ComposerTools.com / Theory / Pitch Class Sets / 6.  Subsets and Supersets

6         Subsets and Supersets

Any of the larger PC Sets can be divided into pieces. These pieces are, of course, also PC Sets in their own right. The smaller PC Sets are said to be "subsets" of the larger PC Set, which is the "superset".

Subsets 1:  =>  [0,2,7] + [1,6,8]           = two quintal/quartal triads

Subsets 2:  =>  [1,8] + [0,2,6,7]           = a simple fifth + a complex chord (a dominant+tonic sound)

Subsets 3:  =>  [1,7] + [0, 2, 6, 8]        = a tritone + whole-tone-scale fragment

Subsets 4:  => [6,7,8] + [0,1,2]            = two chromatic clusters

Subsets 5:  =>  [0,6] + [1,7] + [2,8]     = three tritone intervals

PC subsets and supersets are a very useful compositional technique. Be sure to explore all of the subsets for PC Sets that you use (see ComposerTools.com). This will help you to use, space, and manipulate your harmonies.

6.1          Definition:  Transpositional Combination of Two Common Subsets

6.2          Definition:  Inversional Combination of Two Common Subsets

Copyright 2004 by Paul Nelson, all rights reserved.