source file: mills2.txt Date: Mon, 4 Nov 1996 15:08:06 -0800 Subject: RE: Answering J. Reinhard and others From: PAULE Bringing up the tempo of a piece is actually a good point. I have claimed that just intervals can be tuned with greater precision, by ear, than intervals that are based on logarithmic (equal cents) constructions, only if simultaneities (and the resulting beats) are examined. Another caveat is that the simulataneities must be listened to for long periods of time, while in melodies, equal vs. unequal intervals can be heard even at fast tempi. Tuning two guitar strings a quartertone apart does not require tuning to the 11:8. As long as the beat rate of one quartertone is between those of the two adjacent quartertones, the result will not be more than 0.7 cents off. This is better than the 1.3 cent error from using 11:8, and usually better than the 0.6 cent error from using 11:6. Needless to say, all of these methods are better than just trying to divide the semitone into two melodically (=logarithmically) equal parts, but only if one can listen to the intervals for longer than a fraction of a second at a time. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 5 Nov 1996 00:11 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00632; Tue, 5 Nov 1996 00:12:04 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA00630 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id PAA03878; Mon, 4 Nov 1996 15:12:02 -0800 Date: Mon, 4 Nov 1996 15:12:02 -0800 Message-Id: <9611042308.AA07151@sunfish.musclefish.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu