source file: mills2.txt Date: Fri, 18 Oct 1996 15:55:10 -0700 Subject: RE: Equal beating well temperaments, rep From: PAULE Manuel wrote, > E.B. Intervals Fifths Approximation >6/5 = twice 3/2 698.048 2 schisma This may be mathematically correct, but schismatic temperaments should refer only to those with fifths larger than 700 cents. Otherwise, the diatonic thirds are purer than the schismatic thirds, and the tuning is better characterized as a meantone temperament, quantified by the fraction of a (syntonic) comma by which the fifth is tempered. 5/4 = twice 3/2 698.590 1/7 pyth. comma It doesn't seem useful to characterize a tuning as a tempering of the pythagorean comma unless the tuning in question is an equal temperament. -Paul Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 19 Oct 1996 01:06 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03173; Sat, 19 Oct 1996 01:07:56 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA03174 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id QAA20777; Fri, 18 Oct 1996 16:07:53 -0700 Date: Fri, 18 Oct 1996 16:07:53 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu