Cluster analysis for the computer-assisted statistical analysis of melodies

Computer usage in musicology seems to be developing somewhat more slowly than in other research areas in the humanities. Many papers in the field limit themselves to discussing musical databases, and elementary types of statistical analyses, involving note or interval counts. With some exceptions (for example, Morando, 1979 and Steinbeck, 1976) there is little mention of the powerful statistical techniques that have become everyday tools in other areas. In this paper we will show that some of these techniques can be adapted with relative ease to the needs of research in musicology. Part of our research used standard software packages which, with some adaptation, proved quite adequate to the task. Our main statistical method is cluster analysis. Cluster analysis attempts to classify a set of entities according to their similarity from the point of view of some predefined set of characters, or "indicators." For example, if the set of entities being considered is a set of melodies, and the set of indicators is the set of notes used in each melody, cluster analysis will group together melodies using similar sets of notes. This method has been used to classify melodies from several points of view. We will limit ourselves to the presentation of examples in which songs are classified by scales (i.e., notes used), intervals, and similarity of melodic patterns. The results are immediately useful to a musicologist attempting to