music_theory Namespace Reference

A dependency-free, header-only collection of useful functions for music theory. More...

Classes
class	Transposer
	Provides dependency-free transposition utilities that work with any scale that has 7 diatonic steps and an equal number of divisions of the octave (EDO). The most common Western scales use 12 divisions of the octave, .i.e., 12-EDO. More...

Enumerations
enum class	NoteName : int {   C = 0 , D = 1 , E = 2 , F = 3 ,   G = 4 , A = 5 , B = 6 }
	The available note names in array order.
enum class	DiatonicMode : int {   Ionian = 0 , Dorian = 1 , Phrygian = 2 , Lydian = 3 ,   Mixolydian = 4 , Aeolian = 5 , Locrian = 6 }
	Represents the seven standard diatonic musical modes. More...
enum class	ClefType {   Unknown , G , C , F ,   Percussion1 , Percussion2 , Tab , TabSerif }
	Represents the possible types of clef, irrespective of octave transposition. More...

Functions
int	calcDisplacement (int pitchClass, int octave)
	Calculates the displacement value for a given absolute pitch class and octave.
template<typename T >
constexpr T	sign (T n)
	Calculates the sign of an integer.
template<typename T >
constexpr T	signedModulus (T n, T d)
	Calculates the modulus of positive and negative numbers in a predictable manner.
template<typename T >
constexpr T	positiveModulus (T n, T d, T *q=nullptr)
	Calculates a positive modulus in the range [0, d-1], even for negative dividends.
int	calc12EdoHalfstepsInInterval (int interval, int chromaticAlteration)
	Calculates the number of 12-EDO chromatic halfsteps in the specified interval.
int	calcAlterationFrom12EdoHalfsteps (int interval, int halfsteps)
	Calculates the alteration in chromatic halfsteps for the specified interval/halfsteps combination.
int	calcAlterationFromKeySigChange (int interval, int keySigChange)
	Determines the chromatic alteration needed for a diatonic interval to produce a desired key signature change.

Variables
constexpr int	STANDARD_NUMBER_OF_STAFFLINES = 5
	The standard number of lines on a staff.
constexpr int	STANDARD_DIATONIC_STEPS = 7
	currently this is the only supported number of diatonic steps.
constexpr int	STANDARD_12EDO_STEPS = 12
	this can be overriden when constructing a Transposer instance.
constexpr std::array< int, STANDARD_DIATONIC_STEPS >	MAJOR_KEYMAP = { 0, 2, 4, 5, 7, 9, 11 }
	keymap for 12-EDO major keys
constexpr std::array< int, STANDARD_DIATONIC_STEPS >	MINOR_KEYMAP = { 0, 2, 3, 5, 7, 8, 10 }
	keymap for 12-EDO minor keys
constexpr std::array< std::array< int, 2 >, 7 >	DIATONIC_INTERVAL_ADJUSTMENTS
	Array of diatonic intervals. Each member array contains.

Detailed Description

A dependency-free, header-only collection of useful functions for music theory.

Enumeration Type Documentation

ClefType

enum class music_theory::ClefType

strong

Represents the possible types of clef, irrespective of octave transposition.

Enumerator
Unknown	Unknown clef type (default value with {} initializer)
G	Treble clef.
C	C clef.
F	Bass clef.
Percussion1	2 thick vertical lines centered on middle staff line (corresponds to SMuFL glyph unpitchedPercussionClef1)
Percussion2	Narrow rectangle centered on middle staff line (corresponds to SMuFL glyph unpitchedPercussionClef2)
Tab	Tablature clef (TAB) with non-serif font.
TabSerif	Tablature clef (TAB) with serif font.

DiatonicMode

enum class music_theory::DiatonicMode : int

strong

Represents the seven standard diatonic musical modes.

Values correspond to their roots with no sharps or flats C (0) through B (6).

Enumerator
Ionian	major
Dorian	minor with raised 6
Phrygian	minor with flat 2
Lydian	major with raised 4
Mixolydian	major with flat 7
Aeolian	natural minor
Locrian	diminished with flat 2 and 5

Function Documentation

calc12EdoHalfstepsInInterval()

int music_theory::calc12EdoHalfstepsInInterval ( int  interval, int  chromaticAlteration  )

inline

Calculates the number of 12-EDO chromatic halfsteps in the specified interval.

Parameters

interval	The diatonic displacement (negative for downward intervals).
chromaticAlteration	The chromatic halfstep alteration that defines the chromatic interval.

Returns

The number of 12-EDO divisions (chromatic halfsteps) in the interval (negative means down)

calcAlterationFrom12EdoHalfsteps()

int music_theory::calcAlterationFrom12EdoHalfsteps ( int  interval, int  halfsteps  )

inline

Calculates the alteration in chromatic halfsteps for the specified interval/halfsteps combination.

Parameters

interval	The diatonic displacement (negative for downward transposition).
halfsteps	The number of 12-EDO chromatic halfsteps in the interval (negative means down).

Returns

The number of 12-EDO divisions (chromatic halfsteps) in the interval

calcAlterationFromKeySigChange()

int music_theory::calcAlterationFromKeySigChange ( int  interval, int  keySigChange  )

inline

Determines the chromatic alteration needed for a diatonic interval to produce a desired key signature change.

Parameters

interval	The diatonic interval (e.g. +3 for a perfect fourth up).
keySigChange	The desired change in key signature (positive for sharps added, negative for flats).

Returns

The chromatic alteration in halfsteps required to produce that key signature change with the given diatonic interval.

calcDisplacement()

int music_theory::calcDisplacement ( int  pitchClass, int  octave  )

inline

Calculates the displacement value for a given absolute pitch class and octave.

Parameters

pitchClass	0..6 corresponding to C..B
octave	Octave 4 is the middle-C octave

Returns

A displacement value that can be used to create a Transposer instance.

positiveModulus()

template<typename T >

constexpr T music_theory::positiveModulus ( T  n, T  d, T *  q = nullptr  )

constexpr

Calculates a positive modulus in the range [0, d-1], even for negative dividends.

Template Parameters

T	An integer type.

Parameters

n	The dividend (may be negative).
d	The modulus base (must be positive).
q	Optional pointer to receive the quotient such that n = d * q + result.

Returns

The result of n modulo d in the range [0, d-1].

sign()

template<typename T >

constexpr T music_theory::sign ( T  n )

inlineconstexpr

Calculates the sign of an integer.

Parameters

n	The integer to process.

Returns

-1 for negative; 1 for non-negative.

signedModulus()

template<typename T >

constexpr T music_theory::signedModulus ( T  n, T  d  )

constexpr

Calculates the modulus of positive and negative numbers in a predictable manner.

Template Parameters

T	an integer type

Parameters

n	The number (positive or negative) for which to calculate the modulus
d	The base of the modulus. This must be a positive number.

Returns

For non-negative, the result is the same as %. For negative numbers, the result is -1 * (abs(n) % d).

Variable Documentation

DIATONIC_INTERVAL_ADJUSTMENTS

constexpr std::array<std::array<int, 2>, 7> music_theory::DIATONIC_INTERVAL_ADJUSTMENTS

constexpr

Initial value:

= { {
    { 0,  0 },  
    { 2, -1 },  
    { 4, -2 },  
    {-1,  1 },  
    { 1,  0 },  
    { 3, -1 },  
    { 5, -2 }   
}}

Array of diatonic intervals. Each member array contains.

• the number of fifths to add, which is also the key signature adjustment for the interval
• the number of octaves to subtract