Clarinet Trio

Abstract

The Clarinet Trio (2012) is a special case, because here everything in the music is a reflection of one of seven drawings, and everything in the seven drawings corresponds to something in the music. At the same time, both the drawings and the music are derived rigorously from a (12,3,2) design: 12 notes in the scale, 3 notes in each chord, each pair of notes appearing together twice. In order to construct a system like that one must find 44 chords, or blocks, and one can do this in a number of ways. In fact, the Handbook of Combinatorial Designs [1] informs us that P. R. J. Ostergard has counted exactly 242,995,846 completely different ways to do this. If you don’t believe me, or if you want to know how this was calculated (and if you are not a specialist, you probably don’t), you can consult his article in the Australasian Journal of Combinatorics, No. 22 (2000) [5].