Rethinking Modal Gender in the Context of the Universe of Tn-Types: Definitions and Mathematical Models for Tonicity and Phonicity

Abstract

An indisputable cornerstone of the Western music tradition, the dialectic opposition between the major and minor grammatical modal genders has always been present in the imagination of musicians and music theorists for centuries. Such dialectics of opposition is especially important in the context of nineteenth-century harmonic dualism, with its ideas of tonicity and phonicity. These concepts serve as the main foundation for the way harmonic dualism conceives the major and minor worlds: two worlds with equivalent rights and properties, but with opposed polarities. This paper presents a redefinition of the terms tonicity and phonicity, translating those concepts to the context of post-tonal music theory. The terminologies of generatrix, tonicity, root, phonicity, vertex, and azimuth are explained in this paper, followed by propositions of mathematical models for those concepts, which spring from Richard Parncutt's root-salience model for pitch-class sets. In order to demonstrate the possibilities of using modal gender as a criterion for the study and classification of the universe of Tn-types, we will present a taxonomy of the 351 transpositional set types, which comprises the categories of tonic (major), phonic (minor) and neutral (genderless). In addition, there will be a small discussion on the effect of set symmetries and set asymmetries on the tonic/phonic properties of a Tn-type.