Pitch and Pitch Class

In post-tonal theory, a pitch is a specific note at a specific register — middle C and the C an octave higher are two different pitches. A pitch class (pc), by contrast, groups together all pitches that share the same note name regardless of octave: every C in every register belongs to pitch class C. This abstraction lets analysts compare and relate pitches without committing to a particular register.

Pitch classes are represented by integers 0 through 11, with C assigned the integer 0 and every subsequent semitone incrementing by one: C=0, C♯/D♭=1, D=2, D♯/E♭=3, E=4, F=5, F♯/G♭=6, G=7, G♯/A♭=8, A=9, A♯/B♭=10, B=11. Arithmetic on pitch classes is performed modulo 12, so 11+1=0 (B up a semitone returns to C) and 0−1=11 (C down a semitone is B).

This integer system makes transposition and inversion straightforward algebraic operations. Transposing a pitch class up by n semitones is written T_n and computed as (pc + n) mod 12. Inverting a pitch class around 0 is written I and computed as (−pc) mod 12, or equivalently (12 − pc) mod 12. These operations underlie the entire analytical toolkit of post-tonal theory.