Modeling Harmonic Similarity for Jazz Using Co-occurrence Vectors and the Membrane Area

In jazz, measuring harmonic similarity is complicated by the common practice of reharmonization -- the altering or substitution of chords without fundamentally changing the piece's harmonic identity. This is analogous to natural language processing tasks where synonymous terms can be used interchangeably without significantly modifying the meaning of a text. Our approach to modeling harmonic similarity borrows from NLP techniques, such as distributional semantics, by embedding chords into a vector space using a co-occurrence matrix. We show that the method can robustly detect harmonic similarity between songs, even when reharmonized. The co-occurrence matrix is computed from a corpus of symbolic jazz-chord progressions, and the result is a map from chords into vectors. A song's harmony can then be represented as a piecewise-linear path constructed from the cumulative sum of its chord vectors. For any two songs, their harmonic similarity can be measured as the minimal surface membrane area between their vector paths. Using a dataset of jazz contrafacts, we show that our approach reduces the median rank of matches from 318 to 18 compared to a baseline approach using pitch class vectors.