source file: mills2.txt Date: Wed, 19 Feb 1997 07:47:50 -0800 Subject: RE: Ghosttones and LucyTuning From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE An error in my post: I wrote >If you use a weighted mean, with weights inversely >proportional to the limit (following Partch who said higher-limit intervals >need to be tuned more accurately in proportion to their limit), you get a >perfect fifth of 696.019 cents. "Inversely proportional to the limit" should be "proportional to the square of the limit," the square being used since we are dealing with squared error. Notice how close this result is to the equal-weighted result, 696.165, even though the assumptions seem quite different. One can imagine many different criteria between these two weighting schemes would lead to results within this very narrow range. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 19 Feb 1997 23:15 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA11865; Wed, 19 Feb 1997 23:15:47 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA11857 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id OAA27935; Wed, 19 Feb 1997 14:09:13 -0800 Date: Wed, 19 Feb 1997 14:09:13 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu