Nonlinear Harmonic Spectra

Nonlinear Harmonic Spectra are the frequency structures BPT predicts in place of classical overtone series: harmonics that grow with the square of their index instead of in equal steps. In classical systems such as vibrating strings, air columns and bounded periodic media, harmonics follow f_n = n × f_0 and form a linear additive series. BPT replaces this with Recursive Complexity Growth: harmonics emerge from Prime Pulse Bifurcation working through Recursive State Evolution, where each generation inherits and amplifies the computational load of those before it. Because that load grows quadratically with recursion depth, as in Computational Load Accumulation, L(n) = L_0 + n(n+1)/2, harmonic frequencies scale as (n+1)² and the spectrum becomes nonlinear, reflecting the computational architecture of the binary substrate. The current definition writes the spectrum as H_n = ν_0 × (n + 1)², with ν_0 = 1/①⥂⧗⌂ the fundamental frequency and n the harmonic index. It connects to Recursive Complexity Growth, Harmonic Complexity Scaling, Computational Load Accumulation, Recursive State Evolution, Prime Pulse Bifurcation and the Harmonic Origin Pulse.