THE SPHERICAL TONNETZ: A Coherence-Field Interpretation of Electromagnetic Structure Using Minimal Prime Geometry (2–3–5)

This paper presents a geometric reinterpretation of harmonic structure traditionally represented by Euler’s Tonnetz, reframed as a spherical electromagnetic coherence field. By restricting the system to the minimal prime set {2, 3, 5}, corresponding to enclosure, rotational symmetry, and internal modulation, the Tonnetz resolves naturally into a nested spherical topology. In this framework, harmonic relationships correspond to electromagnetic field geometry, resonance governs behavior, and phase-locked activation replaces linear propagation. Musical systems are treated as early perceptual mappings of this structure rather than its origin, revealing a shared geometric foundation underlying electromagnetic, photonic, and plasma-based systems.