The inverse interval, such that this interval and its inverse add to unison. For example, M3 and m6 are inverses, as are m3 and M6, P4 and P5, and TT and TT.
The diatonic number, within the C major scale. For example M2, m2, d2, and D2 all have a diatonic number of 2. The tritone’s number is null.
The number of semitones. For example, A1 and m2 have one semitone.
Semitones doesn't include narrowing or widening by quality.
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An Interval is the distance between two notes.
An interval has a (possibly null) number, a (possibly null) quality (e.g. major, minor, perfect, etc.), and a semitone count (which is never null).
The semitone count is an integer, and assumes twelve-tone equal temperament.
An interval may be simple (if it is eight scale degrees or fewer), or complex.
Only simple and complex tritones (TT) have a null number and quality.
Two intervals are equal (and therefore
===) if their numbers and qualities are equal (or, for tritones, their semitone counts are equal). For example, TT, augmented P4, and diminished P5 all have the same semitone count, but are distinct intervals. Intervals can be tested for enharmonic equivalence by comparing their semitone counts, e.g.i1.semitones ==== i2.semitones.Intervals are interned. interned. This enables the use of the ECMAScript Set to implement sets of intervals.
See Wikipedia: Interval quality.