ComposerTools.com / Theory / Pitch Class Sets

Paul Nelson - Revised: 5/16/2004

Pitch Class Sets are a method for
describing harmonies in 20^{th} 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.

Table of Contents:

2 Simple Operations on Pitch Classes and Pitch Class Sets

2.1 "Clock" Math or Modulo Math

2.2 Transposing Pitch Class Sets

2.3 Inverting Pitch Class Sets

3.1 Similar Pitch Class Sets: Set Classes & Prime Forms

3.3 Determining the Prime Form: The Rigorous Method

3.4 Determining the Prime Form: Easier Methods

5 The Table of All Prime Forms - Description

5.1 The Columns of Data in the Table

5.2 The Layout of the PC Sets in the Table

5.5 Other Comments on the Table

6.1 Definition: Transpositional Combination of Two Common Subsets

6.2 Definition: Inversional Combination of Two Common Subsets

7.2 PC Set Complements and Their Interval Vectors

7.4 PC Set Complements Used in Twelve Tone Composition

8 More Properties of Pitch Class Sets and Interval Vectors

8.1 Common Tones when Transposed

8.1.1 More Examples and Transpositional Symmetry

9 Other PC Set Similarity Relations

9.1
Special Purpose Relations: R_{p}, R_{0}, R_{1}, R_{2}

9.2 Other techniques for generating related PC Sets

Copyright © 2004 by Paul Nelson, all rights reserved.