Pitchclass

In music theory, a pitch class is the set of all pitches that share the same note name modulo octave; notes separated by octaves are considered equivalent. In twelve-tone equal temperament, there are twelve pitch classes, commonly labeled C, C-sharp, D, D-sharp, E, F, F-sharp, G, G-sharp, A, A-sharp, B, or numbered 0 through 11 with C = 0 and B = 11.

A pitch class is an abstract object that ignores octave and register, focusing only on the chromatic pitch class. Pitches belong to Z, and two pitches are in the same pitch class if their difference is a multiple of the octave (twelve semitones). Thus the pitch classes form the integers modulo 12, denoted Z12.

In pitch-class theory, operations such as transposition and inversion act on the set of pitch classes modulo 12: transposition Tn adds n modulo 12, inversion In maps x to -x + n (mod 12). The concept underlies twelve-tone technique and set theory; pitch-class sets are analyzed for properties like interval content and combinatorial structure, with Forte’s system classifying twelve-tone pitch-class sets up to transposition and inversion through notions such as prime form and normal form.

Applications include music analysis, composition, and computer music; pitch-class representations support algorithmic harmony analysis, chord labeling, and MIDI mapping.