A cluster analysis of pop/rock harmony

Back when I taught music theory at CU–Boulder (2013–16), I taught a course in computational music analysis twice. It was my favorite class. Maymester — three weeks spending all morning, five days a week, with a group of undergraduate and graduate students majoring in music, computer science, or both, reading and discussing articles outside in the Colorado sun, near the feet of the Flatirons, or working in a dingy basement computer lab, munging data and hammering out algorithms. The first time I taught the course, we started a project parsing and analyzing the chord progressions in over 700 pop/rock songs in the McGill Billboard Dataset. The second time I taught the course, we picked up where the first class left off and finished the project.

After I taught it the second time, we moved to Virginia. While I was there starting my two-year stint at the University of Mary Washington, eight of my CU students and I — some from each of my computational analysis classes — collaborated long-distance on an article explaining the methods and findings of our project.

I am happy to announce that that article, "A cluster analysis of harmony in the McGill Billboard dataset", has been published in Empirical Musicology Review.

I'm incredibly proud of my students and what they were able to accomplish. Two groups of about a dozen people each, in three weeks of work (and a little follow-up writing), produced a top-notch piece of music scholarship that will advance the fields of both computational musicology and popular music theory. With some help from their professor, of course. ;) Even though it's being published four years after the project completed, and six years after we started, it still represents a novel approach to how we understand harmony, genre, and style in popular music, and indeed in music in general.

Since it will still be some time before the article hits the open web, I thought I'd at least tease the abstract. Here goes!

We set out to perform a cluster analysis of harmonic structures (specifically, chord-to-chord transitions) in the McGill Billboard dataset, to determine whether there is evidence of multiple harmonic grammars and practices in the corpus, and if so, what the optimal division of songs, according to those harmonic grammars, is. We define optimal as providing meaningful, specific information about the harmonic practices of songs in the cluster, but being general enough to be used as a guide to songwriting and predictive listening. We test two hypotheses in our cluster analysis — first that 5–9 clusters would be optimal, based on the work of Walter Everett (2004), and second that 15 clusters would be optimal, based on a set of user-generated genre tags reported by Hendrik Schreiber (2015).

We subjected the harmonic structures for each song in the corpus to a K-means cluster analysis. We conclude that the optimal clustering solution is likely to be within the 5–8 cluster range. We also propose that a map of cluster types emerging as the number of clusters increases from one to eight constitutes a greater aid to our understanding of how various harmonic practices, styles, and sub-styles comprise the McGill Billboard dataset.

Authors: Kris Shaffer, Esther Vasiete, Brandon Jacquez, Aaron Davis, Diego Escalante, Calvin Hicks, Joshua McCann, Camille Noufi, and Paul Salminen.

We would like to acknowledge the contributions of Erik Kierstead, Andrew Mahan, Christopher Rooney, and J.R. Souders, as well as several other students who wished their contributions to remain anonymous. Their work on this project was indispensable.