The inequality factor: skewness and kurtosis as a measure of set-class cohesion

Abstract

Building on current set-theoretic research, including similarity measures and ‘maximal evenness’, as well as findings in diatonic set theory and our own work on salience, we examine the interval-class content of set classes based on internal consistency (related to ‘cohesion’ and ‘regularity’) and inconsistency (‘skewness’). By systematically comparing one member tone of a set to the others, we posit abstract hierarchies between members based on salience, rather than the presence of specific interval classes or tonal function. Quantifying these factors allows us to hypothesize (1) what gives certain set classes the potential to function in a tonal way; (2) a ‘set-class-sensitive’ method to gauge the level of ‘dissonance’ in a composition (without presuppositions about the quality of specific interval classes); and (3) how different set classes might be deployed compositionally in order to achieve a variety of results.