It has often been observed that one of the more salient effects of listening to music to create expectations within the listener, and that part of the art of making music to create a dynamic interplay of uncertainty, expectation, fulfilment and surprise. It was not until the publication of Shannon's work on information theory, however, that the tools became available to quantify some of these concepts. Since then, there has been sporadic interest in the relationship between information theory and music and aesthetic perception in general.
In this talk, we will examine how a small number of \emph{time-varying} information measures, such as entropies and mutual informations, computed in the context of a dynamically evolving probabilistic model, can be used to characterise the temporal structue of a stimulus sequence, considered as a random process from the point of view of a Bayesian observer.
One such measure is a novel \emph{predictive information rate} which we conjecture may provide an explanation for the `inverted-U' relationship often found between simple measures of randomness (\eg entropy rate) and judgements of aesthetic value (Berlyne 1971). We explore these ideas in the context of Markov chains using both artificially generated sequences and two pieces of minimalist music by Philip Glass, showing that even an overly simple model (the Markov chain), when interpreted according to information dynamic principles, produces a structural analysis which largely agrees with that of an expert human listener.
We will also discuss how the same principles can be applied to models more complex than the fully observed Markov chain (in particular, hidden Markov models), by using online variational Bayesian methods to track the observer's (probabilistic) beliefs about unobserved variables.