The flow of harmony as a dynamical system

When analysing the evolution of harmony within a composition, one can distinguish between two parts: on the one hand a dynamical system and on the other hand the composer. The dynamical system summarises the rules of harmony, whereas the composer intervenes at certain points, e.g. by choosing new initial values. This viewpoint is helpful for the musical analysis of a composition and will be exemplified by analysing the first movement of Beethoven's first symphony. Note that some difficulties occur when considering a discrete phase space with a metric in the definitions of stability. However, we will not go into further detail since we are only interested in the general concept.