The Representation of Music

Abstract

Theories, whether in mathematics or in music, presuppose a world of objects that we can be theorize upon. In mathematics the notion of objects is quite clear, from obvious number domains to high dimensional manifolds. Musical objects, if we may call them thus, are much more elusive. Identifying the musical objects would be nothing less than determining what music ultimately is. So far, no one really knows what happens in the brain when listening to music, what symbolic structures are generated and and how they are processed. The psychology of music does make some inroads, but without effective results useful to the theorizing we have in mind. We are left with the only possibility of grasping musical objects, namely proposing more or less formal schemes for the representation of music, preferably in a mathematical context.