Fuzzy Relational Music Perception: Resemblance and Implication in the Individuation and Assembly of Concepts

Abstract

Fuzzy relational music perception concerns the representation of congruent connections between musical features as fuzzy relations used to individuate and assemble concepts and conceptual hierarchies. This article presents two universal fuzzy domains of discourse, harmony H and grouping G, which partition sets using triangular norms (t-norms) based on generalised harmonic root support and generalised time regularity, respectively. Fuzzy relations between the sets of the domains are formed in the innate fuzzy neural architecture of a dedicated music faculty. Fuzzy relations are shown to be necessary representations for interconnection between the domains to individuate and assemble concepts. Concepts are individuated and assembled by virtue of fuzzy set resemblance relations between domains, or fuzzy logical implication relations in one or both domains through time. Fuzzy resemblance relations comprise the properties of weak reflexivity, weak symmetry and antitransitivity in a H ⨉ G Cartesian product space. Fuzzy implication relations involve fuzzy overlap (or continuation) of elements, calculated using a t-norm operator (min operator), in one or both domains of the product space. Supplementary theory is incorporated to explain polyphonic structure, involving pluralistic superimposition of independent fuzzy relational hierarchies. Broadly, fuzzy relational music perception is a rationalistic model that builds on generative theories and associative–statistical and connectionist approaches by providing a compact and coherent process for determining interaction across musical parameters.