The Tessellation Interference Principle: Consonance as Aligned Grids, Dissonance as Churn, Music Rendered by Overlapping Triangles

Two overlapping rings on the Fibonacci wheel each carry an inscribed triangle, and each triangle can be cut into finer and finer rows, the tessellation levels. This paper reads the pair of grids as a pair of frequencies. The center distance sets a ratio between the two grids, 2(4 − d/R)/3, and at the wheel's named settings that ratio lands on musical ground. The Vesica distance d = R gives exactly 2, the octave and the only exact alignment, the Wide setting gives 1.512, the geometric shadow of the perfect fifth 3:2, and the k = 3 setting gives 1.399, the septimal tritone 7:5, at the same setting whose crossing notes are also a tritone, the same interval arriving through two unrelated systems at once. Where the grids align, the figure is still and consonant. Where they cannot align, and for the deep settings k ≥ 9 they never align at any level, so that region is tessellation-silent, the crossing pattern churns without repeating, the geometric picture of dissonance. Following Tetryonics (Abraham 2021), where the triangular diamond is the shape of a quantized frequency, the overlapping grids are read as interference, an interpretation labeled as such, while the geometry beneath it is verified by direct computation throughout.

Paper 8 of 10 in the music series of The Strassner Series: Fibonacci Geometry and Harmony. The program that checks every number in the paper is printed in its appendix.