Safe Haskell	Safe-Inferred
Language	Haskell2010

Harmonic.Rules.Types.Pitch

Contents

Core Types
Enharmonic Note Names
Transposition (Group Action)
Utilities

Description

This module defines PitchClass as a proper cyclic group with modular arithmetic. All pitch operations automatically wrap within the octave.

Academic Lineage

Data Science In The Creative Process (South, 2018): the MusicData module's pitch-class algebra, where pitch classes are treated as elements of ℤ₁₂ with modular arithmetic operations.

Design

This module sits in the Rules (R) layer: the ℤ₁₂ algebra is part of the language the system's validity rules are written in. (R, E and T describe the creative system as a whole, not individual types — transposition and interval measurement here are algebra, and become traversal or evaluation only in the layers that use them for those purposes.)

Pitch classes are elements of ℤ₁₂, the integers modulo 12:

Addition: transposition
Subtraction: interval measurement
Identity: unison (0)
Inverse: octave complement

Synopsis

newtype PitchClass = P {
- unPitchClass :: Int
}
mkPitchClass :: Int -> PitchClass
data NoteName
- = C
- | C'
- | Db
- | D
- | D'
- | Eb
- | E
- | F
- | F'
- | Gb
- | G
- | G'
- | Ab
- | A
- | A'
- | Bb
- | B
pitchClass :: NoteName -> PitchClass
notesToPCs :: [NoteName] -> [Int]
sharp :: PitchClass -> NoteName
flat :: PitchClass -> NoteName
enharmFromNoteName :: NoteName -> PitchClass -> NoteName
transpose :: Int -> PitchClass -> PitchClass
interval :: PitchClass -> PitchClass -> PitchClass
invert :: PitchClass -> PitchClass
allPitchClasses :: [PitchClass]
pcSet :: [Int] -> [PitchClass]
zeroForm :: [Int] -> [PitchClass]

Core Types

newtype PitchClass Source #

PitchClass represents an element of ℤ₁₂, the cyclic group of integers mod 12. The Num instance ensures all arithmetic automatically wraps to [0..11].

Constructors

P
Fields unPitchClass :: Int

Instances

Instances details

Bounded PitchClass Source #	Bounded instance: pitch classes range from 0 to 11
Instance details Defined in Harmonic.Rules.Types.Pitch Methods minBound :: PitchClass # maxBound :: PitchClass #
Enum PitchClass Source #	Enum instance provides cyclic enumeration
Instance details Defined in Harmonic.Rules.Types.Pitch Methods succ :: PitchClass -> PitchClass # pred :: PitchClass -> PitchClass # toEnum :: Int -> PitchClass # fromEnum :: PitchClass -> Int # enumFrom :: PitchClass -> [PitchClass] # enumFromThen :: PitchClass -> PitchClass -> [PitchClass] # enumFromTo :: PitchClass -> PitchClass -> [PitchClass] # enumFromThenTo :: PitchClass -> PitchClass -> PitchClass -> [PitchClass] #
Generic PitchClass Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Associated Types type Rep PitchClass :: Type -> Type # Methods from :: PitchClass -> Rep PitchClass x # to :: Rep PitchClass x -> PitchClass #
Num PitchClass Source #	Num instance implements ℤ₁₂ group operations. All operations automatically wrap modulo 12.
Instance details Defined in Harmonic.Rules.Types.Pitch Methods (+) :: PitchClass -> PitchClass -> PitchClass # (-) :: PitchClass -> PitchClass -> PitchClass # (*) :: PitchClass -> PitchClass -> PitchClass # negate :: PitchClass -> PitchClass # abs :: PitchClass -> PitchClass # signum :: PitchClass -> PitchClass # fromInteger :: Integer -> PitchClass #
Read PitchClass Source #	Read instance handles legacy DB format "P 0" (with space after P)
Instance details Defined in Harmonic.Rules.Types.Pitch Methods readsPrec :: Int -> ReadS PitchClass # readList :: ReadS [PitchClass] # readPrec :: ReadPrec PitchClass # readListPrec :: ReadPrec [PitchClass] #
Integral PitchClass Source #	Integral instance for compatibility with legacy code
Instance details Defined in Harmonic.Rules.Types.Pitch Methods quot :: PitchClass -> PitchClass -> PitchClass # rem :: PitchClass -> PitchClass -> PitchClass # div :: PitchClass -> PitchClass -> PitchClass # mod :: PitchClass -> PitchClass -> PitchClass # quotRem :: PitchClass -> PitchClass -> (PitchClass, PitchClass) # divMod :: PitchClass -> PitchClass -> (PitchClass, PitchClass) # toInteger :: PitchClass -> Integer #
Real PitchClass Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods toRational :: PitchClass -> Rational #
Show PitchClass Source #	Show instance matches legacy format for DB compatibility: "P 0" not P0
Instance details Defined in Harmonic.Rules.Types.Pitch Methods showsPrec :: Int -> PitchClass -> ShowS # show :: PitchClass -> String # showList :: [PitchClass] -> ShowS #
Eq PitchClass Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods (==) :: PitchClass -> PitchClass -> Bool # (/=) :: PitchClass -> PitchClass -> Bool #
Ord PitchClass Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods compare :: PitchClass -> PitchClass -> Ordering # (<) :: PitchClass -> PitchClass -> Bool # (<=) :: PitchClass -> PitchClass -> Bool # (>) :: PitchClass -> PitchClass -> Bool # (>=) :: PitchClass -> PitchClass -> Bool # max :: PitchClass -> PitchClass -> PitchClass # min :: PitchClass -> PitchClass -> PitchClass #
type Rep PitchClass Source #
Instance details Defined in Harmonic.Rules.Types.Pitch type Rep PitchClass = D1 ('MetaData "PitchClass" "Harmonic.Rules.Types.Pitch" "theHarmonicAlgorithm-3.0.0-1Jyc2qhqYzxBLoiBHPE0av" 'True) (C1 ('MetaCons "P" 'PrefixI 'True) (S1 ('MetaSel ('Just "unPitchClass") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Int)))

mkPitchClass :: Int -> PitchClass Source #

Smart constructor ensuring values stay in [0..11]

Enharmonic Note Names

data NoteName Source #

All standard enharmonic note names within an octave

Constructors

C
C'
Db
D
D'
Eb
E
F
F'
Gb
G
G'
Ab
A
A'
Bb
B

Instances

Instances details

Bounded NoteName Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods minBound :: NoteName # maxBound :: NoteName #
Enum NoteName Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods succ :: NoteName -> NoteName # pred :: NoteName -> NoteName # toEnum :: Int -> NoteName # fromEnum :: NoteName -> Int # enumFrom :: NoteName -> [NoteName] # enumFromThen :: NoteName -> NoteName -> [NoteName] # enumFromTo :: NoteName -> NoteName -> [NoteName] # enumFromThenTo :: NoteName -> NoteName -> NoteName -> [NoteName] #
Read NoteName Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods readsPrec :: Int -> ReadS NoteName # readList :: ReadS [NoteName] # readPrec :: ReadPrec NoteName # readListPrec :: ReadPrec [NoteName] #
Show NoteName Source #	Custom Show instance: renders sharp notation C' as C#, D' as D#, etc. (matches legacy behavior and musical convention)
Instance details Defined in Harmonic.Rules.Types.Pitch Methods showsPrec :: Int -> NoteName -> ShowS # show :: NoteName -> String # showList :: [NoteName] -> ShowS #
Eq NoteName Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods (==) :: NoteName -> NoteName -> Bool # (/=) :: NoteName -> NoteName -> Bool #
Ord NoteName Source #
Instance details Defined in Harmonic.Rules.Types.Pitch Methods compare :: NoteName -> NoteName -> Ordering # (<) :: NoteName -> NoteName -> Bool # (<=) :: NoteName -> NoteName -> Bool # (>) :: NoteName -> NoteName -> Bool # (>=) :: NoteName -> NoteName -> Bool # max :: NoteName -> NoteName -> NoteName # min :: NoteName -> NoteName -> NoteName #

pitchClass :: NoteName -> PitchClass Source #

Extract pitch class from a note name

notesToPCs :: [NoteName] -> [Int] Source #

Convert a list of NoteNames to pitch-class integers Useful for defining chord progressions with note names

sharp :: PitchClass -> NoteName Source #

Map pitch class to sharp enharmonic spelling

flat :: PitchClass -> NoteName Source #

Map pitch class to flat enharmonic spelling

enharmFromNoteName :: NoteName -> PitchClass -> NoteName Source #

Helper function for mapping NoteName to enharmonic function. This determines whether to use sharp or flat spelling based on the root note of a chord (for consistent enharmonic spelling). Ported from legacy MusicData.hs

Transposition (Group Action)

transpose :: Int -> PitchClass -> PitchClass Source #

Transpose a pitch class by an interval (group addition)

interval :: PitchClass -> PitchClass -> PitchClass Source #

Calculate the interval between two pitch classes (group subtraction) Returns the ascending interval from first to second.

invert :: PitchClass -> PitchClass Source #

Invert a pitch class (octave complement) The inverse of n is (12 - n) mod 12

Utilities

allPitchClasses :: [PitchClass] Source #

All 12 pitch classes

pcSet :: [Int] -> [PitchClass] Source #

Convert a list of integers to a set of unique pitch classes

zeroForm :: [Int] -> [PitchClass] Source #

Normalize a pitch set to start from zero (transposition-invariant form) Ported from legacy MusicData.hs