The Enigma of Entropy in Extended Tonality

Abstract

This article considers music that stages the decline of the tonal system through “entropy”—the process conceived in the domain of thermodynamics by which energy is wasted through randomized dispersal or decrease in organization. Tonal organization faced challenges at the turn of the twentieth century, much of the music possessing a sense of tonal drive but with an increased array of outlets for this drive’s tension to be released. This article regards the dominant-seventh complex and its variant configurations as paradigms of this tonal drive and attempts to understand their new ambiguities and the increased richness of possibility they enjoy. In order to achieve this, the study engages in probability theory to create a unique profile for each tonal drive in a given piece, effectively measuring its strength. The fluctuating strengths can be mapped and the process of entropy tracked through a single piece, potentially even across repertoires. Using a new method of visually laying out the patterns of these dominant drives, combined with concepts from information theory that allow us to measure and compare levels of entropy mathematically, I attempt to combine qualitative and quantitative data to model the entropic processes that inhere in early twentieth-century music.