An HMM-Based Approach for Cross-Harmonization of Jazz Standards

This paper presents a methodology for generating cross-harmonizations of jazz standards, i.e., for harmonizing the melody of a jazz standard (Song A) with the harmonic context of another (Song B). Specifically, the melody of Song A, along with the chords that start and end its sections (chord constraints), are used as a basis for generating new harmonizations with chords and chord transitions taken from Song B. This task involves potential incompatibilities between the components drawn from the two songs that take part in the cross-harmonization. In order to tackle such incompatibilities, two methods are introduced that are integrated in the Hidden Markov Model and the Viterbi algorithm. First, a rudimentary approach to chord grouping is presented that allows interchangeable utilization of chords belonging to the same group, depending on melody compatibility. Then, a "supporting" harmonic space of chords and probabilities is employed, which is learned from the entire dataset of the available jazz standards; this space provides local solutions when there are insurmountable conflicts between the melody and constraints of Song A and the harmonic context of Song B. Statistical and expert evaluation allow an analysis of the methodology, providing valuable insight about future steps.