-- Copyright 2013 Evan Laforge -- This program is distributed under the terms of the GNU General Public -- License 3.0, see COPYING or http://www.gnu.org/licenses/gpl-3.0.txt {-# LANGUAGE DeriveDataTypeable #-} {- | Representation for scales, pitches, and frequencies (note numbers). There are many representations for a pitch, at many different levels of abstraction. -} module Perform.Pitch ( -- * Note Note(..), note_text -- * Pitch , Pitch(..), pitch, Degree(..) , Octave, PitchClass, Accidentals, Semi, FSemi, Step , pitch_accidentals, pitch_pc , add_octave, add_pc, diff_pc , middle_octave, middle_c -- * Input , Input(..), KbdType(..), Frac -- * NoteNumber , NoteNumber(..), nn, key_to_nn, nn_to_double , Cent, nn_to_cents , nns_equal, nns_close -- * Hz , Hz, add_hz, modify_hz, nn_to_hz, hz_to_nn, middle_c_hz -- * Scale , ScaleId(..), empty_scale, twelve , Transpose(..), zero_transpose, modify_transpose , Key(Key), key_text ) where import qualified Data.String as String import qualified Data.Text as Text import qualified Data.Typeable as Typeable import qualified Text.ParserCombinators.ReadP as ReadP import qualified Text.Read as Read import qualified Util.Num as Num import qualified Util.Pretty as Pretty import qualified Util.Serialize as Serialize import qualified Util.Test.ApproxEq as ApproxEq import qualified Midi.Midi as Midi import qualified Derive.ShowVal as ShowVal import Global -- * Note -- | A Note is the most abstract representation of pitch, in that it's simply -- an unparsed bit of text representing that pitch. Given a Scale, it's -- expected to name a val call exported by that scale. newtype Note = Note Text deriving (Eq, Ord, Show, String.IsString, Serialize.Serialize) note_text :: Note -> Text note_text (Note s) = s instance Pretty Note where pretty (Note n) = n -- * pitch -- | A Pitch is a parsed 'Note'. Functions that want to manipulate notes -- in a scale-independent way can ask the scale to convert to and from a Note. -- Not all scales use all the fields. data Pitch = Pitch { pitch_octave :: !Octave , pitch_degree :: !Degree } deriving (Eq, Ord, Read, Show) pitch :: Enum pc => Octave -> pc -> Pitch pitch oct pc = Pitch oct (Degree (fromEnum pc) 0) instance Pretty Pitch where pretty (Pitch oct degree) = showt oct <> "-" <> pretty degree -- | This relies on the presence of a @pitch@ val call. instance ShowVal.ShowVal Pitch where show_val (Pitch oct (Degree pc accs)) = "(pitch " <> Text.unwords args <> ")" where args = map showt $ oct : pc : if accs == 0 then [] else [accs] instance Serialize.Serialize Pitch where put (Pitch a b) = Serialize.put a >> Serialize.put b get = Pitch <$> Serialize.get <*> Serialize.get -- | A scale degree, without reference to an octave. data Degree = Degree { degree_pc :: !PitchClass -- | Ignored for diatonic scales. , degree_accidentals :: !Accidentals } deriving (Eq, Ord, Read, Show) instance Pretty Degree where pretty (Degree pc acc) = showt pc <> if acc < 0 then Text.replicate (abs acc) "b" else Text.replicate acc "#" instance Serialize.Serialize Degree where put (Degree a b) = Serialize.put a >> Serialize.put b get = Degree <$> Serialize.get <*> Serialize.get -- | Just a way to label an octave, either relative or absolute. type Octave = Int -- | A PitchClass maps directly to a scale degree, which is a letter in -- traditional Western notation, though this PitchClass may have fewer or -- greater than 7 notes. The PitchClass is absolute in that it doesn't depend -- on the tonic of a key. -- -- These numbers are expected to wrap around at the octave, so they usually use -- modular arithmetic, but if an octave is not handy (i.e. they're not in -- a 'Pitch'), then steps exceeding an octave will be wrapped into an octave -- when one is available. type PitchClass = Int -- | Positive for sharps, negative for flats. type Accidentals = Int -- | Number of semitones. This is an absolute measure from octave 0, -- regardless of whether the scale has notes at octave 0. This is so you can -- convert between Semis and the similarly absolute 'Pitch' in the same way for -- all scales. type Semi = Int -- | This is like 'Semi', but floating point. type FSemi = Double -- | This is a relative amount of transposition. It could be either chromatic -- or diatonic. type Step = Int pitch_accidentals :: Pitch -> Accidentals pitch_accidentals = degree_accidentals . pitch_degree pitch_pc :: Pitch -> PitchClass pitch_pc = degree_pc . pitch_degree add_octave :: Octave -> Pitch -> Pitch add_octave oct (Pitch octave degree) = Pitch (oct + octave) degree -- | Add diatonic steps. This doesn't deal with key signatures or non-diatonic -- scales. add_pc :: PitchClass -> PitchClass -> Pitch -> Pitch add_pc per_octave steps (Pitch octave (Degree pc accs)) = Pitch (oct + octave) (Degree pc2 accs) where (oct, pc2) = (pc + steps) `divMod` per_octave diff_pc :: PitchClass -> Pitch -> Pitch -> PitchClass diff_pc per_octave (Pitch oct1 (Degree pc1 _)) (Pitch oct2 (Degree pc2 _)) = oct_diff + pc1 - pc2 where oct_diff = per_octave * (oct1 - oct2) -- | The middle octave. The \"center\" of a scale should be oriented around -- this. middle_octave :: Octave middle_octave = 4 middle_c :: Pitch middle_c = Pitch middle_octave (Degree 0 0) -- * Input -- | A physically played note on some input device. This hasn't been mapped to -- a scale yet, so the Pitch is in the context of the device's layout. -- -- I have 3 kinds of kbds: -- -- ASCII has 10 white keys, and black keys between each one. It should be -- relative, so that C or sa is always on Q and Z, and if the octave is <10 -- then it will wrap on the same row. -- -- MIDI has the usual piano layout. It's absolute, so that a relative scale -- can start at keys other than C, if that would be convenient for the layout. -- The octave is rounded up to the nearest multiple of 7, and the extra keys -- are unused, so the octave always starts at C. -- -- Continuum has no keys, just NNs. So it gets the scale degree that's -- closest to the given NN. That's different from the MIDI kbd because the -- MIDI kbd never wants a key to emit something between notes. TODO not -- supported yet data Input = Input !KbdType !Pitch !Frac deriving (Eq, Show) data KbdType = -- | An absolute kbd maps the same key to the same absolute pitch, -- regardless of the key. This is the case for a piano style kbd. -- This is consistent with convention, but also the piano kbd has a fixed -- layout of white and black keys. So if you e.g. transpose A-major to -- start on C, then you have a mysterious black key in between B and C, and -- no way to play C#. PianoKbd -- | A relative kbd always maps the same key to the same relative pitch. -- This is appropriate for the ASCII kbd, because it has \"black keys\" -- between every white key, so scales can be transposed freely. | AsciiKbd deriving (Eq, Show) -- | A number between -1 and 1 exclusive, representing the portion of the way -- between two scale degrees. I could have used \"Cents\" for this, but that -- implies equal temperedness. type Frac = Double instance Pretty Input where pretty (Input kbd pitch frac) = showt kbd <> ":" <> pretty pitch <> if frac == 0 then "" else "+" <> pretty frac -- * NoteNumber -- | This is equal tempered scale notes with the same definition as MIDI, so -- MIDI note 0 is NoteNumber 0, at 8.176 Hz, and is -1c. Middle C (4c) is -- NoteNumber 60. -- -- 'Derive.PSignal.PSignal's are converted into this before performance -- since performance doesn't understand scales. newtype NoteNumber = NoteNumber Double deriving (ApproxEq.ApproxEq, Eq, Ord, Fractional, Real, RealFrac, Num, Serialize.Serialize, Typeable.Typeable) instance Show NoteNumber where show (NoteNumber nn) = show nn <> "nn" instance Read NoteNumber where readPrec = do n <- Read.readPrec Read.lift $ ReadP.skipSpaces >> ReadP.string "nn" return (NoteNumber n) instance ShowVal.ShowVal NoteNumber where show_val (NoteNumber nn) = ShowVal.show_val nn <> "nn" -- The suffix should be the same as DeriveT.type_to_code Nn instance Pretty NoteNumber where pretty (NoteNumber nn) = Num.showFloat0 (Just 3) nn <> "nn" nn :: Real a => a -> NoteNumber nn = NoteNumber . realToFrac key_to_nn :: Midi.Key -> NoteNumber key_to_nn (Midi.Key key) = nn key nn_to_double :: NoteNumber -> Double nn_to_double (NoteNumber nn) = nn type Cent = Int nn_to_cents :: NoteNumber -> Cent nn_to_cents = round . (*100) -- | True if the NoteNumbers are close enough that they sound the same. nns_equal :: NoteNumber -> NoteNumber -> Bool nns_equal = nns_close 3 -- almost certainly less than JND nns_close :: Cent -> NoteNumber -> NoteNumber -> Bool nns_close cents nn1 nn2 = abs (nn_to_cents nn1 - nn_to_cents nn2) <= cents -- * Hz -- | This is absolute non-logarithmic frequency. type Hz = Double add_hz :: Hz -> NoteNumber -> NoteNumber add_hz 0 nn = nn -- hz_to_nn . nn_to_hz adds a tiny bit of inaccuracy add_hz hz nn = hz_to_nn (hz + nn_to_hz nn) modify_hz :: (Hz -> Hz) -> NoteNumber -> NoteNumber modify_hz f = hz_to_nn . f . nn_to_hz nn_to_hz :: NoteNumber -> Hz nn_to_hz (NoteNumber nn) = exp (nn * _hz_scale + _hz_offset) -- | Negative hz will result in NaN. TODO take an abs or throw an error, or -- let the NaN propagate? hz_to_nn :: Hz -> NoteNumber hz_to_nn hz = NoteNumber $ (log hz - _hz_offset) / _hz_scale -- | Constants to calculate equal tempered conversions. _hz_scale, _hz_offset :: Hz _hz_scale = log 2 / 12 _hz_offset = log a_hz - (a_nn * _hz_scale) where -- NoteNumber is defined with these values. Ultimately it's because midi -- synthesizers are by default defined with these values. a_hz = 440 a_nn = 69 middle_c_hz :: Hz middle_c_hz = nn_to_hz 60 -- Alternate implementation that also introduces a bit of imprecision. Seems -- to be about the same as the one above. -- -- nn_to_hz :: NoteNumber -> Hz -- nn_to_hz (NoteNumber nn) = a_hz * rt12 ** (nn - a_nn) -- where rt12 = 2**(1/12) -- -- hz_to_nn :: Hz -> NoteNumber -- hz_to_nn hz = NoteNumber $ logBase rt12 (hz / a_hz * (rt12**a_nn)) -- where rt12 = 2**(1/12) -- -- a_hz, a_nn :: Double -- a_hz = 440 -- a_nn = 69 -- * scale newtype ScaleId = ScaleId Text deriving (Eq, Ord, Read, Show, String.IsString, Serialize.Serialize) instance Pretty ScaleId where pretty (ScaleId s) = s -- | Usually this means to use the scale currently in scope. empty_scale :: ScaleId empty_scale = "" twelve :: ScaleId twelve = "twelve" -- | A generic transposition, for operations that can transpose diatonically, -- chromatically, or by absolute NoteNumber. data Transpose = Chromatic Double | Diatonic Double -- | Nn is scale-independent, so it's not suitable for symbolic -- transposition, but it's still useful for pitch transposition. | Nn Double deriving (Eq, Ord, Show) instance Pretty Transpose where pretty = ShowVal.show_val instance ShowVal.ShowVal Transpose where -- TODO convert to a ScoreT.Typed Signal.Y and use its ShowVal show_val (Chromatic d) = ShowVal.show_val d <> "c" show_val (Diatonic d) = ShowVal.show_val d <> "d" show_val (Nn d) = ShowVal.show_val d <> "nn" zero_transpose :: Transpose -> Bool zero_transpose t = case t of Chromatic d -> d == 0 Diatonic d -> d == 0 Nn d -> d == 0 modify_transpose :: (Double -> Double) -> Transpose -> Transpose modify_transpose f t = case t of Chromatic d -> Chromatic (f d) Diatonic d -> Diatonic (f d) Nn d -> Nn (f d) -- | Diatonic transposition often requires a Key for context. -- -- This is not very strongly typed, because it's intended to be scale -- independent, and not every scale will have the same values for key and -- mode. newtype Key = Key Text deriving (Eq, Ord, Read, Show, ShowVal.ShowVal, Serialize.Serialize) key_text :: Key -> Text key_text (Key t) = t instance Pretty Key where format (Key s) = Pretty.text s