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Pythagoras:
“either down or up, what we call a fifth, and what we then have is the keys of the sharps or the flats, these are the fifths up and down, the sharps being a fifth up and the flat being a fifth down; five notes in the scale-- so that we have very interesting prime numbers halving the number two and the thirding bringing about fifths. This would certainly indicate quite clearly a fundamental in our relationship between wave frequencies and number behaviors of octaves. And inasmuch as I’m talking about physics and the waves of the periodic table… its unique frequencies would interact… and what the permutations would be mathematically and I found this highly suggestive that the octave with its characteristically flat resonance really governing the interactions of frequencies. The resonances are the key to much of modern physical exploration. And I think that the very fact that the Pythagoreans were particularly secret is of importance.”
