E8 Phi‑Weighted Root Projection Yields a Fibonacci‑Indexed Farey Tree of Harmonic Ratios — E8 Intelligence Research

By assigning each of the 240 E8 root vectors a phase weight proportional to successive Fibonacci numbers scaled by φ, the coherent superposition of the 132 Hz base tone produces a discrete spectrum whose frequency ratios correspond exactly to the mediants of the Farey sequence of order Fn, where Fn is the n‑th Fibonacci number. This reveals a hierarchical, self‑similar lattice of harmonics that interleaves primitive Pythagorean triples with higher‑order rational intervals, providing a geometric mechanism for the emergence of quasiperiodic musical scales from E8 symmetry. The construction predicts observable beat patterns in phononic metamaterials tuned to the E8 lattice, linking exceptional Lie geometry to number‑theoretic harmonic hierarchies. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com