HarmTrace.Base.Chord.Analysis

Summary: Analyses and transforms musical chords

Analysis

Triads and Sevenths

analyseTriad :: IntSet -> Triad

Analyses a degree list and returns MajTriad, MinTriad or NoTriad if the degrees make a chord a major, minor, or no triad, respectively.

analyseTetra :: IntSet -> Shorthand

Analyses the structure of an IntSet and returns an appropriate ShortHand, if possible

toTriad :: Chord a -> Triad

Takes a Chord and determines the Triad

>>> toTriad (Chord (Note Nat C) Min [NoAdd (Note Fl I3),Add (Note Nat I3)] 0 0)
maj

>>> toTriad (Chord (Note Nat C) HDim7 [Add (Note Sh I11)] 0 0)
dim

>>> toTriad (Chord (Note Nat C) Min [NoAdd (Note Fl I3)] 0 0)
NoTriad

N.B. toTriad throws an error when applied to a NoChord or UndefChord.

toMajMinChord :: ChordLabel -> ChordLabel

applies toMajMin to a Chord, in case there is no triad, e.g. :sus4 or :sus2, an UndefChord is returned. Also, chord additions are removed. NoChords and UndefChords are returned untouched.

Chord components

data Third

A Third can by major, minor or absent

Constructors

MajThird

MinThird

NoThird

Instances

Eq Third

Methods

(==) :: Third -> Third -> Bool

(/=) :: Third -> Third -> Bool

Show Third

Methods

showsPrec :: Int -> Third -> ShowS

show :: Third -> String

showList :: [Third] -> ShowS

data Fifth

A Fifth can be perfect, diminished, augmented or absent

Constructors

DimFifth

PerfFifth

AugFifth

NoFifth

Instances

Eq Fifth

Methods

(==) :: Fifth -> Fifth -> Bool

(/=) :: Fifth -> Fifth -> Bool

Show Fifth

Methods

showsPrec :: Int -> Fifth -> ShowS

show :: Fifth -> String

showList :: [Fifth] -> ShowS

data Sevth

A seventh can be major, minor, diminished, or absent

Constructors

DimSev

MinSev

MajSev

NoSev

Instances

Eq Sevth

Methods

(==) :: Sevth -> Sevth -> Bool

(/=) :: Sevth -> Sevth -> Bool

Show Sevth

Methods

showsPrec :: Int -> Sevth -> ShowS

show :: Sevth -> String

showList :: [Sevth] -> ShowS

analyseThird :: IntSet -> Third

analyses the third in a degree list

analyseFifth :: IntSet -> Fifth

analyses the fifth in a degree list

analyseSevth :: IntSet -> Sevth

analyses the fifth in a degree list

Misc

toMode :: Triad -> Mode

Converts a Shorthand to a Mode

toMajMin :: Triad -> ClassType

Converts a Shorthand to either a MajClass, MinClass or NoClass ClassType.

toClassType :: Chord a -> ClassType

Returns the ClassType given a Chord. This function uses analyseDegClassType to analyse a chord and derive the ClassType

isSus2 :: ChordLabel -> Bool

Returns True if the ChordLabel has a major second, no third, and no fourth.

isSus4 :: ChordLabel -> Bool

Returns True if the ChordLabel has a no major second, no third, but has a fourth.

Scale degree transposition

transposeRoot :: Root -> Int -> Root

Transposes a Root with a Int semitones up

transposeCL :: ChordLabel -> Int -> ChordLabel

Transposes a ChordLabel with a Int semitones up

transposeSD :: ScaleDegree -> Int -> ScaleDegree

Transposes a scale degree with Int semitones up

toChordDegree :: Key -> ChordLabel -> ChordDegree

Given a Key, calculates the the ChordDegree (i.e. relative, ScaleDegree based Chord) for an absolute ChordLabel using toScaleDegree.

toScaleDegree :: Key -> Root -> ScaleDegree

Transformes a absolute Root Note into a relative ScaleDegree, given a Key.

intervalToPitch :: Root -> Interval -> Root

Similar to toScaleDegree, an interval is transformed into an absolute Root pitch, given another Root that serves as a basis.

>>> intervalToPitch (Note Sh G) (Note Fl I13)
>>> E

>>> intervalToPitch (Note Nat C) (Note Sh I11)
>>> F#

pitchToInterval :: Root -> Root -> Interval

The inverse of intervalToPitch

toChord :: Root -> IntSet -> Interval -> Chord Root

Given an IntSet (Interval Set), a Root Note and an optional bass Interval, returns a Chord