Melodic Cue Abstraction, Similarity, and Category Formation: A Formal Model

Abstract

In the first part of this article, the notions of identity, similarity, categorization, and feature salience are explored; musical examples are provided at various stages of the discussion. Then, formal working definitions are proposed that inextricably bind these concepts together. These definitions readily lend themselves to the development of a formal model for clustering - the Unscramble algorithm - which, given a set of objects and an initial set of properties, generates a range of plausible categorizations for a given context. Finally, as a test case, the clustering algorithm is used to organize a number of melodic segments, taken from a monophonic piece by J. S. Bach, into motivic categories; the algorithm also determines a prototype for each cluster and uses these prototypical descriptions for membership prediction tasks. The results of the computational system are compared with the empirical results obtained for the same data in two earlier studies (I. Delièège, 1996, 1997).