Music.Pitch.Common.Types

Common (Western classical) pitches, intervals and related types.

Even octaves and steps

data Octaves

Number of octaves. May be negative, indicating a downward interval.

Instances

Enum Octaves

Eq Octaves

Integral Octaves

Num Octaves

Ord Octaves

Real Octaves

Show Octaves

data DiatonicSteps

Number of diatonic steps. May be negative, indicating a downward interval.

Instances

Enum DiatonicSteps

Eq DiatonicSteps

Integral DiatonicSteps

Num DiatonicSteps

Ord DiatonicSteps

Real DiatonicSteps

Show DiatonicSteps

ToJSON DiatonicSteps

AdditiveGroup DiatonicSteps

data ChromaticSteps

Number of chromatic steps. May be negative, indicating a downward interval.

Instances

Enum ChromaticSteps

Eq ChromaticSteps

Integral ChromaticSteps

Num ChromaticSteps

Ord ChromaticSteps

Real ChromaticSteps

Show ChromaticSteps

ToJSON ChromaticSteps

AdditiveGroup ChromaticSteps

HasSemitones ChromaticSteps

type Semitones = ChromaticSteps

Number of semitones. May be negative, indicating a downward interval.

Intervals

data Number

The number component of an interval (fourth, fifth) etc. May be negative, indicating a downward interval.

Instances

Enum Number

Eq Number

Integral Number

Num Number

Ord Number

Real Number

Show Number

HasNumber Number

data Quality

The quality component of an interval (minor, major, augmented). Generalized from single/double augmented/diminished to any number of steps.

Constructors

Major

Minor

Perfect

Augmented Integer

Diminished Integer

Instances

Eq Quality

Ord Quality

Show Quality

Augmentable Quality

Augmentable Quality instance

This Augmentable instance exists solely for use of the extractQuality function, which ensures that there is never any ambiguity around diminishedaugmented intervals turning into majorminor/perfect intervals.

HasQuality Quality

data QualityType

The alteration implied by a quality is dependent on whether it is attached to a major/minor vs. a perfect-style number. This type represents the two possibilities.

Constructors

PerfectType

MajorMinorType

Instances

Eq QualityType

Ord QualityType

Read QualityType

Show QualityType

data IntervalBasis

This type represents standard basis for intervbals.

Constructors

Chromatic

Diatonic

Instances

Enum IntervalBasis

Eq IntervalBasis

Ord IntervalBasis

Show IntervalBasis

newtype Interval

Interval type.

Constructors

Interval

Fields

getInterval :: (ChromaticSteps, DiatonicSteps)

Instances

Eq Interval

Num Interval

Avoid using '(*)', or signum on intervals.

Ord Interval

Lexicographical ordering, comparing the d2 component of the Interval first, as it's tied to the Number which is expected to be bigger than the Quality, assuming ordinary tuning systems

Show Interval

ToJSON Interval

Monoid Interval

Semigroup Interval

IsInterval Interval

Augmentable Interval

HasBasis Interval

VectorSpace Interval

AdditiveGroup Interval

HasNumber Interval

HasQuality Interval

HasSemitones Interval

Typeable * Interval

type Basis Interval = IntervalBasis

type Scalar Interval = Integer

Pitch

data Name

Pitch name component.

Constructors

C

D

E

F

G

A

B

Instances

Enum Name

Eq Name

Ord Name

Show Name

data Accidental

Accidental, represented as number of alterations. Generalized from natural and single/double sharp/flat to any number of steps.

Instances

Enum Accidental

Eq Accidental

Integral Accidental

Num Accidental

Ord Accidental

Real Accidental

Show Accidental

Alterable Accidental

(IsPitch a, Alterable a) => IsPitch (Accidental -> a)

Magic instance that allow us to write c sharp instead of sharpen c.

newtype Pitch

Pitch type.

Constructors

Pitch

Fields

getPitch :: Interval

Instances

Enum Pitch

Eq Pitch

Num Pitch

Ord Pitch

Show Pitch

ToJSON Pitch

IsPitch Pitch

Alterable Pitch

AffineSpace Pitch

Typeable * Pitch

type Diff Pitch = Interval