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:

1 Basic Definitions. 1

1.1 Pitches.1

1.2 Pitch Classes. 2

1.3 Pitch Class Sets. 2

2 Simple Operations on Pitch Classes and Pitch Class Sets. 2

2.1 “Clock” Math or Modulo Math. 2

2.2 Transposing Pitch Class Sets. 3

2.3 Inverting Pitch Class Sets. 3

3 The Prime Form.. 4

3.2 Uses for The Prime Form.. 4

3.3 Determining the Prime Form: The Rigorous Method. 4