Compositional Data Analysis of Harmonic Structures in Popular Music

While analysing large corpora of music, many of the questions that arise involve the proportion of some musical entity relative to one or more similar entities, for example, the relative proportions of tonic, dominant, and subdominant chords. Traditional statistical techniques, however, are fraught with problems when answering such questions. Compositional data analysis is a more suitable approach, based on sounder mathematical (and musicological) ground. This paper introduces some basic techniques of compositional data analysis and uses them to identify and illustrate changes in harmonic usage in American popular music as it evolved from the 1950s through the 1990s, based on the McGill Billboard data set of chord transcriptions.