set theory
A method of analysing atonal music by treating pitches as members of mathematical sets
In Depth
Pitch-class set theory, developed primarily by Allen Forte and Milton Babbitt, provides tools for analysing music that lacks traditional tonal function. Pitches are represented as integers 0–11, and groups of pitches form sets that can be transposed, inverted, and compared. Each set has a prime form and an interval-class vector that describes its sonic fingerprint. The system reveals structural relationships in atonal music by Schoenberg, Webern, Berg, and their successors that are invisible to traditional harmonic analysis.
Allen Forte catalogued all possible pitch-class sets in his 1973 book, assigning each a label that is still used universally — like a periodic table for atonal harmony.