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Symmetry: Culture and Science
Volume 33, Number 2, pages 115-135 (2022)
https://doi.org/10.26830/symmetry_2022_2_115

DISCRETE LATTICES ON THE SINGLE BEARING SPIRAL: “MUSICAL CRYSTALLOGRAPHY”

Dmitriy Gurevich

Geologist, Consultant
Almaty, Kazakhstan
Email: dmgurevich@gmail.com

Abstract: This article continues the investigations concerning Discrete lattices on a single bearing spiral (Gurevich, 2020, 2021). It focuses on the geometrical models of musical rhythms and musical temperament systems. Spiral lattice [1/12], built on a logarithmic spiral, is considered to be a model of the equal temperament and a design of a new musical instrument – the dodecachord. [m/n] lattices and “rolling stones”, in the form of symmetrical polygons, are used to create geometrical or “crystallographic” models of time signatures and rhythmic structures of specific musical fragments.

Keywords: discrete lattices, spiral symmetry, symmetry groups, genetic spiral, equal temperament, just intonation, time signature, Dodecachord, Rhythmic figure, Rolling Stone, Crystalline Note, Glass Bead Game.

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