Musical Structure as Coherence Management: The EOS Framework v2.1

This paper proposes the Emergent Order Systems (EOS) framework as a physics-grounded analytical lens for understanding musical structure across diverse forms and traditions. By treating music as a system of structured oscillation governed by coherence maintenance, EOS provides unified descriptive vocabulary capable of spanning tonal, rhythmic, and texture-based practices. Core Contribution: EOS identifies coherence as the invariant structural principle underlying diverse musical systems, operating across three primary signal dimensions: Pitch-frequency alignment (harmonic coherence) Temporal-phase alignment (metrical coherence) Spectral-density organization (timbral coherence) The framework is positioned as complementary to existing music theory rather than prescriptive, synthesizing insights from classical acoustics (Helmholtz), information theory (Meyer, Huron), hierarchical models (Lerdahl & Jackendoff), spectral analysis (Smalley), and complexity science. Analytical Applications: Applied analysis demonstrates how EOS accounts for structural stability in contemporary and nontraditional musical forms—including ambient, electroacoustic, and texture-oriented music—that resist conventional analytical approaches. The framework reveals these works not as structurally deficient, but as coherence-carrying through spectral and temporal dimensions rather than pitch hierarchy. Scope and Methodology: EOS is presented as interpretive and non-normative: it does not prescribe compositional methods, evaluate aesthetic quality, or propose generative models. Instead, it provides signal-level descriptive language for cross-genre analysis, enabling comparison between musical systems that conventional theory often treats as incompatible. Target Audience: Music theorists, composers, sound studies researchers, acousticians, and interdisciplinary scholars interested in physics-based approaches to musical structure. Version 2.0 Update (December 2025) This version extends the theoretical framework established in v1.0 with applied analytical demonstrations. Section 8 introduces the EOS Analysis Template and stress-tests it through comparative case studies (J.S. Bach, Brian Eno, Miles Davis), demonstrating framework portability across classical, ambient, and jazz repertoires. Appendix A provides a structured worksheet for independent analysis. Five new references added (Berliner; two Eno entries; Fux; Smalley). Version 1.0 remains accessible through Zenodo's version history. Version 2.1 Update (July 2026) Adds a completed worked example (Appendix A.1) applying the analysis template to Miles Davis's "So What," so the worksheet demonstrates its own use. Includes minor editorial clarifications: "Elastic Limit" is identified as a qualitative comparative descriptor rather than a quantified metric, and the framing citations (Fux, Smalley, Berliner) are reframed as triangulation across analytical vocabularies. No changes to theoretical claims or scope.