Basics of Twelve-Tone Theory

Twelve-tone music is organized around a tone row (also called a series): a specific ordering of all twelve pitch classes in which each appears exactly once. The row is not a melody to be repeated note-for-note but a pitch-class sequence that governs the order in which pitch classes may appear throughout a piece. By exhausting all twelve pitch classes before any recurs, twelve-tone technique avoids privileging any single pitch class as a tonic.

The row's identity lies in the ordering of its intervals, not in its register or rhythm. Any pitch class in the row may appear in any octave, and the durations assigned to the pitches are independent of the row structure. In practice, composers often present the row as a clearly audible melodic line, but it can also be distributed across several instruments, stated simultaneously as chords (a technique called verticalizing the row), or broken into smaller sub-groups called row segments or hexachords.

The two halves of the row — each containing six pitch classes — are called hexachords (hexachord 1 and hexachord 2). Within any single row these two hexachords are always complementary, since together they exhaust all twelve pitch classes; the analytically interesting question is how a hexachord relates to the hexachords of the row's transformations. When a hexachord of one row form combines with a hexachord of a transposed or inverted form to complete a full twelve-pitch-class aggregate, the row is said to be combinatorial — a property composers like Schoenberg and Webern prized for building chords and counterpoint. Understanding the internal structure of the row is essential to understanding how a twelve-tone piece is composed.