Equal-temperament tones can form mathematical groups {sound dodeconion}. The twelve octave tones and half-tones have equally spaced frequencies. A regular 12-vertex dodecagram has points separated by 30 degrees and can represent the twelve tones, and rotations by 30-degree multiples result in same geometric figure.
frequency ratios
Tone pairs have frequency ratios. Octave from middle-C to high-C has tone frequency ratio 2/1. Middle tone, such as middle-G, makes reciprocal tone ratios, such as middle-C/middle-G, 3/2, and middle-G/high-C, 4/3.
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Date Modified: 2022.0224