Mezzo.Model.Harmony.Chords

Types and type functions modelling harmonic chords.

Chords

data TriadType

The type of a triad.

Constructors

MajTriad

MinTriad

AugTriad

DimTriad

Instances

Primitive TriadType MajTriad

Associated Types

type Rep MajTriad (a :: MajTriad) :: *

Methods

prim :: sing a -> Rep MajTriad a

pretty :: sing a -> String

Primitive TriadType MinTriad

Associated Types

type Rep MinTriad (a :: MinTriad) :: *

Methods

prim :: sing a -> Rep MinTriad a

pretty :: sing a -> String

Primitive TriadType AugTriad

Associated Types

type Rep AugTriad (a :: AugTriad) :: *

Methods

prim :: sing a -> Rep AugTriad a

pretty :: sing a -> String

Primitive TriadType DimTriad

Associated Types

type Rep DimTriad (a :: DimTriad) :: *

Methods

prim :: sing a -> Rep DimTriad a

pretty :: sing a -> String

type Rep TriadType MajTriad

type Rep TriadType MajTriad = Int -> [Int]

type Rep TriadType MinTriad

type Rep TriadType MinTriad = Int -> [Int]

type Rep TriadType AugTriad

type Rep TriadType AugTriad = Int -> [Int]

type Rep TriadType DimTriad

type Rep TriadType DimTriad = Int -> [Int]

data SeventhType

The type of a seventh chord.

Constructors

MajSeventh

MajMinSeventh

MinSeventh

HalfDimSeventh

DimSeventh

Doubled TriadType

Instances

Primitive SeventhType MajSeventh

Associated Types

type Rep MajSeventh (a :: MajSeventh) :: *

Methods

prim :: sing a -> Rep MajSeventh a

pretty :: sing a -> String

Primitive SeventhType MajMinSeventh

Associated Types

type Rep MajMinSeventh (a :: MajMinSeventh) :: *

Methods

prim :: sing a -> Rep MajMinSeventh a

pretty :: sing a -> String

Primitive SeventhType MinSeventh

Associated Types

type Rep MinSeventh (a :: MinSeventh) :: *

Methods

prim :: sing a -> Rep MinSeventh a

pretty :: sing a -> String

Primitive SeventhType HalfDimSeventh

Associated Types

type Rep HalfDimSeventh (a :: HalfDimSeventh) :: *

Methods

prim :: sing a -> Rep HalfDimSeventh a

pretty :: sing a -> String

Primitive SeventhType DimSeventh

Associated Types

type Rep DimSeventh (a :: DimSeventh) :: *

Methods

prim :: sing a -> Rep DimSeventh a

pretty :: sing a -> String

FunRep TriadType Int [Int] c => Primitive SeventhType (Doubled c)

Associated Types

type Rep (Doubled c) (a :: Doubled c) :: *

Methods

prim :: sing a -> Rep (Doubled c) a

pretty :: sing a -> String

type Rep SeventhType MajSeventh

type Rep SeventhType MajSeventh = Int -> [Int]

type Rep SeventhType MajMinSeventh

type Rep SeventhType MajMinSeventh = Int -> [Int]

type Rep SeventhType MinSeventh

type Rep SeventhType MinSeventh = Int -> [Int]

type Rep SeventhType HalfDimSeventh

type Rep SeventhType HalfDimSeventh = Int -> [Int]

type Rep SeventhType DimSeventh

type Rep SeventhType DimSeventh = Int -> [Int]

type Rep SeventhType (Doubled c)

type Rep SeventhType (Doubled c) = Int -> [Int]

data Inversion

The inversion of a chord.

Constructors

Inv0

Inv1

Inv2

Inv3

Instances

Primitive Inversion Inv0

Associated Types

type Rep Inv0 (a :: Inv0) :: *

Methods

prim :: sing a -> Rep Inv0 a

pretty :: sing a -> String

Primitive Inversion Inv1

Associated Types

type Rep Inv1 (a :: Inv1) :: *

Methods

prim :: sing a -> Rep Inv1 a

pretty :: sing a -> String

Primitive Inversion Inv2

Associated Types

type Rep Inv2 (a :: Inv2) :: *

Methods

prim :: sing a -> Rep Inv2 a

pretty :: sing a -> String

Primitive Inversion Inv3

Associated Types

type Rep Inv3 (a :: Inv3) :: *

Methods

prim :: sing a -> Rep Inv3 a

pretty :: sing a -> String

type Rep Inversion Inv0

type Rep Inversion Inv0 = [Int] -> [Int]

type Rep Inversion Inv1

type Rep Inversion Inv1 = [Int] -> [Int]

type Rep Inversion Inv2

type Rep Inversion Inv2 = [Int] -> [Int]

type Rep Inversion Inv3

type Rep Inversion Inv3 = [Int] -> [Int]

data TriType t

The singleton type for TriadType.

Constructors

TriType

data SevType t

The singleton type for SeventhType.

Constructors

SevType

data Inv t

The singleton type for Inversion.

Constructors

Inv

type family InvertChord (c :: ChordType n) :: ChordType n where ...

Equations

InvertChord (Triad r t Inv2) = Triad r t Inv0

InvertChord (Triad r t i) = Triad r t (InvSucc i)

InvertChord (SeventhChord r t i) = SeventhChord r t (InvSucc i)

data ChordType :: Nat -> Type where

A chord type, indexed by the number of notes.

Constructors

Triad :: RootType -> TriadType -> Inversion -> ChordType 3

SeventhChord :: RootType -> SeventhType -> Inversion -> ChordType 4

Instances

(IntRep RootType r, FunRep TriadType Int [Int] t, FunRep Inversion [Int] [Int] i) => Primitive (ChordType 3) (Triad r t i)

Associated Types

type Rep (Triad r t i) (a :: Triad r t i) :: *

Methods

prim :: sing a -> Rep (Triad r t i) a

pretty :: sing a -> String

(IntRep RootType r, FunRep SeventhType Int [Int] t, FunRep Inversion [Int] [Int] i) => Primitive (ChordType 4) (SeventhChord r t i)

Associated Types

type Rep (SeventhChord r t i) (a :: SeventhChord r t i) :: *

Methods

prim :: sing a -> Rep (SeventhChord r t i) a

pretty :: sing a -> String

(IntRep RootType r, FunRep TriadType Int [Int] tt, FunRep Inversion [Int] [Int] i) => Primitive (ChordType 4) (SeventhChord r (Doubled tt) i)

Associated Types

type Rep (SeventhChord r (Doubled tt) i) (a :: SeventhChord r (Doubled tt) i) :: *

Methods

prim :: sing a -> Rep (SeventhChord r (Doubled tt) i) a

pretty :: sing a -> String

type Rep (ChordType 3) (Triad r t i)

type Rep (ChordType 3) (Triad r t i) = [Int]

type Rep (ChordType 4) (SeventhChord r t i)

type Rep (ChordType 4) (SeventhChord r t i) = [Int]

type Rep (ChordType 4) (SeventhChord r (Doubled tt) i)

type Rep (ChordType 4) (SeventhChord r (Doubled tt) i) = [Int]

data Cho c

Constructors

Cho

type family FromChord (c :: ChordType n) (l :: Nat) :: Partiture n l where ...

Convert a chord to a partiture with the given length (one voice for each pitch).

Equations

FromChord c l = VectorToColMatrix (ChordToPitchList c) l

type family ChordsToPartiture (v :: Vector (ChordType n) l) (d :: Nat) :: Partiture n (l * d) where ...

Equations

ChordsToPartiture None l = None

ChordsToPartiture (c :-- cs) d = FromChord c d +|+ ChordsToPartiture cs d