Pitch-Class Set Calculator — after Forte (1973)

I · The Clock-Face

II · Transformations

T_n · transpose 0

III · Audition

IV · Examples

V · Set-Theoretic Readout

unordered { }

normal [ ]

prime ( )

forte № —

interval vec. <0,0,0,0,0,0>

cardinality 0

complement —

No set yet. Click a pitch on the clock, press a number key 0–9 / Q / W, or pick an example.

VI · Interval-Class Vector

On this calculator

The pitch-class set, as Allen Forte codified it in The Structure of Atonal Music (Yale, 1973), is an unordered collection of mod-12 integers — a way of describing harmonic content in Schoenberg, Webern, Varèse and elsewhere, where tonal labels falter. Two sets share a set class if one is the T_n or T_nI transform of the other; the canonical representative is the prime form.

This calculator follows Rahn's variant (John Rahn, Basic Atonal Theory, 1980): most-packed-to-the-left, walking each interval inward. Forte's original 1973 packing rule produces a slightly different prime in a few cases (e.g. 5-20, 6-Z29). The Forte-number table embedded here is the standard catalogue, all 223 set classes.

Two cautions. Dmitri Tymoczko (A Geometry of Music, 2011) argues pc-set equivalence classes flatten the voice-leading and context that make atonal music musical — a chord becomes a label rather than an event. Philip Ewell (2020) places the discipline within a wider critique of theory's canon, of which Forte is a central figure. Both arguments are worth holding alongside this tool.

A Calculator for the Pitch-Class Set

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