PREDICTION AND ENTROPY OF MUSIC

Abstract

This thesis develops and evaluates predictive theories of music. Good theories should model a particular class of music and predict new pieces in the class with high probability. Attention is restricted to melody alone--harmony and polyphony are not considered. Theories are constructed using an empirical learning approach, and to construct and evaluate them, one hundred Bach chorale melodies are analyzed. Theories are evaluated by a data compression measure, which is a strong indicator of their predictive power. The entropy of the chorales is estimated by averaging the amount of compression given to a test set using a theory learned from a training set. The central hypothesis is that the chorales are quite redundant in the information theoretic sense. A novel approach to the induction of sequence generating rules, called multiple viewpoints, is created. This method is based on the variable-order Markov model, with extensions to incorporate timescales and parallel streams of description. A multiple viewpoint system comprises two parts: a long-term theory which adapts to a class of sequences, and a short-term theory which adapts to a particular instance of the class. Predictions from both are combined into an overall prediction. The performance of several different multiple viewpoint systems is assessed on the chorale data. The redundancy of the chorales is thereby estimated to be 55%. This thesis concludes that the estimate must be compared with human performance at the same predictive task. The theory should also be evaluated in terms of the quality of the new chorales it generates, and by its ability to discriminate chorales from non-chorales.