Musical Structure as Coherence Management: The EOS Framework v2.2

Abstract

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. Version 2.2 Update (August 2026) Adds Section 8.4, a fourth case study extending the template to works whose coherence regime transforms mid-performance rather than remaining fixed. The case examines the individual-voice ("free release") aleatoric ending technique, grounded in Knut Nystedt's Immortal Bach, Op. 153 (1988), in which a choir dissolves from synchronized unison into individually-paced voices while sustaining shared melodic and harmonic material. The analysis demonstrates that coherence channels can be reallocated in real time (a "channel handoff"), that attractor topology can deform continuously between point-like and plateau states within a single performance, and that drift tolerance can be stratified across individual and aggregate levels. One new reference added (Nystedt); Bach's Komm, süßer Tod (BWV 478) is also newly cited as the work's source material. The section includes a brief first-person illustration of the author's experience performing a related individual-voice technique at a district choral festival; this account is explicitly non-evidentiary and does not ground the analytical claims, which rest on the documented Nystedt score. No changes to theoretical claims or scope established in prior versions.