Interval

Directed intervals and spelling-preserving transposition. More...

Collaboration diagram for Interval:

Classes
class	MCC::Interval
	Directed interval: a diatonic step count and a chromatic semitone count (SPEC-INT-1). More...
class	MCC::IntervalNumber
	1-based interval number: 1 unison, 3 third, 8 octave, 10 tenth (SPEC-INT-2, SPEC-INT-3). More...
class	MCC::IntervalQuality
	Interval quality: perfect, major, minor, or augmented/diminished repeated one to four times (SPEC-INT-4). More...

Enumerations
enum class	MCC::IntervalDirection : int8_t { Descending = -1 , Unison = 0 , Ascending = 1 }
	Direction of an interval (SPEC-INT-2). More...
enum class	MCC::IntervalQualityKind : uint8_t {   Diminished = 0 , Minor = 1 , Perfect = 2 , Major = 3 ,   Augmented = 4 }
	Kind of an interval quality.

Functions
constexpr bool	MCC::IsEnharmonic (Interval a, Interval b) noexcept
	Returns true when a and b are valid and span the same signed number of semitones: an ascending augmented fourth and an ascending diminished fifth are enharmonic. Any invalid operand yields false.
MCC_CONSTEXPR14 Interval	MCC::IntervalBetween (Pitch from, Pitch to) noexcept
	Returns the directed interval from from to to (SPEC-INT-1): the difference of their diatonic and chromatic indices. B#3 to C4 is an ascending diminished second; C4 to Cb4 is a descending augmented unison (SPEC-INT-5).
MCC_CONSTEXPR14 Interval	MCC::IntervalBetween (NoteName from, NoteName to) noexcept
	Returns the interval from from up to the next to, which is a simple ascending interval of 0-6 steps: B to C is a minor second and E to C is a minor sixth. Between two spellings of the same letter the result is a unison, descending when to is lower (C to Cb, SPEC-INT-5).
MCC_CONSTEXPR14 Pitch	MCC::operator+ (Pitch pitch, Interval interval) noexcept
	Transposes pitch by interval preserving spelling (SPEC-INT-7): the letter moves by the diatonic steps and the accidental is whatever the semitones require. E4 + major third = G#4; B3 + minor second = C4.
MCC_CONSTEXPR14 Pitch	MCC::operator- (Pitch pitch, Interval interval) noexcept
	Transposes pitch down by interval: pitch + interval.Reversed().
MCC_CONSTEXPR14 NoteName	MCC::operator+ (NoteName noteName, Interval interval) noexcept
	Transposes a note name by interval preserving spelling (SPEC-INT-7): E + major third = G#, B + minor second = C. Octaves in the interval do not change a note name.
MCC_CONSTEXPR14 NoteName	MCC::operator- (NoteName noteName, Interval interval) noexcept
	Transposes a note name down by interval.

Detailed Description

Directed intervals and spelling-preserving transposition.

MCC::Interval stores a diatonic step count and a semitone count, from which its MCC::IntervalDirection, MCC::IntervalNumber and MCC::IntervalQuality are derived. MCC::IntervalBetween() measures the interval between two pitches or note names, and pitch + interval transposes while preserving spelling: E4 + M3 = G#4, never Ab4. See Music-Domain Specification (SPEC-INT-*).

Available when MCC_INTERVAL is defined. Requires the Pitch module.

Enumeration Type Documentation

IntervalDirection

enum class MCC::IntervalDirection : int8_t

strong

Direction of an interval (SPEC-INT-2).

The direction follows the written letters: an interval whose second letter is higher is ascending even if it is a diminished interval. Only the perfect unison has direction Unison; an augmented unison is ascending or descending (SPEC-INT-5).

Function Documentation

IntervalBetween()

MCC_CONSTEXPR14 Interval MCC::IntervalBetween ( Pitch from, Pitch to )

noexcept

Returns the directed interval from from to to (SPEC-INT-1): the difference of their diatonic and chromatic indices. B#3 to C4 is an ascending diminished second; C4 to Cb4 is a descending augmented unison (SPEC-INT-5).

The result is invalid when either pitch is invalid or the quality would need more than four augmentations or diminutions (for example Cbbbb4 to C####4).

operator+() [1/2]

MCC_CONSTEXPR14 NoteName MCC::operator+ ( NoteName noteName, Interval interval )

noexcept

Transposes a note name by interval preserving spelling (SPEC-INT-7): E + major third = G#, B + minor second = C. Octaves in the interval do not change a note name.

The result is invalid when an operand is invalid or the accidental would leave [-4, +4] (SPEC-ACC-3).

operator+() [2/2]

MCC_CONSTEXPR14 Pitch MCC::operator+ ( Pitch pitch, Interval interval )

noexcept

Transposes pitch by interval preserving spelling (SPEC-INT-7): the letter moves by the diatonic steps and the accidental is whatever the semitones require. E4 + major third = G#4; B3 + minor second = C4.

The result is invalid when an operand is invalid, the accidental would leave [-4, +4] (SPEC-ACC-3) or the octave would leave [-128, 127] (SPEC-OCT-4).