On 25 Sep 2009, at 14:44, Graham Breed wrote:
what I don't understand:
How many cents are an alteration of 10/1023?
It's a fraction of 200 cents. So 200 * 10/1023 = 2000/1023 =
1.955... cents, which looks like a schisma.
From my computations, it corresponds choosing an approximation in
E12276 (tonestep 7181) of the interval ratio (3/2) which gives an
accuracy of -3.33477112590685e-05 cents. How did you choose this?
It might be more natural to choose from the series of successive
continued fraction convergents of log2(3/2):
0/1, 1/1, 1/2, 3/5, 7/12, 24/41, 31/53, 179/306, 389/665,
9126/15601, ...
Or E12, E41, E53, E306, E665, E15601, ...
E665 is less acurate that your choice, but within 0.000113647342336876
cents; E15601 is better: -2.01904306607048e-06 cents. E306 is good,
too: -0.00578344833810363 cents.
Hans
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