In the 1920s a German scientist, Hans Kayser, a student of Pythagoras, found that the mathematical ratios of musical harmonics were identical to those at the basis of all the laws of chemistry, physics, astronomy, architecture, and botany. In fact, all the natural sciences; including Crystallography.
Musical Ratios are calculated by use of the Monochord, (dividing a string on a musical instrument into fractions. These precise fractions locate the harmonics on the string). Following the logic of these facts, musical ratios correspond to those used in geometry. Think of the radius of a circle.
Harmony effects the environment, which echoes harmonics in reply. (For example, to a note struck on an instrument, or sung). Musicians are well acquainted with this phenomenon, but to the layperson it may take a little concentration. Try singing a note in a silent room, and listening for the echo. If there is…
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