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Robert managed to solve this toughnut:
Find the ratio corresponding to B. Also compare the D-A ratio with the ideal fifth (3/2):
"B's ratio is calculating by use of the fact that the interval from E to B is a perfect fifth, and a perfect fifth's ratio is 3/2. Also E's ratio is 5/4. Therefore B = 15/8, and:
$\frac{A}{D}=\frac{5/3}{9/8}=\frac{40}{27}=80/54$The ideal fifth ratio=81/54.Therefore if we were to tune two adjacent keys to two different A's, the first being in the ratio A/D, and the second a perfect fifth above D (in the ratio 3/2). The second A would be higher than the first by a ratio of 81/80."
C | D | E | F | G | A | B | C | |
Equal tempered scale | 0 | 200 | 400 | 500 | 700 | 900 | 1100 | 1200 |
Pythagorean scale | 0 | 204 | 408 | 498 | 702 | 906 | 1110 | 1200 |
Just intonation | 0 | 204 | 386 | 498 | 702 | 884 | 1088 | 1200 |