Mezzo.Model.Harmony.Chords

Types and type functions modelling harmonic chords.

Chords

data DyadType

The type of a dyad.

Constructors

MinThird

MajThird

PerfFourth

PerfFifth

PerfOct

Instances

Primitive DyadType MinThird

Associated Types

type Rep MinThird (a :: MinThird) :: *

Methods

prim :: sing a -> Rep MinThird a

pretty :: sing a -> String

Primitive DyadType MajThird

Associated Types

type Rep MajThird (a :: MajThird) :: *

Methods

prim :: sing a -> Rep MajThird a

pretty :: sing a -> String

Primitive DyadType PerfFourth

Associated Types

type Rep PerfFourth (a :: PerfFourth) :: *

Methods

prim :: sing a -> Rep PerfFourth a

pretty :: sing a -> String

Primitive DyadType PerfFifth

Associated Types

type Rep PerfFifth (a :: PerfFifth) :: *

Methods

prim :: sing a -> Rep PerfFifth a

pretty :: sing a -> String

Primitive DyadType PerfOct

Associated Types

type Rep PerfOct (a :: PerfOct) :: *

Methods

prim :: sing a -> Rep PerfOct a

pretty :: sing a -> String

type Rep DyadType MinThird

type Rep DyadType MinThird = Int -> [Int]

type Rep DyadType MajThird

type Rep DyadType MajThird = Int -> [Int]

type Rep DyadType PerfFourth

type Rep DyadType PerfFourth = Int -> [Int]

type Rep DyadType PerfFifth

type Rep DyadType PerfFifth = Int -> [Int]

type Rep DyadType PerfOct

type Rep DyadType PerfOct = Int -> [Int]

data TriadType

The type of a triad.

Constructors

MajTriad

MinTriad

AugTriad

DimTriad

DoubledD DyadType

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

FunRep DyadType Int [Int] c => Primitive TriadType (DoubledD c)

Associated Types

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

Methods

prim :: sing a -> Rep (DoubledD c) 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]

type Rep TriadType (DoubledD c)

type Rep TriadType (DoubledD c) = Int -> [Int]

data TetradType

The type of a tetrad.

Constructors

MajSeventh

MajMinSeventh

MinSeventh

HalfDimSeventh

DimSeventh

DoubledT TriadType

Instances

Primitive TetradType MajSeventh

Associated Types

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

Methods

prim :: sing a -> Rep MajSeventh a

pretty :: sing a -> String

Primitive TetradType MajMinSeventh

Associated Types

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

Methods

prim :: sing a -> Rep MajMinSeventh a

pretty :: sing a -> String

Primitive TetradType MinSeventh

Associated Types

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

Methods

prim :: sing a -> Rep MinSeventh a

pretty :: sing a -> String

Primitive TetradType HalfDimSeventh

Associated Types

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

Methods

prim :: sing a -> Rep HalfDimSeventh a

pretty :: sing a -> String

Primitive TetradType 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 TetradType (DoubledT c)

Associated Types

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

Methods

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

pretty :: sing a -> String

type Rep TetradType MajSeventh

type Rep TetradType MajSeventh = Int -> [Int]

type Rep TetradType MajMinSeventh

type Rep TetradType MajMinSeventh = Int -> [Int]

type Rep TetradType MinSeventh

type Rep TetradType MinSeventh = Int -> [Int]

type Rep TetradType HalfDimSeventh

type Rep TetradType HalfDimSeventh = Int -> [Int]

type Rep TetradType DimSeventh

type Rep TetradType DimSeventh = Int -> [Int]

type Rep TetradType (DoubledT c)

type Rep TetradType (DoubledT 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 DyaType t

The singleton type for DyadType

Constructors

DyaType

data TriType t

The singleton type for TriadType.

Constructors

TriType

data TetType t

The singleton type for TetradType.

Constructors

TetType

data Inv t

The singleton type for Inversion.

Constructors

Inv

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

Invert a chord once.

Equations

InvertChord (Dyad r t Inv0) = Dyad r t Inv1

InvertChord (Dyad r t Inv1) = Dyad r t Inv0

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

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

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

data ChordType :: Nat -> Type where

A chord type, indexed by the number of notes.

Constructors

Dyad :: RootType -> DyadType -> Inversion -> ChordType 2

A dyad, consisting of two pitches.

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

A triad, consisting of three pitches.

Tetrad :: RootType -> TetradType -> Inversion -> ChordType 4

A tetrad, consisting of four pitches.

Instances

(IntRep RootType r, FunRep DyadType Int [Int] t, FunRep Inversion [Int] [Int] i) => Primitive (ChordType 2) (Dyad r t i)

Associated Types

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

Methods

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

pretty :: sing a -> String

(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 DyadType Int [Int] dt, FunRep Inversion [Int] [Int] i) => Primitive (ChordType 3) (Triad r (DoubledD dt) i)

Associated Types

type Rep (Triad r (DoubledD dt) i) (a :: Triad r (DoubledD dt) i) :: *

Methods

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

pretty :: sing a -> String

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

Associated Types

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

Methods

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

pretty :: sing a -> String

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

Associated Types

type Rep (Tetrad r (DoubledT tt) i) (a :: Tetrad r (DoubledT tt) i) :: *

Methods

prim :: sing a -> Rep (Tetrad r (DoubledT tt) i) a

pretty :: sing a -> String

type Rep (ChordType 2) (Dyad r t i)

type Rep (ChordType 2) (Dyad r t i) = [Int]

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

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

type Rep (ChordType 3) (Triad r (DoubledD dt) i)

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

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

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

type Rep (ChordType 4) (Tetrad r (DoubledT tt) i)

type Rep (ChordType 4) (Tetrad r (DoubledT tt) i) = [Int]

data Cho c

The singleton type for ChordType.

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