Harmonic Ratio

The Harmonic Ratio is the ratio of a toroidal universe's two radii, its global containment R against its local recursion r, the ratio that decides whether its loops resonate. Near-integer ratios give Resonance Stability; irrational ratios give quasi-crystalline interference and Phase Turbulence, which leads to structural collapse or to the Recursive Genesis of daughter universes at other octaves. It connects to UniSpheral Harmonic Ratio Function, Resonance Stability, Local Recursion and Toroidal Geometry.