Metanumbers as Tones Phase Boundaries, Regime Transitions, and the Harmonic Infrastructure of Metaformal Arithmetic

We develop a metaformal theory of metanumbers as tones, where numerical structure emerges from harmonic organization rather than quantitative magnitude. We show that the harmonic basis of metaformal arithmetic consists of six active whole tones organized cyclically, together with a phase-switch boundary (Do) that separates and connects harmonic cycles. Contrary to naïve counting, the apparent seven-note structure arises from six tones plus one active boundary, not seven independent harmonic units. We demonstrate that Mi–Fa and Si–Do are not chromatic semitone refinements but structural regime transitions, while sharpened tones (e.g., Fa♯, Do♯) encode internal phase tension and fractal dimensional expansion rather than new harmonic units. In particular, we interpret Do♯ as the internal dynamical structure of the harmonic singularity itself, allowing potentially unbounded fractal refinement. This framework resolves the discrepancy between musical scales, vowel systems, and numerical structure, and establishes metanumbers as the harmonic substrate underlying language, arithmetic, and chimera states in metaformalism.