Pitch-Class Set Genera: My Theory, Forte's Theory

Abstract

Theories of pitch-class set genera proceed from the general premise that within the larger universe of 208 pitch-class set-classes that fill the range of from three to nine elements, smaller sub-groups may be identified that is, genera whose members evince a markedly higher degree of structural relatedness than is the case for the universe as a whole. Moreover, these genera are also distinguishable one from another by marked differences in their structural attributes. Allen Forte set forth such a theory in his excellent monograph-article, 'Pitch-Class Set Genera and the Origin of Modern Harmonic Species' (Forte 1988)2 in which he identified twelve genera by means of inclusion relations focused about trichords. In Forte's theory, the genera serve as models of inclusion desiderata, to each of which the pitch constructs of a given musical object may be compared for 'good fit'. Soon after Forte, I published an implicit theory of pc set genera in The Music of Claude Debussy (Parks 1989), an extended analytical study in which I identified five genera by means of inclusion relations converging upon various scales and otherwise distinctive pitch constructs. The differences between my theory and Forte's are considerable in formulation, in the analytical procedures they require, and in the analytical harvests they engenderyet they share some important points of contact. As a set of definitions, Forte's theory could be understood to constitute a 'special case' within the terms of my more general theory. However, in terms of the qualifying premises by which each of us limits the number of useful genera within the larger universe of possible genera, our theories are very different. In this article I enumerate eight deElnitions for a theory of pitch-set genera encompassing my genera as well as Forte's. Comparing my genera with his, I will show how the balance between ensuring a 'good fit' of genus-model to musical passage, on the one hand, and limiting the range of possible genera to a manageable number, on the other, tips one way for my theory and the other way for his. Next, I will summarise my additional limiting premises and compare them with Forte's; and finally, I will provide a brief analytical demonstration that models a few musical passages by means of the genera I have described.