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 that 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 a conceptually simple explanation for the ‘inverted-U’ relationship often found between simple measures of randomness (e.g. entropy rate) and judgements of aesthetic value [Berlyne, D.E. (1971), Aesthetics and Psychobiology, New York: Appleton Century Crofts.]. 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. Thus, we propose that our approach could form the basis of a theoretically coherent yet computationally plausible model of human perception of formal structure, potentially including seemingly abstract qualities like interestingness and aesthetic goodness.