source file: mills3.txt Date: Tue, 23 Dec 1997 20:46:49 +0100 Subject: Basic Principle of Temperament From: Gregg Gibson I believe I said (correctly) in an earlier post that the three pairs of consonances vary independently under temperament. In fact, to be more precise, this is true for equal temperaments only; in unequal temperaments of value one can arrange for (at most) two of the three pairs to vary together, but never all three. In the 1/3 mesotonic for example, the fifth and major third are diminished by 1/3 comma, while the minor third is held just. In the 1/4 comma mesotonic the fifth and minor third are diminished by 1/4 comma, while the major third is held just. In unequal temperaments indeed one could arrange for the consonances to vary together (except for the 'wolves') but the result would be execrable octaves. All this is a commonplace for the cognoscenti. I set it down here as a help to those whose musical education ? in other respects perhaps quite excellent ? has not much prepared them for tuning questions. SMTPOriginator: tuning@eartha.mills.edu From: Gregg Gibson Subject: 19-tone Equal Tetrachords PostedDate: 23-12-97 21:02:13 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 23-12-97 21:00:04-23-12-97 21:00:05,23-12-97 20:59:36-23-12-97 20:59:36 DeliveredDate: 23-12-97 20:59:36 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256576.006DDB33; Tue, 23 Dec 1997 21:01:51 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA24651; Tue, 23 Dec 1997 21:02:13 +0100 Date: Tue, 23 Dec 1997 21:02:13 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA24593 Received: (qmail 28151 invoked from network); 23 Dec 1997 12:02:10 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 23 Dec 1997 12:02:10 -0800 Message-Id: <34A07AA7.7F5@ww-interlink.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu