Searching for better measures: Generating similarity functions for abstract musical objects

Several similarity and distance measures have been developed for different purposes and applications in various research fields. For example, scholars have used them to evaluate similarities between tonalities, melodies and rhythms for music information retrieval. In this study, similarity functions are generated automatically. We focus on similarities between the so-called pitch-class sets that belong to the field of pitch-class set theory. Pitch-class set theory offers a well-defined mathematical framework for categorising musical objects and describing their relationships. An output, consisting of similarity values between the abstract pitch-class sets, is produced by means of a generated function. We then compare these values with empirical results by means of statistical methods. We also compare the performance of a generated function with that of REL (David Lewin 1980), perhaps the most successful similarity function in the field. The achieved results are encouraging: some of the generated functions are able to produce stronger correlations with empirical data than REL. As a satisfying by-product, the results hint at the fact that there may be a connection between the perceived closeness of pitch-class sets and Shepard´s universal cognitive models. While the present application context is musical set theory, we stress that similar procedures can be applied to other areas of research as well.