Interval

This page details all the functions that create, transform or query Interval vectors.

Creating Intervals

Interval vectors can be initialised directly:

Interval m = { 3, 0 }; // initialised to an augmented 4th

It’s often more convenient, however, to be able to create new Intervals from old, or to assign them values by parsing strings in accepted formats.

`interval_from_name`

int interval_from_name(const char *s, Interval *out);

Parses an Interval from a standard abbreviated name. Outputs via a passed in Interval pointer. Returns 1 if anything went wrong during parsing.

Interval name can be in the scientific style. For example:

“M3” will make a major third.
“m3” will make a minor third.
“P5” will make a perfect fifth.
“A6” will make an augmented 6th.
“d5” will make a diminished 5th.

It can also be in the “jazz” style:

Plain numbers like “5” and “7” will default to major.
b or # will alter intervals from these default positions, and can be stacked.

So “m7” and “b7” will both produce a minor 7th Interval vector.

Safe usage if the string is being passed in dynamically:

Interval m;
if (int interval_from_name(str, &p)) {
    // handle parsing error
}

`interval_from_spn`

int interval_from_spn(const char *p_str, const char *q_str, Interval *out);

Parses two strings into Pitch vectors from Scientific Pitch Notation to generate an Interval vector from. Outputs via a passed in Interval pointer. Returns 1 if anything went wrong during parsing.

Safe usage if the string is being passed in dynamically:

Interval m;
if (int interval_from_spn(str1, str2, &p)) {
    // handle parsing error
}

`interval_between`

Interval interval_between(Pitch p, Pitch q);

Creates an Interval from two Pitch vectors by subtracting the first from the second.

Common Queries

`interval_chroma`

int interval_chroma(Interval m);

Returns the number of perfect fifths (signed) separating an Interval from the unison. Abstracts octave information away.

`stepspan`

int stepspan(Interval m);

Returns the number of diatonic steps subtended by an interval. Basically the same as the standard generic interval sizes used in musical discourse, except zero-indexed so a “third” will have a stepspan of 2, not 3.

This format is more amenable to basic arithmetic, and allows negative stepspans to represent descending horizontal intervals, or voice crossed vertical intervals.

`interval_quality`

int interval_quality(Interval m);

Returns an Interval’s quality as a signed integer:


Augmented	2
Major	1
Perfect	0
Minor	-1
Diminished	-2

etc. for doubly-augmented/diminished intervals and beyond.

`intervals_equal`

bool intervals_equal(Interval m, Interval n);

Predicate function that checks whether two Interval vectors are equal.

`intervals_enharmonic`

bool intervals_enharmonic(Interval m, Interval n, int edo);

Predicate function that checks whether two Pitch vectors are enharmonics in a given EDO tuning system. The third parameter edo is for passing in the tuning system to check against. So for example:

Interval m, n;
interval_from_name("A6", &m);
interval_from_name("m7", &n);
intervals_enharmonic(m, n, 12); // true; A6 and m7 are enharmonic in 12tet
intervals_enharmonic(m, n, 31); // false; A6 and m7 are not enharmonic in 31tet

interval_from_name("dddd10", &m);
interval_from_name("p8", &n);
intervals_enharmonic(m, n, 31); // true;
intervals_enharmonic(m, n, 12); // false;

Transformations

`interval_negate`

Interval interval_negate(Interval m);

Flips the direction of an Interval. Horizontally, an ascending major 3rd will become a descending major 3rd. Vertically, flipping an Interval represents voices swapping locations.

`intervals_add`

Interval intervals_add(Interval m, Interval n);

Adds two Interval vectors to produce a new Interval.

`interval_simple`

Interval interval_simple(Interval m);

Reduces an interval’s size until it is smaller than an octave. This includes the octave, which is considered a compound unison here.