Pitch-Class Set Orders and Forms

set class

Berg - Wozzeck

transpose level

0

1

2

3

4

5

6

7

8

Forte number: 4-19

cardinal number: 4

interval vector: {1, 0, 1, 3, 1, 0}

original set	{0, 1, 4, 8}
transpose at level 0	{0, 1, 4, 8}
normal form	{0, 1, 4, 8}
prime form	{0, 1, 4, 8}
inversion	{12, 11, 8, 4}

Pitch-class set theory emerged during the 20th century as a manner of analyzing the atonal compositions of various composers. A pitch-class set is a subset of the pitches of the chromatic scale, represented by integers 0 through 11. Important information about each set, including the Forte number (an identifier), cardinal number (number of elements in a set), interval vector (interval content of a set), and matrix are shown, as well as several important orderings and transformations of the set: the transpose, normal form, prime form, and inversion. The definitions of these orderings and transformations are given in the Details section. Many of the set classes in this Demonstration are labeled by citing a musical composition in which they occur.