Musical Probability and the Music of Claude Debussy

This article explores the relationship between musical expectancy and information through the use of both hidden Markov models, Bayesian probability and their application to Claude Debussy’s Prélude (…Bruyères) and his string quartet. (…Bruyères), which is one of the most conservative of the Préludes, is an interesting example of the composer’s use of “vagrant” sonorities which persist despite a perceived tonal hierarchy. An analysis of the varying levels of information, determined by the levels of expectancy which arise throughout the composition, illustrates an aspect of analysis which has not yet been applied to Debussy’s music. A study of musical information will inevitably lead to the study of probabilty, as a greater degree of information is expressed by events which could be considered to be less probable. Much of the research that has been done thus far in musical probability has used as a priori a collection of stylistic precepts, which are referred to as likely events. This article, however, attempts to determine probabilistic events based on “intra-opus” events by using David Temperley’s Bayesian approach to determine likely events within a composition. These are classified as events within a hidden Markov model, which examines the interrelationships of variables, some of which are perceived and some which are simply implied. A statistical “extra-opus” methodology is employed and compared to the Bayesian style. In the seond part of the article, melodic probability in a polyphonic context is discussed by examining the several sections from Debussy’s string quartet. The probabalistic fluctuations between voices in the quartet are then compared to the single melody of (…Bruyères).