PREDICTION AND ENTROPY OF MUSIC
Date
1990-04-01
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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.
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Computer Science