PIφonic G₃₆: A Corpus-First Microtonal Scale System Derived from the Golden Ratio

We present PIφonic G₃₆, a 36-note microtonal scale system derived from the golden ratio φ. Unlike prior work that constructs φ-based scales and observes which traditions they approximate, we fix a corpus of 98 intervals from 10 musical traditions before any optimization, then apply a greedy set cover algorithm to select the optimal subset of the φ orbit. G₃₆ achieves 100% coverage of the 98-interval corpus at ±15 cents, outperforms all tested EDO systems with fewer notes (37 vs 41-TET), covers 90.3% of 124 world music traditions at ±20 cents, and ranks in the top 3.7% of 50,000 random generators in a Monte Carlo benchmark. The corpus-first inversion of the standard methodology is the central contribution.