source file: mills2.txt Date: Fri, 13 Oct 1995 06:26:28 -0700 Subject: RE: 12-tet in China From: Michael Wathen 556-9565 >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 Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 13 Oct 1995 15:39 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id GAA29490; Fri, 13 Oct 1995 06:39:20 -0700 Date: Fri, 13 Oct 1995 06:39:20 -0700 Message-Id: <199510131343.JAA21906@cerberus.Ensoniq.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu