Forte number

In musical set theory, a Forte number is the pair of numbers Allen Forte assigned to the prime form of each pitch class set of three or more members in The Structure of Atonal Music (1973, ISBN 0-300-02120-8).

[1][2] In the 12-TET tuning system (or in any other system of tuning that splits the octave into twelve semitones), each pitch class may be denoted by an integer in the range from 0 to 11 (inclusive), and a pitch class set may be denoted by a set of these integers.

Its (transposed) inversion, which happens to be the minor chord, contains the pitch classes 0, 3, and 7; and is the prime form.

Sets of pitches which share the same Forte number have identical interval vectors.

For example, the Forte prime form for 6-31 is [011232538193] whereas the Rahn algorithm chooses [011341527293], where adjacency intervals are shown here by subscripts between pitch-class numerals.

Set 3-1 has three possible rotations/inversions; the normal form ( left ) is the most compact, corresponding to the smallest sector
Major and minor chords on C Play ⓘ Play ⓘ .
C major diatonic scale Play ⓘ .
Locrian mode on C Play ⓘ .