Composing from a Geometric Model: Five-Leaf Rose

When one considers the vast range of possible applications of mathematics to music, composing from a geometric model would appear to be one of the simpler things to do. Certainly the geometry I have used in composing Five-Leaf Rose is conceptually simpler than most applications of set theory or stochastic processes. The purpose of using any such method, of course, is to aid structural integration and unity. What gives this geometric approach useful musical properties is the depth to which it can be applied in a computer-generated composition. The unity is not achieved merely by the idea of a geometric figure, but by having a coordinated pattern of control on many different aspects of the composition. Nearly everything in Five-Leaf Rose, from the formal structure to the acoustic details, is tied to this single model. The one exception, inelody, is freely composed against the background of these highly organized elements. The geometric figure as such may not be discernible to the audience, but the musical relationships derived from the fig-