Information dynamics: patterns of expectation and surprise in the perception of music

Measures such as entropy and mutual information can be used to characterise random processes. In this paper, we propose the use of several time-varying information measures, computed in the context of a probabilistic model which evolves as a sample of the process unfolds, as a way to characterise temporal structure in music. One such measure is a novel predictive information rate which we conjecture may provide an explanation for the ‘inverted-U’ relationship often found between simple measures of randomness (e.g. entropy rate) and judgements of aesthetic value (1). 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 such a manifestly simplistic 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.