Scale-Recursive Non-Uniform Domain Tiling in Musical Structure: A Unified Framework for Acoustic Physics, Harmonic Organization, Musical Form, and Rhythm

Abstract We propose that Scale-Recursive Non-Uniform Domain Tiling (SRNUDT), the organizational principle identified in brain architecture (Ploof 2026a) and proposed as a cross-scale unifying framework (Ploof 2026c), is instantiated in musical structure at every level of its organization, from acoustic physics through harmonic syntax to formal architecture. The SRNUDT pattern consisting of sovereign domain tiling with continuous boundaries and a generative remainder, appears at four levels of musical organization: (1) in the overtone series, where vibrating bodies generate spectral territories whose uncontainable remainder constitutes timbre; (2) in functional harmony, where tonal regions generate tension they cannot internally resolve, driving motion to the next organizational level; (3) in musical form, where structural sections generate developmental material that propels the architecture forward; and (4) in rhythm, where metric territories generate remainder that drives temporal motion. We further propose that music's capacity to produce strong emotional responses, including dopaminergic reward, autonomic arousal, and emotionally-laden memory retrieval, derives in part from structural resonance between two SRNUDT systems: the acoustic system generating the music and the neural system processing it. This is not a claim that music is reducible to physics. It is a claim that the organizational principle shared by both systems provides a mechanistic framework for understanding why musical resolution registers as affectively significant. Testable predictions are offered.