Harmonic Frequency Scaling

Harmonic Frequency Scaling is the law of Part 7.1 that harmonic frequencies grow with the square of the harmonic index, H_n = ν₀ × P(n) = ν₀ × (n + 1)², from the fundamental ν₀ = 1/①⥂⧗⌂. It is the harmonic model's postulate: the pulse density P(n) = (n + 1)² grows quadratically with recursion depth, motivated by the Computational Load Accumulation L(n) = L₀ + n(n + 1)/2 ≈ P(n)/2, and the frequencies inherit the same scaling, so overtones do not follow the linear spacing of classical harmonic systems. The BPT Energy Quantization E_n = ħω⥂ × (n + 1)² and the Effective Light Speed 𝒞→⊹,n = 𝒞→₀/(n + 1)², the temporal drag on causality at depth n, carry the same factor. The index n here is the recursion depth of the quadratic family (Parts 3.2 and 7.4), not the harmonic number of the General Harmonic Mode fₙ = n/①⥂⧗ nor the harmonic index of Data Harmonics; with ν₀ at the Tempo the predictions are stated for a system's own fundamental, ν₀ being the substrate case. The book writes H_n = ν_0 × P(n) = ν_0 × (n + 1)², where H_n is the nth harmonic frequency [𝕋⁻¹], ν₀ the fundamental, 1/①⥂⧗⌂ ≈ 1.855 × 10⁴³ Hz [𝕋⁻¹], P(n) the pulse density [∅] and n the recursion depth [∅]: [𝕋⁻¹] × [∅] = [𝕋⁻¹]. It connects to Computational Load Accumulation, BPT Energy Quantization, Effective Light Speed, Temporal Drag, General Harmonic Mode and Data Harmonics.