source file: mills2.txt Date: Wed, 12 Mar 1997 10:16:33 -0800 Subject: RE: Meaner tones again (Paul E) From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE >Paul E: The weights I used were 3, 5, and 5. My error function >was thus 3*(F-X)^2 + 5*(TM-4*X+2*OCT)^2 + 5*(MS-3*X+0CT)^2. >(F=cents(3/2), TM=Cents(5/4), MS= cents(5/3), OCT= 1200) >Your weights are 9 25 25, the squares of these. I weighted >the derivatives, you the squared errors themselves. I'm not >sure which is more correct mathematically, but your unweighted >gives a slightly lower sum of sq'ed errors. A slightly lower unweighted sum of sq'ed errors, duh, by definition. My weighting scheme is based on Partch's "Observation One" which claims that the field of attraction, in cents, of an interval is inversely proportional to the (odd-number) limit of the interval. Therefore the errors must be multiplied by the limit to get the error in units of the field of attraction. Your weighting scheme can be seen as a compromise between this and equal-weighting. I think leaning towards equal weighting is appropriate when the music tends to use complete chords and the various intervals reinforce one another. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 12 Mar 1997 19:40 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03550; Wed, 12 Mar 1997 19:40:41 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA03548 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id KAA21966; Wed, 12 Mar 1997 10:39:03 -0800 Date: Wed, 12 Mar 1997 10:39:03 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu