Prediction of dissimilarity judgments between tonal sequences using information theory

Abstract

Several studies have investigated the entropy characteristics of musical notations (in the information-theoretic sense). What appears to be lacking is an empirical study of the connection between entropy and musical perception. This paper describes results of an experiment designed to determine the relevance of entropy to subjects' dissimilarity judgments on pairs of melodic sequences. The hypothesis was that dissimilarity judgments by subjects on pairs of unfamiliar tonal sequences drawn from a common pitch set are largely a function of average sequence entropy and average sequential interval size, when the sequences are uniform in all respects except for the ordering of pitches. Five stationary ergodic Markov-1 chains of increasing entropy were defined on a common pitch set. From each chain, two sequences of identical entropy were generated: the first sampled directly from the chain, and the second by applying to each sequence element of the first a random permutation of the pitch set. In this fashion, entropy and average interval size variables could be varied quasi-independently. Timbre, duration, and loudness were held constant. Subjects heard all possible unordered pairs of synthesizer-generated sequences through headphones, and indicated a subjective dissimilarity rating for each pair. Two forms of analysis yielded different results. Subject dissimilarity judgments between sequences were shown to be well correlated with a Euclidean distance function on average interval size and entropy. However, multidimensional scaling analysis revealed only average interval size to be a salient judgment factor, not entropy.