Recrel : A Similarity Measure for Set-Classes

Abstract

n the field of pitch-class set theory, a number of different similarity relations have been developed with the purpose of identifying aspects of similarity between pcsets and set-classes. Out of these, the present study concentrates on similarity relations which compare interval-class or subset-class vectors. The focus is especially on simi­larity measures, i.e. similarity relations assigning a degree of similarity for two set­classes. Such a degree is given as a numeric value on some known scale of values. Three main categories of similarity relations are identified. First, similarity re- . lations not returning numeric values. Second, similarity measures comparing only two interval-class or subset-class vectors at a time. Third, total measures comparing all subset-class vectors belonging to two set-classes. This ordering of the categories is considered to reflect increasing 'descriptive powers. A set of relevance criteria which each similarity relation should fulfil is determined. 21 similarity relations pre­sented previously in the pitch-class set-theoretical literature are then evaluated with these criteria. Other means of demonstrating the strengths and weaknesses of indi­vidual similarity relations are also used. The RECREL similarity measure, belonging to the total measure category, is introduced and evaluated with the set of criteria. The values it produces are exam­ined from different viewpoints. Also, it is used to analyse aspects of Arnold Schönberg's Op. 11, No. 1. A demonstrational computer program constitutes a part of the study. With it the user can examine the various stages of a RECREL comparison, as well as ma­nipulate RECREL values in a number of different ways.