is* on the board.
399 -- The "superfluous" cells are set to Absorb above.
400 nec' = neighbor N nec
401
402
403 -- Look up a cell
404 lookupCell :: Board -> Pos -> Cell
405 lookupCell b p = if onBoard p then b ! p else (Absorb, 1)
406
407
408 ------------------------------------------------------------------------------
409 -- Play Head
410 ------------------------------------------------------------------------------
411
412 -- A play head is characterised by:
413 -- * Current position
414 -- * Number of beats before moving
415 -- * Direction of travel
416 -- If an action involves playing a note, this is repeated once for
417 -- each beat the play head is staying, with the rest of the action
418 -- carried out at the last beat.
419
420 data PlayHead =
421 PlayHead {
422 phPos :: Pos,
423 phBTM :: Int,
424 phDir :: Dir
425 }
426 deriving (Eq, Show)
427
428
429 ------------------------------------------------------------------------------
430 -- Start Heads
431 ------------------------------------------------------------------------------
432
433 startHeads :: Board -> [PlayHead]
434 startHeads bd =
435 [ PlayHead {
436 phPos = p,
437 phBTM = n,
438 phDir = d
439 }
440 | (p, (ChDir True _ d, n)) <- assocs bd ]
441
442
443 ------------------------------------------------------------------------------
444 -- State transition
445 ------------------------------------------------------------------------------
446
447 -- Advance the state of a single play head.
448 --
449 -- The result is a list of heads to be actioned at the *next* beat
450 -- later) and possibly a note to be played at *this* beat.
451
452 advanceHead :: Board -> BeatNo -> RelPitch -> Strength -> PlayHead
453 -> ([PlayHead], Maybe Note)
454 advanceHead bd bn tr st ph = ahAux (moveHead bd ph)
455 where
456 ahAux ph@PlayHead {phPos = p, phBTM = btm, phDir = d} =
457 case fst (lookupCell bd p) of
458 Inert -> ([ph], Nothing)
459 Absorb -> ([], Nothing) -- No point waiting until BTM=0
460 Stop na -> (newPHs [], mkNote p bn tr st na)
461 ChDir _ na d' -> (newPHs [ph {phDir = d'}],
462 mkNote p bn tr st na)
463 Split na -> (newPHs [ PlayHead {
464 phPos = p,
465 phBTM = 0,
466 phDir = d'
467 }
468 | a <- [-2 .. 2],
469 let d' = turn d a
470 ],
471 mkNote p bn tr st na)
472 where
473 newPHs phs = if btm == 0 then phs else [ph]
474
475
476 -- Moves a play head if the BTM counter has reached 0, otherwise decrement BTM.
477 -- Any encountered cells where the repeat count is < 1 are skipped.
478 moveHead :: Board -> PlayHead -> PlayHead
479 moveHead bd (ph@PlayHead {phPos = p, phBTM = btm, phDir = d})
480 | btm == 0 = let
481 p' = neighbor d p
482 btm' = snd (lookupCell bd p')
483 in
484 moveHead bd (ph {phPos = p', phBTM = btm'})
485 | btm > 0 = ph {phBTM = btm - 1}
486 | otherwise = ph -- Repeat indefinitely
487
488 mkNote :: Pos -> BeatNo -> RelPitch -> Strength -> NoteAttr -> Maybe Note
489 mkNote p bn tr st na@NoteAttr {naDur = d}
490 | d <= 0 = Nothing -- Notes of non-positive length are silent.
491 | otherwise = Just
492 Note {
493 notePch = posToPitch p tr,
494 noteStr = articStrength st bn (naArt na),
495 noteDur = naDur na,
496 noteOrn = naOrn na
497 }
498
499
500 -- Advance a list of heads, collecting all resulting heads and notes.
501 -- Any duplicate play heads are eliminated (or their number may uselessly
502 -- grow very quickly), and a cap (50, arbitrary, but should be plenty,
503 -- expecially given the board size) on the number of simultaneous playheads
504 -- per layer is imposed.
505 advanceHeads :: Board -> BeatNo -> RelPitch -> Strength -> [PlayHead]
506 -> ([PlayHead], [Note])
507 advanceHeads bd bn tr st phs =
508 let
509 (phss, mns) = unzip (map (advanceHead bd bn tr st) phs)
510 in
511 (take 50 (nub (concat phss)), catMaybes mns)
512
513
514 -- Given a board with start counters, run a board indefinitely, optionally
515 -- restarting every ri bars.
516 --
517 -- Arguments:
518 -- (1) Board (bd)
519 -- (2) Beats Per Bar (bpb); > 0
520 -- (3) Optioal repeat Interval (mri); In bars.
521 -- (4) Transposition (tr)
522 -- (5) Strength (st)
523 --
524 -- Returns:
525 -- Stream of notes played at each beat.
526 --
527 -- In the real implementation:
528 -- * A layer beat clock would be derived from the system beat (as a
529 -- fraction/multiple, adding any swing) and each clock event be tagged
530 -- with the beat number.
531 -- * The board (bd) would not necessarily be a constant input. (One might
532 -- consider allowing editing a layer while the machine is running)
533 -- * The time signature, and thus the beats per par (bpb), along with
534 -- repeat interval (ri) would likely be static (only changeable while
535 -- automaton is stopped).
536 -- * The transposition (tr) would be dynamic, the sum of a per layer
537 -- transposition that can be set through the user interface and the
538 -- difference between the MIDI note number of the last external
539 -- note received for the layer and middle C (say).
540 -- * The strength (st) would be dynamic, configurable as either the strength
541 -- set through the user interface or the strength of the last external
542 -- note received for the layer (derived from its MIDI velocity).
543
544 runRMCA :: Board -> BeatsPerBar -> Maybe Int -> RelPitch -> Strength
545 -> [[Note]]
546 runRMCA bd bpb mri tr st
547 | bpb > 0 =
548 case mri of
549 Nothing -> nss
550 Just ri
551 | ri > 0 -> cycle (take (ri * bpb) nss)
552 | otherwise -> error "The repeat interval must be at \
553 \least 1 bar."
554 | otherwise = error "The number of beats per bar must be at least 1."
555 where
556 nss = runAux 1 (startHeads bd)
557
558 runAux bn phs = ns : runAux (nextBeatNo bpb bn) phs'
559 where
560 (phs', ns) = advanceHeads bd bn tr st phs
561
562
563 -- Print played notes in a time-stamped (bar, beat), easy-to-read format.
564
565 ppNotes :: BeatsPerBar -> [[Note]] -> IO ()
566 ppNotes bpb nss = ppnAux (zip [(br,bn) | br <- [1..], bn <- [1..bpb]] nss)
567 where ppnAux :: [((Int,BeatsPerBar),[Note])] -> IO ()
568 ppnAux [] = return ()
569 ppnAux ((_, []) : tnss) = ppnAux tnss
570 ppnAux ((t, ns) : tnss) = do
571 putStrLn (leftJustify 10 (show t) ++ ": "
572 ++ intercalate ", " (map show ns))
573 ppnAux tnss
574
575
576 leftJustify :: Int -> String -> String
577 leftJustify w s = replicate (w - length s) ' ' ++ s
578
579 {-
580 ------------------------------------------------------------------------------
581 -- Simple tests
582 ------------------------------------------------------------------------------
583
584 testBoard1 =
585 makeBoard [((0,0), mkCell (ChDir True na1 N)),
586 ((0,1), mkCell (ChDir False na1 SE)),
587 ((1,1), mkCell (Split na1)),
588 ((1,-1), mkCell (Split na1)),
589 ((-1,0), mkCell (ChDir False na2 NE))]
590
591 testBoard1a =
592 makeBoard [((0,0), mkCell (ChDir False na1 N)),
593 ((0,1), mkCell (ChDir False na1 SE)),
594 ((1,1), mkCell (Split na1)),
595 ((1,-1), mkCell (Split na1)),
596 ((-1,0), mkCell (ChDir False na2 NE))]
597
598 testBoard2 =
599 makeBoard [((0,0), mkCell (ChDir True na1 N)),
600 ((0,2), mkCellRpt (ChDir False na2 SE) 3),
601 ((2,1), mkCell (ChDir False na1 SW)),
602 ((1,1), mkCellRpt (ChDir False na1 N) 0) {- Skipped! -},
603 ((0,4), mkCellRpt (ChDir True na1 N) (-1)) {- Rpt indef. -},
604 ((0, -6), mkCell (ChDir True na1 N)),
605 ((0, -2), mkCell (ChDir False na3 S) {- Silent -})]
606
607 testBoard3 =
608 makeBoard [((0,0), mkCell (ChDir True na1 N))]
609
610 na1 = NoteAttr {
611 naArt = Accent13,
612 naDur = 1 % 4,
613 naOrn = Ornaments Nothing [] NoSlide
614 }
615
616 na2 = NoteAttr {
617 naArt = NoAccent,
618 naDur = 1 % 16,
619 naOrn = Ornaments Nothing [(10, MIDICVRnd)] SlideUp
620 }
621
622 na3 = NoteAttr {
623 naArt = Accent13,
624 naDur = 0,
625 naOrn = Ornaments Nothing [] NoSlide
626 }
627
628
629 bpb :: Int
630 bpb = 4
631
632 main = ppNotes bpb (take 50 (runRMCA testBoard3 bpb (Just 2) 0 0.8))
633 -}