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LARGE & small semitones.

🔗"Robin Perry" <jinto83@...>

11/16/1998 6:32:07 AM
Here's an interesting phenomenon involving two tempered steps of
different size.

The 200th root of 2 (6 cents) raised to the 15th power is 90 cents.
The 200th root of 2 raised to the 19th power is 114 cents.

Combinations of these two provide very close approximations to intervals
up to 10/9.

2/1 = 5(114) + 7(90) =1200 (0 cents)
3/2 = 3(114) + 4(90) =702 (0 cents)
4/3 = 2(114) + 3(90) =498 (0 cents)
5/4 = 1(114) + 3(90) =384 (-2 cents)
6/5 = 2(114) + 1(90) =318 (+2 cents)
7/6 = 3(90) =270 (+3 cents)
8/7 = 2(114) =228 (-3 cents)
9/8 = 1(114) + 1(90) =204 (0 cents)
10/9= 2(90) =180 (-2 cents)

For whatever this may be worth.....????

Robin Perry

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