Pitch class

Why am I learning this?
You have already been using the concept without realizing it, because you have treated notes an octave apart as somehow the same. It is useful to make the concept explicit for studying twentieth- and twenty-first century music, because there are many relations that cannot be easily understood or expressed just with the basic tools of letter names and staff notation. Very shortly, pitch classes will seem equally basic.

A pitch class is the set of all pitches that can have the same name, for example, all the Cs. In themselves, pitch classes do not favor one enharmonic spelling or another, although they can take on particular spellings in various scalar or chordal contexts. In fact, pitch classes are often called by number, starting with C=0. To avoid confusion with other sets of numbers, this wiki uses letter names. Musicians often imagine pitch classes as locations in a space. Pitch classes are used in groups called sets or collections.


In ancient and early modern times, Western musicians mostly dealt just with pitches. There was a particular set of available pitches (or rather pitch names—there was no standard like A440), and everything above and below was disregarded. With the emergence of tonal music, people regularly used letter names, solfège syllables, and scale-degree numbers without regard to register, but they had no way to refer to pitch classes except in these terms. Finally, in the 1950s Milton Babbitt distinguished between specific pitches and pitch classes. In the 1970s and beyond, Allen Forte and others developed pitch-class set theory.

Pitch-class space

It is helpful to imagine pitches and pitch classes as locations in different kinds of space. While pitch space is a line, similar to a keyboard, pitch-class space is a circle, visualized with a diagram called the clock face, with a point for each pitch class, starting with C at 12:00 and going clockwise:

The clock face is like the circle of fifths, except it goes by semitone instead of perfect fifth.

Pitch-class set (pitch-class collection)

Main article: Pitch-class set (pitch-class collection)
A pitch-class set or pitch-class collection is a group of pitch classes. Pitch-class sets can be used as chords, scales, and motives. For example, G7 is a pitch-class set, G–B–D–F, and so is the C-major scale, except C in this context has two locations in pitch space (the beginning and end of the scale) and one in pitch-class space. While set and collection are synonymous, the term collection usually refers to a set used as a scale. The term scale is often used (loosely) to refer to its pitch-class set.

Example: Richard McQuillan, Le tombeau de Pierre Boulez (2013): The composition is based on the pitch-class sets Bb–A–C–H (a cipher of “Bach”) and Bb–A–C–Eb (a cipher of “Boulez”).

Further reading:

  • Stephen Kostka, Materials and Techniques of Post-Tonal Music, Chapter 9
  • Miguel Roig-Francolí, Understanding Post-Tonal Music, Chapter 1
  • Joseph Straus, Introduction to Post-Tonal Theory, Chapter 1

External links

The Wikipedia article on pitch class is informative but very dense.



Twentieth- and Twenty-First-Century Music Copyright © by Matthew Arndt. All Rights Reserved.

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