UC Santa Barbara

This dissertation develops a universal meta-theoretical framework for music that formalizes the conditions under which musical concepts arise. Grounded in Charles Sanders Peirce's triadic theory of signs and realized through a structure theory based on presheaves over the category of sets and relations, the framework provides a unified basis for theorizing musical objects and their interrelations. Drawing on philosophical, mathematical, and compositional insights, the dissertation proceeds in three stages. First, it establishes a semiotic foundation rooted in Peirce’s conception of signs, followed by an investigation of concepts as a special class of signs. Second, it introduces a formal structure theory capable of encoding diverse musical concepts within a generalized categorical setting. Third, it applies this structure theory to construct a ramified theory of musical networks, demonstrating its generative and analytic capacities. Rather than offering a single stylistic or analytical agenda, this metamusical framework provides a conceptual architecture in which multiple theories and practices may coexist, interrelate, and be critically examined. It offers both a philosophical inquiry into the foundations of musical reality and a mathematical formalism for encoding musical structures, with implications for music theory, analysis, composition, and pedagogy.