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→Inconsistencies between 12 Tones and Pure Intervals
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7136.05 HZ is not 55 HZ multiplied by some power of 2. A8 should be 2x A7, 4x A6, 8x A5...128x A1. 55 HZ x 128 = 7040 HZ. We are sharp by 1.364%. What gives? '''This is simply an anomoly of trying to marry the mathematically incompatible concepts of pure-tuned intervals to the 12-note chromatic scale.''' This is highlighted clearly when trying to marry the 3:2 ratio 5th interval with the 2:1 ratio octave:
n * (3/2)^x = n * 2^y