set theory

theoryset THEE-uh-reefrom English

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.

Did you know?

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.

Related Terms

pitch class atonal twelve-tone

More in Theory

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accidental

A sharp, flat, or natural sign that alters a note from the prevailing key signature.

accidentals explained

Symbols placed before notes to raise or lower their pitch by a semitone or return them to their natural state

acoustic

Relating to sound or the properties of sound, especially music produced without electronic amplification.

Aeolian mode

The natural minor scale, with the pattern W-H-W-W-H-W-W, producing the most common minor tonality in Western music.

aleatory

Music in which some element of the composition is left to chance or to the performer's discretion.

alto

The second-highest voice type, or an instrument pitched between soprano and tenor.

amplitude

The measure of a sound wave's intensity, perceived as loudness or volume.

anacrusis

One or more notes before the first full bar of a piece, also called a pickup or upbeat.

Keep Exploring

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