source file: mills2.txt Date: Mon, 3 Mar 1997 12:51:15 -0800 Subject: RE: More Meantones From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE John Chalmers wrote, >It seems to me that the 5/3 and 6/5 are not independent of the 5/4 >and 3/2 and not really necessary As a result of this assumption, most of the tunings that John derives have significantly worse major sixths and minor thirds than the ones I derived. If one wants these intervals to be smooth just as much as one wants the major third and minor sixth to be smooth, including them certainly is necessary! I would like to propose a test so that anyone can decide for themselves whether I or John Chalmers have better specified the problem of finding a tuning with the best triads. Compare major and minor triads in 15-equal to those in 10-equal. The perfect fifth is identical in both tunings. The major third is 14 cents sharp in 15-equal, and 16 cents flat in 10-equal. So John Chalmers would rate the two tunings as equally good. However, the minor third is 4 cents sharp in 15-equal and 44 cents sharp in 10-equal. So I would rate 15-equal as much better than 10-equal. Listen for yourself and decide! Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 3 Mar 1997 22:19 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03356; Mon, 3 Mar 1997 22:19:26 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA03410 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id NAA17964; Mon, 3 Mar 1997 13:13:08 -0800 Date: Mon, 3 Mar 1997 13:13:08 -0800 Message-Id: <009B0BA8237A1272.5B8B@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu