source file: mills2.txt Date: Tue, 22 Oct 1996 01:36:46 -0700 Subject: RE: More on equal beating tunings From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) Temperings with parts of the Pythagorean comma are usually circulating temperaments. They have no wolf fifth. This implies that the Pythagorean comma is distributed somewhat evenly along the circle of fifths. Vallotti & Young are circulating temperaments with 6 fifths tempered by 1/6 Pyth. comma and 6 pure fifths. The temperaments that I gave aren't circulating temperaments, and have only one size of fifth (apart from the wolf). However they could be completed with pure fifths after the cycle that completes a whole Pythagorean comma. Or have the pure and tempered fifths in another permutation. So for instance 1/11 Pyth. comma temperament would have one perfect fifth and fourth, 1/10 Pyth. comma temp. could have that and a Pythagorean minor seventh, 1/9 Pyth. comma that and a 32/27, and so on. Of course that would decrease the number of equal beating triads in the scale. There remains one fifth that's tempered very nearly part of a Pyth. comma in the equal beating temperaments presented. One in John's last post: 3/2 = twice 6/5 equal: 695.337, opposite: 694.13653 The latter is very very close to a 1/3 Pyth. comma tempered fifth. Manuel Op de Coul coul@ezh.nl Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 22 Oct 1996 15:06 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07830; Tue, 22 Oct 1996 15:07:59 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA07773 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id GAA11692; Tue, 22 Oct 1996 06:07:44 -0700 Date: Tue, 22 Oct 1996 06:07:44 -0700 Message-Id: <961022130429_71670.2576_HHB56-4@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu