A Similarity Index for Pitch-Class Sets

Abstract

The last twenty-five years have seen the rise of several systems of classification of unordered sets of pcs (henceforth, sets) for both compositional and analytical use in music.2 Most of these systems involve the explicit or implicit notion of the set-class (SC) which breaks up the entire corpus of 4,096 sets into a smaller repertory of set-types, each containing many sets. The criterion of membership in a particular settype or SC is often that all included sets are related to one another by Tn, I, or both. One reason for using such an inclusion rule is that all the sets within a SC will be identical from the point of view of interval-class content since any ic (interval-class) is invariant under Tn and/or I. Presumably, sets that are so related will be aurally as well as logically related somewhat independently of their compositional realization. It is therefore rational to assume that compositions will derive sonic and syntactic unity from the use of sets selected from the same SC.

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