source file: mills2.txt Date: Fri, 13 Oct 1995 07:52:57 -0700 Subject: Re: 12-tet in China From: Michael Wathen 556-9565 >The algorithm for calculating a root is actually not so difficult. >This calculates a square root: > > Answer := Of_Number; > loop > Delta := (Of_Number / Answer) - Answer; > if abs Delta <= Answer * Epsilon then > return Answer; > end if; > Answer := Answer + 0.5 * Delta; > end loop; >Epsilon indicates the required precision and is the smallest number that >makes a difference. >I suppose that modifying this to do the twelfth root of 2 is easy. >It converges very rapidly so it's doable by hand. It's very elementary >so it must have been known for a very long time >Manuel Op de Coul coul@ezh.nl This algorithm was known by the Babylonians. I remember this from a Math History Course I took several years ago. I'm not quite sure but I think that dates it to 1000 B.C. Is this adaptable to the 12th root of two? My immediate hunch is no. It is probably only good for roots that can be expressed as powers of 2. I'll have to think about it. Maybe Mr. Canright would have something to say about this. 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 17:00 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA04791; Fri, 13 Oct 1995 08:00:23 -0700 Date: Fri, 13 Oct 1995 08:00:23 -0700 Message-Id: <9510130751.aa19350@cyber.cyber.net> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu