General Harmonic Mode

The General Harmonic Mode is the Alpha String's harmonic ladder: every allowed frequency is a whole multiple of one over the Pulse Tempo, fₙ = n / ①⥂⧗. Each rung is a Resonant Standing Wave of the Alpha String, echoing from atoms to galaxies: stable rungs make the observable cosmos, unstable rungs birth new realities (the Harmonic Ladder of Existence). The mode's wavelength is λₙ = 2·PD / n = ①⥂⦜⌂ / n (Alpha Wavelength of Harmonics), so the fundamental runs one Pulse Length a Tempo, at 𝒞→. The first four rungs are the Novas: the Prime Pulse sounded by the Null Nova as Toroidal Genesis; Dimensional Genesis, the Data Nova; Temporal Stabilization, the Physical Nova; and the Dimensional Saturation Threshold. Modes above n = 4 add resonant echoes but no new axes. The same law appears as the Alpha Harmonic Overtones, fₙ = n × f₁ with f₁ = 1/①⥂⧗⌂ the Alpha Note Frequency; the quadratic Harmonic Frequency Scaling of Part 7.1, H_n = ν₀(n + 1)², is a different model with a different index. The book writes fₙ = n / ①⥂⧗ [𝕋⁻¹], where fₙ is the frequency of the nth harmonic mode [𝕋⁻¹], n the harmonic number (1, 2, 3, …) [∅] and ①⥂⧗ the Pulse Tempo [𝕋]: [∅] ÷ [𝕋] = [𝕋⁻¹]. It connects to Alpha Harmonic Overtones, Alpha Note Frequency, Alpha Wavelength of Harmonics, Harmonic Frequency Scaling and Resonant Standing Waves.