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20th Century Music Theory

Pitch Class Sets

Pitch Class Sets are a method for describing harmonies in 20th century music. These notations and methods can describe and manipulate any type of chord that can be created within a 12-tone (equally tempered) scale. It is an extremely useful technique for composers to help understand and control the harmonies which make up their music.

Pitch class sets are the chemistry of harmonic color. Modern composers will use pitch class sets like chemistry, to mix and create interesting and vibrantly colorful harmonic sounds, which they then use to create works of music.

The following tutorials provide definitions, theory, algorithms and examples on how to understand, use, and manipulate Pitch Class Sets.

A tutorial on Pitch Class Sets - HTML
A tutorial on Pitch Class Sets - PDF

The following links provide a table of all PC Set prime forms, which is essentially a table of all possible chord types that can be constructed within a 12-tone equal tempered scale. Note that these tables include the Prime Forms as well as the Inverted Forms.

The Prime Forms Table - HTML
The Prime Forms Table - PDF

Recommended Books

If you are new to modern music composition, the following textbooks should be very helpful. Note: All of these textbooks assume that you have a solid foundation in music fundamentals (i.e. music notation, intervals, chords, rhythms, etc.).
  • Introduction to Post-Tonal Theory (2nd Edition) by Joseph N. Straus - A complete an thorough text which goes from the very basics (e.g. What is a "Pitch Class") to advanced 12 tone composition (e.g. "Schoenberg and hexachordal combinatoriality"). Note that this book is exclusively a 20th century harmony book, and does not cover any of the other, very important, 20th century techniques such as aleatory, electronics, sound textures, etc.
  • Materials and Techniques of Twentieth-Century Music (2nd Edition) by Stefan Kostka - A broad overview of 20th century music including a wide range of techniques from exotic scales to electronic music concrete in clear, straightforward language. Note that this book covers a lot of ground, and so you will likely need to engage in further study / experimentation / listening before you feel comfortable composing in a new style.
The following books are all very highly regarded as seminal texts in the field of 20th Century Music Theory. However, these texts are also much more difficult to read and understand.