source file: mills2.txt Date: Sat, 19 Oct 1996 13:21:57 -0700 Subject: More on equal beating tunings From: John Chalmers Before exhausting this thread, I want to clarify one statement I made in my last post about equal beating temperaments. The equal and equal & opposite labels (which I now see as ill-chosen) refer to the equations, not the intervals. I've not checked to see whether the beating intervals themselves are each flatter or sharper than their just values in each case. While Paul Erlich's point about dividing the ditonic comma is well-taken, historically linear and "irregular" temperaments were constructed by dividing it as well as the syntonic comma. See J. M. Barbour's "Tuning and Temperament." The usual term for a regular cyclic tuning whose fifths are sharper than 12-tet (700 cents) is "positive." Examples are Helmholtz's 1/8-th skhisma tuning with just major thirds and Sabat-Garibaldi's 1/9-th shkhisma tuning with just minor thirds. These are the positive analogs of the 1/4 and 1/3 comma "negative" meantone tunings. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 19 Oct 1996 22:32 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03627; Sat, 19 Oct 1996 22:34:12 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA03632 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id NAA26064; Sat, 19 Oct 1996 13:34:10 -0700 Date: Sat, 19 Oct 1996 13:34:10 -0700 Message-Id: <961019203038_71670.2576_HHB65-3@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu