MODELING HARMONIC SIMILARITY USING A GENERATIVE GRAMMAR OF TONAL HARMONY
Wolfgang Haas, Martin Rohrmeier, Remco C. Veltkamp, Frans Wiering · 2009
In this paper we investigate a new approach to the similarity of tonal harmony. We create a fully functional remodeling of an earlier version of Rohrmeier’s grammar of harmony. With this grammar an automatic harmonic analysis of a sequence of symbolic chord labels is obtained in the form of a parse tree. The harmonic similarity is determined by finding and examining the largest labeled common embeddable subtree (LLCES) of two parse trees. For the calculation of the LLCES a new O(min(n, m)nm) time algorithm is presented, where n and m are the sizes of the trees. For the analysis of the LLCES we propose six distance measures that exploit several structural characteristics of the Combined LLCES. We demonstrate in a retrieval experiment that at least one of these new methods significantly outperforms a baseline string matching approach and thereby show that using additional musical knowledge from music cognitive and music theoretic models actually helps improving retrieval performance. 1.