Directed interval: a diatonic step count and a chromatic semitone count (SPEC-INT-1). More...

#include <Interval.h>

Collaboration diagram for MCC::Interval:

Public Member Functions
constexpr	Interval () noexcept
	Creates the invalid interval (SPEC-ERR-2).
MCC_CONSTEXPR14	Interval (IntervalQuality quality, IntervalNumber number, IntervalDirection direction=IntervalDirection::Ascending) noexcept
	Creates the interval of quality and number in direction, for example Interval(IntervalQuality::Major(), IntervalNumber(3)).
constexpr bool	IsValid () const noexcept
	Returns true unless this is the invalid interval.
constexpr int16_t	DiatonicSteps () const noexcept
	Returns the signed diatonic step count, or InvalidSteps for the invalid interval (SPEC-ERR-7).
constexpr int16_t	Semitones () const noexcept
	Returns the signed semitone count, or 0 for the invalid interval (SPEC-ERR-7).
MCC_CONSTEXPR14 IntervalDirection	Direction () const noexcept
	Returns the direction (SPEC-INT-2); Unison for the perfect unison and for the invalid interval (SPEC-ERR-7).
MCC_CONSTEXPR14 IntervalNumber	Number () const noexcept
	Returns the 1-based number (SPEC-INT-2); invalid if invalid.
MCC_CONSTEXPR14 IntervalQuality	Quality () const noexcept
	Returns the quality (SPEC-INT-4); invalid if invalid.
MCC_CONSTEXPR14 bool	IsSimple () const noexcept
	Returns true for numbers 1-8 (SPEC-INT-3).
MCC_CONSTEXPR14 bool	IsCompound () const noexcept
	Returns true for numbers above 8 (SPEC-INT-3).
MCC_CONSTEXPR14 Interval	Simple () const noexcept
	Removes whole octaves while keeping direction and quality (SPEC-INT-3): a major tenth becomes a major third; an octave stays an octave.
MCC_CONSTEXPR14 Interval	Inverted () const noexcept
	Returns the inversion of the simple interval, in the same direction (SPEC-INT-6): numbers add up to 9, major and minor swap, augmented and diminished swap. Compound intervals invert their simple part.
MCC_CONSTEXPR14 Interval	Reversed () const noexcept
	Returns the same interval in the opposite direction.

Static Public Member Functions
static MCC_CONSTEXPR14 Interval	FromSteps (int32_t diatonicSteps, int32_t semitones) noexcept
	Creates the interval spanning diatonicSteps letters and semitones semitones, both signed (SPEC-INT-1).
static constexpr Interval	Invalid () noexcept
	Returns the invalid interval.
static MCC_CONSTEXPR14 Interval	Unison () noexcept
	Returns the perfect unison.

Static Public Attributes
static constexpr int16_t	MaximumSteps = IntervalNumber::Maximum - 1
	Largest step magnitude: IntervalNumber::Maximum - 1.
static constexpr int16_t	MaximumSemitones = 3079
	Largest semitone magnitude between two writable pitches.
static constexpr int16_t	InvalidSteps = 32767
	Sentinel returned by DiatonicSteps() for the invalid interval (SPEC-ERR-7). Do not rely on it; check IsValid().

Friends
MCC_CONSTEXPR14 Interval	operator+ (Interval a, Interval b) noexcept
	Adds two intervals by adding their steps and semitones: major third + minor third = perfect fifth. The result is invalid when either operand is invalid or the sum is unrepresentable.
constexpr bool	operator== (Interval a, Interval b) noexcept
	Written equality: same steps and semitones. An augmented fourth and a diminished fifth are different intervals. All invalid intervals are equal (SPEC-ERR-6).
constexpr bool	operator!= (Interval a, Interval b) noexcept

Detailed Description

Directed interval: a diatonic step count and a chromatic semitone count (SPEC-INT-1).

Both counts are signed. The direction follows the diatonic steps, or the semitones for a unison, so Cb from C is a descending augmented unison and no diminished unison exists (SPEC-INT-2, SPEC-INT-5). Number and quality are derived from the magnitudes: an ascending major third is +2 steps and +4 semitones; a descending one is -2 and -4.

An interval is valid when its counts lie within the span of writable pitches and its quality is perfect, major, minor, or augmented/diminished at most four times (SPEC-INT-4). Default construction and every other input produce the single invalid value (SPEC-ERR-1..3).

Constructor & Destructor Documentation

◆ Interval()

MCC_CONSTEXPR14 MCC::Interval::Interval	(	IntervalQuality	quality,
		IntervalNumber	number,
		IntervalDirection	direction = IntervalDirection::Ascending )

inlinenoexcept

Creates the interval of quality and number in direction, for example Interval(IntervalQuality::Major(), IntervalNumber(3)).

The result is invalid when the quality does not apply to the number (a perfect third, a major fifth), for a diminished unison (SPEC-INT-5), for direction Unison with anything but a perfect unison, or when either argument is invalid. A perfect unison ignores direction.

Member Function Documentation

◆ FromSteps()

MCC_CONSTEXPR14 Interval MCC::Interval::FromSteps	(	int32_t	diatonicSteps,
		int32_t	semitones )

inlinestaticnoexcept

Creates the interval spanning diatonicSteps letters and semitones semitones, both signed (SPEC-INT-1).

The result is invalid when either count exceeds the writable span or the quality would need more than four augmentations or diminutions (SPEC-ERR-3, SPEC-ERR-5).

◆ Inverted()

MCC_CONSTEXPR14 Interval MCC::Interval::Inverted ( ) const

inlinenoexcept

Returns the inversion of the simple interval, in the same direction (SPEC-INT-6): numbers add up to 9, major and minor swap, augmented and diminished swap. Compound intervals invert their simple part.

An augmented octave inverts to a descending augmented unison, because a diminished unison does not exist (SPEC-INT-5).

The documentation for this class was generated from the following file:

src/MCC/Interval/Interval.h

Public Member Functions

Static Public Member Functions