In music, specifically, musical set theory an interval class, or unordered pitch-class interval, is an interval measured by the distance between its two pitch classes ordered so they are as close as possible. It was created to account for octave and inversional equivalency. Since there are 12 pitch classes in the equal tempered scale the largest interval class is 6 semitones, since any interval larger than that is not the closest ordering, see complement. For example, the interval of a perfect fifth, or 7, is the interval class 5, or a perfect fourth.
Using integer notation and modulo 12, the unordered pitch-class interval, i(a,b), may be defined as:
- i(a,b) = the smaller of i < a,b > and i < b,a >
i<a,b> being ordered pitch class interval. (Rahn)
- Rahn, John. Basic Atonal Theory.