On the Entropy of Music: An Experiment with Bach Chorale Melodies

Abstract

The information content, or "entropy", of a piece of music cannot be determined in the abstract, but depends on the listener's familiarity with, and knowledge of, the genre to which it belongs. This paper describes an experiment designed to investigate human listeners' models of music by having them guess successive notes in a piece. The experiment was administered by a computer program, and in order to elicit subjective probabilities, listeners gambled on the notes they guessed. The study was restricted to the music of the Bach Chorales, and, in particular, on the succession of pitches that comprise the melody--although our methodology is also generally applicable to other musical parameters, and to other genres. A tournament was held, with categories of novice, intermediate, and expert musician. As well as providing an overall measure of entropy for each of two chorale melodies, the results yield entropy profiles for the individual chorales. These give an objective, scientifically repeatable record of the note-by-note information content of the melodies, which can be interpreted musically in terms of expectation, suspense, and resolution in the music.

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