# The 29 Tetrachords and Other Set Classes

The 29 Tetrachords and Other Set Classes

In the study of 12-tone atonal music, a "set class" is a collection of subsets of the 12 notes (or more formally, pitch-classes) of the chromatic scale. This Demonstration uses a common specific definition of a set class as an equivalence class under the relations of both (musical) transposition and inversion. A well-known fact is that there are exactly 29 tetrachords—set classes consisting of four tones. Mathematically, a set class can be viewed as a 12-bead necklace with beads of exactly two colors. This Demonstration allows you to visualize and listen to all set classes consisting of 3, 4, 5, or 6 notes. You can also find and listen to the inverted set class for each of these classes.