Statistical Parsing and Interpretation for Jazz Chord Sequences

The paper describes work with Mark Granroth-Wilding on the problem of parsing and interpreting chord sequences using a grammar of tonal harmony. The grammar is drawn from the same "nearly context-free" class that is strongly adequate for natural languages, and supports a model theory of harmony. Though the grammar is much smaller than language grammars, the degree of ambiguity is much greater, in the sense that any chord can have an unboundedly large number of increasingly preposterous interpretations. Parsing requires the use of a supervised statistical model to limit search, of the same kind that is required for parsing natural language at scale. We evaluate its performance on held-out data against a baseline Markov model, which it outperforms, showing that the grammar is doing useful cognitive work.