Evaluating tonal distances between pitch-class sets and predicting their tonal centres by computational models

Abstract

The pitch-class set belongs to the core concepts within musical set theory. The mathematical properties of pitch-class sets (in terms of interval-class content, evenness, etc.) as well as their mutual relations to other sets have been widely studied. In this paper, we concentrate on investigating them as carriers of tonal implications. Results provided by four algorithmic models, which propose hypothetical tonal centres for pitch-class sets, are compared. In addition to finding reference pitch class(es) for each set class of cardinality 3-9, the models are used for evaluating tonal distances between pitch-class sets. They are applied as 'similarity measures' in conjunction with an automated, computer-aided analysis method called comparison set analysis. © 2009 Springer Berlin Heidelberg.