source file: mills2.txt Date: Mon, 18 Mar 1996 08:03:59 -0800 Subject: Thanks for the compliments From: non12@delta1.deltanet.com (John Chalmers) I appreciate the enthusiastic comments I've received on my little essay on approximating cents with a four-function calculator. In my own work, I do indeed use a calculator with a ln/exp key and I recommend that everybody else do too for accurate calculations of cents. However, if one is ever stuck with only a four-function device, usefully accurate approximations to cents are still relatively easy to compute. I find this fact quite remarkable and very non-intuitive, so I decided to share it with the List. I found the approximation for ln[(x-e)/(x+e)] in Rektorys's "Survey of Applicable Mathematics." Without this background, Ellis's procedure is very mysterious and thus easy to ignore in favor of logs. BTW, has anyone looked up Ellis's and Sauveur's papers on this topic? Of course, if one is using JI, then simply memorizing the cent values of a small set of key intervals such as 3/2, 5/4, 7/4, 11/8, 13/8, etc. would be sufficient. --John Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 18 Mar 1996 18:00 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA14053; Mon, 18 Mar 1996 08:59:56 -0800 Date: Mon, 18 Mar 1996 08:59:56 -0800 Message-Id: <9603181654.AA27877@ravel.theo-physik.uni-kiel.de> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu