The formal structure of tonal theory

• Main Author: Horton, Timothy James
• Published: University of Cambridge 2004
• Subjects: 780
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604242

This thesis is concerned with the form of our mental representations of tonal pitch structure. It examines some of the considerations that are relevant to determining the form of such representations and, drawing upon some ideas from formal language theory, it outlines an elementary theory based upon these considerations. It is suggested that the goal of cognitivist tonal theory must be to account for the productivity and systematicity of our total cognition, a claim that has important ramifications for the architecture of the representational system involved. In particular, it requires that we describe tonal structure in terms of a finite set of primitives and a finite set of principles for combining them into larger structures, that is, in a way that explicitly recognises their combinatorial organisation. It also requires that we acknowledge the compositionality of tonal structures, namely, the way in which the nature of complex constructions is determined by the nature of their constituent parts and the syntactic principles by which these are combined. Following an examination of the plausible candidates, it is proposed that harmonic functions constitute the primitive vocabulary of the syntactic structure of tonal music. This involves a detailed investigation of the nature of harmonic function and a reformation of the concept in cognitivist terms. This reformulations, in turn, permits a study of how harmonic function interacts with the hierarchical organisation of tonal structure, where it is demonstrated that harmonic function has the potential to form the basis of dependency relations in tonal music. The range of possible functional categories is also considered, and some suggestions made as to how the traditional system of three functions might plausibly be extended. The types of structural relation that underlie the hierarchical organisation of tonal music are also a major focus of this thesis. The syntactic relations of constituency and dependency are discussed, and their manifestation in tonal music is examined in detail. Here it is argued that our mental representations of tonal structure must explicitly encode constituency, and thus a descriptively adequate form of tonal theory must be a combinatorial syntax.