source file: mills2.txt Date: Tue, 17 Oct 1995 06:07:38 -0700 Subject: Re: Chinese 12TET - overkill? From: Michael Wathen 556-9565 I don't know who wrote this because they didn't sign their name. My software does not import the authors' names only Tuning...Eartha..Whatever.. >1. Square the guess => guess sixth root of 2. >2. Square that => guessed cube root of 2. >3. Multiply by result of step 1 => guessed square root of 2. >4. Square that => guess of 2. How would you guess the sixth root of two???? My point seems to be lost. We all seem so delighted with the ease at which we are able to do these things. So let me shed some additional light on the subject. Hindu-Arabic number system along with its place holder notation was assimilated by west around 825 A.D. The decimal system appears about 1600 A.D. and shortly thereafter we get logarithms. Next comes the 2 space coordinate system followed by Calculus. With calculus we get a deep insight into the nature of solving problems which previously were very demanding even though solutions of sorts had been known for millenniums. To guess the sixth root of two? The method thought to be employed since Greek times for comparing the sizes of two ratios is that of continued fractions. It ain't easy by a long shot. As for the post from our pool player (I don't have his name either only his Email address) which gave the formula for the twelfth with the powers of eleven, this formula is a direct result of Newton's Method hence it requires the knowledge of Calculus. I believe that the same could be said about Manuel Op de Coul's formula. I think there is a slight difference between his and the Babylonian rendition. I looked up in my Math History textbook and found that the Babylonians were able to do cube roots. The Chinese have had a type of decimal system for nearly as long with algorithms for these two problems as well. I also remember reading that the man who discovered logarithms used the twelfth root of two as the first problem solved using this new system. I believe that the answer was not as important to them as was the method and its basis were, or what they could learn about the deeper nature of things by studying the problem. Such is the life of a mathematician. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 17 Oct 1995 16:51 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id HAA00176; Tue, 17 Oct 1995 07:50:39 -0700 Date: Tue, 17 Oct 1995 07:50:39 -0700 Message-Id: <951017144436_71670.2576_HHB17-4@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu