A Deterministic Hybrid Z60/Z72 Lattice Method for Analyzing Historical Musical Temperaments

This publication discloses a deterministic computational method for analyzing musical tuning systems using a discrete lattice framework. A Z60 (sexagesimal) lattice is treated as the primary geometric representation of pitch space, while a Z72 lattice is employed only when perceptual error thresholds are exceeded. The method does not propose a new temperament, but functions as an analytical filter for evaluating how historical tuning systems distribute structural and perceptual error. In addition to standard cent deviation, a geometry-native error metric (“sexa error”) is introduced to quantify deviation directly in Z60 lattice units. When applied to historical temperaments including Pythagorean, quarter-comma meantone, Werckmeister III, and Vallotti, the method recovers known distinctions between structurally stable and perceptually sensitive intervals without encoding temperament-specific logic. All results are reproducible using a deterministic Python implementation with hash-verified outputs. This record is published as a defensive disclosure to establish prior art.