RE: 12-tet in China

>About 1595, Prince Tsai-Yu" calculated the 12th roots of 2 to 9 significant
>figures on a fundamental of 1,000,000,000.
>
>--John

That's hard to believe. I don't know if anyone has mentioned this but most
of the fascination with the twelfth root of two was in the problem
of actually calculating these numbers. It was a considerable task that
required strange algorithms to give approximations. These days we seem
to be out of touch with just how difficult problems like this were. We can
just pick up a little calculator to get an answer. These calculators employ
algorithms usually based on some type of an equivalent series approximations in
terms of Sines and Cosines and the Sines and Cosines are based on another type
series. These series are in essence infinite series but are terminated at some
point to conform to some type of error function that guarantees the accuracy of
the significant digits. This way of solving the problem comes from Euler and
Fourier. I don't know off hand what their dates are as I am writing this off the
top of my head.

One might also notice that there were more mathematicians and science types
engrossed in this problem than there were musicians which ought to reaffirm
my main point.

Michael Wathen



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