Mezzo.Model.Types

Types modeling basic musical constructs at the type level.

Note properties

data PitchClass

The diatonic pitch class of the note.

Constructors

C

D

E

F

G

A

B

Instances

Primitive PitchClass C

Associated Types

type Rep C (a :: C) :: *

Methods

prim :: sing a -> Rep C a

pretty :: sing a -> String

Primitive PitchClass D

Associated Types

type Rep D (a :: D) :: *

Methods

prim :: sing a -> Rep D a

pretty :: sing a -> String

Primitive PitchClass E

Associated Types

type Rep E (a :: E) :: *

Methods

prim :: sing a -> Rep E a

pretty :: sing a -> String

Primitive PitchClass F

Associated Types

type Rep F (a :: F) :: *

Methods

prim :: sing a -> Rep F a

pretty :: sing a -> String

Primitive PitchClass G

Associated Types

type Rep G (a :: G) :: *

Methods

prim :: sing a -> Rep G a

pretty :: sing a -> String

Primitive PitchClass A

Associated Types

type Rep A (a :: A) :: *

Methods

prim :: sing a -> Rep A a

pretty :: sing a -> String

Primitive PitchClass B

Associated Types

type Rep B (a :: B) :: *

Methods

prim :: sing a -> Rep B a

pretty :: sing a -> String

type Rep PitchClass C

type Rep PitchClass C = Int

type Rep PitchClass D

type Rep PitchClass D = Int

type Rep PitchClass E

type Rep PitchClass E = Int

type Rep PitchClass F

type Rep PitchClass F = Int

type Rep PitchClass G

type Rep PitchClass G = Int

type Rep PitchClass A

type Rep PitchClass A = Int

type Rep PitchClass B

type Rep PitchClass B = Int

data Accidental

The accidental applied to a note.

Constructors

Natural

Flat

Sharp

Instances

Primitive Accidental Natural

Associated Types

type Rep Natural (a :: Natural) :: *

Methods

prim :: sing a -> Rep Natural a

pretty :: sing a -> String

Primitive Accidental Flat

Associated Types

type Rep Flat (a :: Flat) :: *

Methods

prim :: sing a -> Rep Flat a

pretty :: sing a -> String

Primitive Accidental Sharp

Associated Types

type Rep Sharp (a :: Sharp) :: *

Methods

prim :: sing a -> Rep Sharp a

pretty :: sing a -> String

type Rep Accidental Natural

type Rep Accidental Natural = Int

type Rep Accidental Flat

type Rep Accidental Flat = Int

type Rep Accidental Sharp

type Rep Accidental Sharp = Int

data OctaveNum

The octave where the note resides (middle C is Oct4).

Constructors

Oct_1

Oct0

Oct1

Oct2

Oct3

Oct4

Oct5

Oct6

Oct7

Oct8

Instances

Primitive OctaveNum Oct_1

Associated Types

type Rep Oct_1 (a :: Oct_1) :: *

Methods

prim :: sing a -> Rep Oct_1 a

pretty :: sing a -> String

Primitive OctaveNum Oct0

Associated Types

type Rep Oct0 (a :: Oct0) :: *

Methods

prim :: sing a -> Rep Oct0 a

pretty :: sing a -> String

Primitive OctaveNum Oct1

Associated Types

type Rep Oct1 (a :: Oct1) :: *

Methods

prim :: sing a -> Rep Oct1 a

pretty :: sing a -> String

Primitive OctaveNum Oct2

Associated Types

type Rep Oct2 (a :: Oct2) :: *

Methods

prim :: sing a -> Rep Oct2 a

pretty :: sing a -> String

Primitive OctaveNum Oct3

Associated Types

type Rep Oct3 (a :: Oct3) :: *

Methods

prim :: sing a -> Rep Oct3 a

pretty :: sing a -> String

Primitive OctaveNum Oct4

Associated Types

type Rep Oct4 (a :: Oct4) :: *

Methods

prim :: sing a -> Rep Oct4 a

pretty :: sing a -> String

Primitive OctaveNum Oct5

Associated Types

type Rep Oct5 (a :: Oct5) :: *

Methods

prim :: sing a -> Rep Oct5 a

pretty :: sing a -> String

Primitive OctaveNum Oct6

Associated Types

type Rep Oct6 (a :: Oct6) :: *

Methods

prim :: sing a -> Rep Oct6 a

pretty :: sing a -> String

Primitive OctaveNum Oct7

Associated Types

type Rep Oct7 (a :: Oct7) :: *

Methods

prim :: sing a -> Rep Oct7 a

pretty :: sing a -> String

Primitive OctaveNum Oct8

Associated Types

type Rep Oct8 (a :: Oct8) :: *

Methods

prim :: sing a -> Rep Oct8 a

pretty :: sing a -> String

type Rep OctaveNum Oct_1

type Rep OctaveNum Oct_1 = Int

type Rep OctaveNum Oct0

type Rep OctaveNum Oct0 = Int

type Rep OctaveNum Oct1

type Rep OctaveNum Oct1 = Int

type Rep OctaveNum Oct2

type Rep OctaveNum Oct2 = Int

type Rep OctaveNum Oct3

type Rep OctaveNum Oct3 = Int

type Rep OctaveNum Oct4

type Rep OctaveNum Oct4 = Int

type Rep OctaveNum Oct5

type Rep OctaveNum Oct5 = Int

type Rep OctaveNum Oct6

type Rep OctaveNum Oct6 = Int

type Rep OctaveNum Oct7

type Rep OctaveNum Oct7 = Int

type Rep OctaveNum Oct8

type Rep OctaveNum Oct8 = Int

type Duration = Nat

The duration of the note (a whole note has duration 32).

Singleton types for note properties

data PC pc where

The singleton type for PitchClass.

Constructors

PC :: Primitive pc => PC pc

data Acc acc where

The singleton type for Accidental.

Constructors

Acc :: Primitive acc => Acc acc

data Oct oct where

The singleton type for Octave.

Constructors

Oct :: Primitive oct => Oct oct

data Dur dur where

The singleton type for Duration.

Constructors

Dur :: Primitive dur => Dur dur

Pitches

data PitchType where

The type of pitches.

Constructors

Pitch :: PitchClass -> Accidental -> OctaveNum -> PitchType

A pitch made up of a pitch class, an accidental and an octave.

Silence :: PitchType

Silence, the pitch of rests.

Instances

Primitive PitchType Silence

Associated Types

type Rep Silence (a :: Silence) :: *

Methods

prim :: sing a -> Rep Silence a

pretty :: sing a -> String

(IntRep PitchClass pc, IntRep Accidental acc, IntRep OctaveNum oct) => Primitive PitchType (Pitch pc acc oct)

Associated Types

type Rep (Pitch pc acc oct) (a :: Pitch pc acc oct) :: *

Methods

prim :: sing a -> Rep (Pitch pc acc oct) a

pretty :: sing a -> String

type Rep PitchType Silence

type Rep PitchType Silence = Int

type Rep PitchType (Pitch pc acc oct)

type Rep PitchType (Pitch pc acc oct) = Int

data Pit p where

The singleton type for pitches.

Constructors

Pit :: Primitive p => Pit p

type family (p :: PitchType) =?= (q :: PitchType) :: Bool where ...

Enharmonic equality of pitches.

Equations

Silence =?= Silence = True

Silence =?= _ = False

_ =?= Silence = False

(Pitch pc acc oct) =?= (Pitch pc acc oct) = True

(Pitch C Flat o1) =?= (Pitch B Natural o2) = o1 .~. OctSucc o2

(Pitch C Natural o1) =?= (Pitch B Sharp o2) = o1 .~. OctSucc o2

(Pitch E Natural oct) =?= (Pitch F Flat oct) = True

(Pitch E Sharp oct) =?= (Pitch F Natural oct) = True

(Pitch F Flat oct) =?= (Pitch E Natural oct) = True

(Pitch F Natural oct) =?= (Pitch E Sharp oct) = True

(Pitch B Natural o1) =?= (Pitch C Flat o2) = OctSucc o1 .~. o2

(Pitch B Sharp o1) =?= (Pitch C Natural o2) = OctSucc o1 .~. o2

(Pitch pc1 Sharp oct) =?= (Pitch pc2 Flat oct) = ClassSucc pc1 .~. pc2

(Pitch pc1 Flat oct) =?= (Pitch pc2 Sharp oct) = pc1 .~. ClassSucc pc2

_ =?= _ = False

type family (p1 :: PitchType) <<=? (p2 :: PitchType) where ... infixl 3

Greater than or equal to for pitches.

Equations

p1 <<=? p2 = PitchToNat p1 <=? PitchToNat p2

type family (p1 :: PitchType) <<? (p2 :: PitchType) where ... infixl 3

Greater than for pitches.

Equations

p1 <<? p2 = (p1 <<=? p2) .&&. Not (p1 .~. p2)

Harmonic types

data Mode

The mode of a key: major or minor.

Constructors

MajorMode

MinorMode

Instances

Primitive Mode MajorMode

Associated Types

type Rep MajorMode (a :: MajorMode) :: *

Methods

prim :: sing a -> Rep MajorMode a

pretty :: sing a -> String

Primitive Mode MinorMode

Associated Types

type Rep MinorMode (a :: MinorMode) :: *

Methods

prim :: sing a -> Rep MinorMode a

pretty :: sing a -> String

type Rep Mode MajorMode

type Rep Mode MajorMode = Bool

type Rep Mode MinorMode

type Rep Mode MinorMode = Bool

data ScaleDegree

The seven scale degrees.

Constructors

I

II

III

IV

V

VI

VII

Instances

Primitive ScaleDegree I

Associated Types

type Rep I (a :: I) :: *

Methods

prim :: sing a -> Rep I a

pretty :: sing a -> String

Primitive ScaleDegree II

Associated Types

type Rep II (a :: II) :: *

Methods

prim :: sing a -> Rep II a

pretty :: sing a -> String

Primitive ScaleDegree III

Associated Types

type Rep III (a :: III) :: *

Methods

prim :: sing a -> Rep III a

pretty :: sing a -> String

Primitive ScaleDegree IV

Associated Types

type Rep IV (a :: IV) :: *

Methods

prim :: sing a -> Rep IV a

pretty :: sing a -> String

Primitive ScaleDegree V

Associated Types

type Rep V (a :: V) :: *

Methods

prim :: sing a -> Rep V a

pretty :: sing a -> String

Primitive ScaleDegree VI

Associated Types

type Rep VI (a :: VI) :: *

Methods

prim :: sing a -> Rep VI a

pretty :: sing a -> String

Primitive ScaleDegree VII

Associated Types

type Rep VII (a :: VII) :: *

Methods

prim :: sing a -> Rep VII a

pretty :: sing a -> String

type Rep ScaleDegree I

type Rep ScaleDegree I = Int

type Rep ScaleDegree II

type Rep ScaleDegree II = Int

type Rep ScaleDegree III

type Rep ScaleDegree III = Int

type Rep ScaleDegree IV

type Rep ScaleDegree IV = Int

type Rep ScaleDegree V

type Rep ScaleDegree V = Int

type Rep ScaleDegree VI

type Rep ScaleDegree VI = Int

type Rep ScaleDegree VII

type Rep ScaleDegree VII = Int

data KeyType

The of a scale, chord or piece.

Constructors

Key PitchClass Accidental Mode

Instances

(IntRep PitchClass pc, IntRep Accidental acc, IntRep Mode mo) => Primitive KeyType (Key pc acc mo)

Associated Types

type Rep (Key pc acc mo) (a :: Key pc acc mo) :: *

Methods

prim :: sing a -> Rep (Key pc acc mo) a

pretty :: sing a -> String

type Rep KeyType (Key pc acc mo)

type Rep KeyType (Key pc acc mo) = Int

data RootType where

The root of a chord.

Constructors

PitchRoot :: PitchType -> RootType

A pitch constructs a diatonic root.

DegreeRoot :: KeyType -> ScaleDegree -> RootType

A key and a scale degree constructs a scalar root.

Instances

IntRep PitchType p => Primitive RootType (PitchRoot p)

Associated Types

type Rep (PitchRoot p) (a :: PitchRoot p) :: *

Methods

prim :: sing a -> Rep (PitchRoot p) a

pretty :: sing a -> String

type Rep RootType (PitchRoot p)

type Rep RootType (PitchRoot p) = Int

data Mod m

The singleton type for Mode.

Constructors

Mod

data ScaDeg sd

The singleton type for ScaleDegree

Constructors

ScaDeg

data KeyS k

The singleton type for KeyType.

Constructors

KeyS

data Root r where

The singleton type for Root.

Constructors

Root :: Primitive r => Root r

Instances

IntRep PitchType p => Primitive * (Root (PitchRoot p))

Associated Types

type Rep (Root (PitchRoot p)) (a :: Root (PitchRoot p)) :: *

Methods

prim :: sing a -> Rep (Root (PitchRoot p)) a

pretty :: sing a -> String

(IntRep PitchType p, (~) PitchType (RootToPitch (DegreeRoot k sd)) p, Primitive ScaleDegree sd) => Primitive * (Root (DegreeRoot k sd))

Associated Types

type Rep (Root (DegreeRoot k sd)) (a :: Root (DegreeRoot k sd)) :: *

Methods

prim :: sing a -> Rep (Root (DegreeRoot k sd)) a

pretty :: sing a -> String

type Rep * (Root (PitchRoot p))

type Rep * (Root (PitchRoot p)) = Int

type Rep * (Root (DegreeRoot k sd))

type Rep * (Root (DegreeRoot k sd)) = Int

type family RootToPitch (dr :: RootType) :: PitchType where ...

Convert a root to a pitch.

Note: the default octave for scalar roots is Oct2.

Equations

RootToPitch (PitchRoot p) = p

RootToPitch (DegreeRoot (Key pc acc m) d) = HalfStepsUpBy (Pitch pc acc Oct2) (DegreeOffset m d)

type family PitchToNat (p :: PitchType) :: Nat where ...

Convert a pitch to a natural number (equal to its MIDI code).

Equations

PitchToNat Silence = TypeError (Text "Can't convert a rest to a number.")

PitchToNat (Pitch C Natural Oct_1) = 0

PitchToNat (Pitch C Sharp Oct_1) = 1

PitchToNat (Pitch D Flat Oct_1) = 1

PitchToNat (Pitch C Natural Oct1) = 24

PitchToNat (Pitch C Natural Oct2) = 36

PitchToNat (Pitch C Natural Oct3) = 48

PitchToNat (Pitch C Natural Oct4) = 60

PitchToNat (Pitch C Natural Oct5) = 72

PitchToNat (Pitch C Natural Oct6) = 84

PitchToNat p = 1 + PitchToNat (HalfStepDown p)

type family Sharpen (r :: RootType) :: RootType where ...

Sharpen a root.

Equations

Sharpen r = PitchRoot (HalfStepUp (RootToPitch r))

type family Flatten (r :: RootType) :: RootType where ...

Flatten a root.

Equations

Flatten r = PitchRoot (HalfStepDown (RootToPitch r))

type family Dot (d :: Duration) :: Duration where ...

Form a dotted duration.

Equations

Dot 1 = TypeError (Text "Can't have dotted thirty-seconds.")

Dot n = n + HalfOf n

type family FromRoot (r :: RootType) (d :: Nat) :: Partiture 1 d where ...

Create a new partiture with one voice of the given pitch.

Equations

FromRoot r d = (RootToPitch r +*+ d) :-- None

type family FromSilence (d :: Nat) :: Partiture 1 d where ...

Create a new partiture with one voice of silence.

Equations

FromSilence d = (Silence +*+ d) :-- None

Specialised musical vector types

type Voice l = OptVector PitchType l

A Voice is made up of a sequence of pitch repetitions.

type Partiture n l = Matrix PitchType n l

A Partiture is made up of a fixed number of voices.

Intervals

data IntervalSize

The size of the interval.

Constructors

Unison

Second

Third

Fourth

Fifth

Sixth

Seventh

Octave

data IntervalClass

The class of the interval.

Constructors

Maj

Perf

Min

Aug

Dim

data IntervalType where

The type of intervals.

Constructors

Interval :: IntervalClass -> IntervalSize -> IntervalType

An interval smaller than 13 semitones, where musical rules can still be enforced.

Compound :: IntervalType

An interval larger than 13 semitones, which is large enough so that dissonance effects are not significant.

type family MakeInterval (p1 :: PitchType) (p2 :: PitchType) :: IntervalType where ...

Make an interval from two arbitrary pitches.

Equations

MakeInterval Silence Silence = TypeError (Text "Can't make intervals from rests.")

MakeInterval Silence p2 = TypeError (Text "Can't make intervals from rests.")

MakeInterval p1 Silence = TypeError (Text "Can't make intervals from rests.")

MakeInterval p1 p2 = If (p1 <<=? p2) (MakeIntervalOrd p1 p2) (MakeIntervalOrd p2 p1)

type family HalfStepsUpBy (p :: PitchType) (n :: Nat) :: PitchType where ...

Move a pitch up by the specified number of semitones.

Equations

HalfStepsUpBy p 0 = p

HalfStepsUpBy p n = HalfStepUp (HalfStepsUpBy p (n - 1))

type family HalfStepsDownBy (p :: PitchType) (n :: Nat) :: PitchType where ...

Move a pitch down by the specified number of semitones.

Equations

HalfStepsDownBy p 0 = p

HalfStepsDownBy p n = HalfStepDown (HalfStepsDownBy p (n - 1))

type family RaiseBy (p :: PitchType) (i :: IntervalType) :: PitchType where ...

Raise a pitch by an interval.

Equations

RaiseBy Silence _ = Silence

RaiseBy _ Compound = TypeError (Text "Can't shift by compound interval")

RaiseBy p (Interval Min is) = HalfStepDown (HalfStepsUpBy p (IntervalWidth (Interval Min is) + 1))

RaiseBy p (Interval Dim is) = HalfStepDown (HalfStepsUpBy p (IntervalWidth (Interval Dim is) + 1))

RaiseBy p i = HalfStepsUpBy p (IntervalWidth i)

type family LowerBy (p :: PitchType) (i :: IntervalType) :: PitchType where ...

Lower a pitch by an interval.

Equations

LowerBy Silence _ = Silence

LowerBy _ Compound = TypeError (Text "Can't shift by compound interval")

LowerBy p (Interval Maj is) = HalfStepUp (HalfStepsDownBy p (IntervalWidth (Interval Maj is) + 1))

LowerBy p (Interval Aug is) = HalfStepUp (HalfStepsDownBy p (IntervalWidth (Interval Aug is) + 1))

LowerBy p i = HalfStepsDownBy p (IntervalWidth i)

type family RaiseAllBy' (ps :: Vector PitchType n) (i :: IntervalType) :: Vector PitchType n where ...

Raise multiple pitches by an interval.

Equations

RaiseAllBy' None _ = None

RaiseAllBy' (p :-- ps) i = RaiseBy p i :-- RaiseAllBy' ps i

type family LowerAllBy' (ps :: Vector PitchType n) (i :: IntervalType) :: Vector PitchType n where ...

Lower multiple pitches by an interval.

Equations

LowerAllBy' None _ = None

LowerAllBy' (p :-- ps) i = LowerBy p i :-- LowerAllBy' ps i

type family RaiseByOct (p :: PitchType) :: PitchType where ...

Raise a pitch by an octave.

Equations

RaiseByOct p = RaiseBy p (Interval Perf Octave)

type family LowerByOct (p :: PitchType) :: PitchType where ...

Lower a pitch by an octave.

Equations

LowerByOct p = LowerBy p (Interval Perf Octave)

type family RaiseAllByOct (ps :: Voice l) :: Voice l where ...

Equations

RaiseAllByOct v = RaiseAllBy v (Interval Perf Octave)

Orphan instances

KnownNat n => Primitive Nat n

Associated Types

type Rep n (a :: n) :: *

Methods

prim :: sing a -> Rep n a

pretty :: sing a -> String