IX. Twelve-Tone Music

This section introduces “twelve-tone” music and the related concept of serialism. We will explore the core technical details of rows, transformations, matrices, and more, but also consider this repertoire as real music through analysis and composition.


To make the most of this section, it will be useful to have a working familiarity with Pitch Class Sets. This section (and that chapter) also assume a familiarity with the topics covered in Fundamentals.


The chapters are organized as follows:

  • Basics begins this section with some core definitions and ideas.
  • Naming Conventions then deals in detail with the different conventions for naming rows and transformations (including matrices). This is an important preparation for students preparing to read other writings on twelve-tone music.
  • Row Properties looks at some of the “special” rows that have attracted composers. It’s worth looking at the Twelve-Tone Anthology in combination with this.
  • Analysis Examples – Webern op. 21 and 24 turns to a more thorough kind of analysis, considering two of the early “classics” both in terms of their technical details and in a wider, more contextual sense.
  • Composing with Twelve Tones invites students to “learn by doing.” As we have emphasized elsewhere in the textbook, it’s often helpful to get to know a topic by approaching it in different ways: theoretical, analytical, and practical. Twelve-tone music is no different.
  • History and Context concludes this section by “zooming out” to consider some of the wider context around this music, and the motivations for writing it.


The Anthology part of the textbook includes a dedicated Twelve-Tone Anthology that sets out hundreds of examples of rows used in the repertoire according to their properties and discusses their relative rarity.


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OPEN MUSIC THEORY Copyright © 2023 by Mark Gotham; Kyle Gullings; Chelsey Hamm; Bryn Hughes; Brian Jarvis; Megan Lavengood; and John Peterson is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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