Ratios are more harmonic if numerator and denominator have smaller integers {harmonic ratios and neurons}. The most-harmonic ratios are 1:1 and 2:1. The second-most harmonic ratios are 3/2, 4/3, 5/3, 5/4, and 6/5.
Adding 1 to 1, for duplication, makes 2/1 ratio. Dividing 1 by 2, for splitting, makes 1/2 ratio. Repeated doubling and splitting can make all whole-number ratios. Because they can add and divide, neuron assemblies can build harmonic ratios.
Opponent-process output is a ratio with range from 1 to 2. Therefore, high end to low end has ratio 2/1. Middle to low end has ratio 1.5 = 3/2. Middle, of low end to middle, to low end has ratio 1.25 = 5/4. Middle, of middle to high end, to low end has ratio 1.33 = 4/3. Continuing makes ratios 6/5, 7/6, 8/7, 9/8, and so on, including 15/8, 7/4, 5/3, and 7/5. Opponent-process harmonic ratios can indicate categories.
line length
Line lengths have ratios. Geometric figures with sides in harmonic ratios have symmetries and high information. Geometric figures with sides in non-harmonic ratios have few symmetries and low information.
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Date Modified: 2022.0224