source file: mills3.txt Date: Wed, 17 Dec 1997 01:53:11 +0100 Subject: Just Interval Progressions From: Gregg Gibson I have enumerated all the progressions, derived from the consonances, by which one can arrive at the first 61 just intervals. For example, here are the progressions by which one arrives at 16:15 (112 cents, the diatonic semitone, the diminished minor tone:) 4/3 x 8/5 4/3 x 4/5 8/5 x 4/3 8/5 x 2/3 32/25 x 5/3 32/25 x 5/6 16/9 x 6/5 16/9 x 3/5 64/45 x 3/2 64/45 x 3/4 128/75 x 5/4 128/75 x 5/8 Similar enumerations were made many centuries ago, but always so far as I can discover, from a strictly diatonic and/or fifth-based standpoint. My method uses all the consonances, and is equally well-adapted to serve as a theoretical basis for chromatic and enharmonic music. The modern just intonationists have performed many notable and instructive calculations involving the 5-limit, although their doctrinaire insistence on the sacredness of the ratios, their obsession with the 7-limit (and still more indefensibly, their musical castles-in-the-air concerning the purely dissonant and quite imperceptible 9-, 11-, 13-limits, etc.) and their refusal to seriously consider the problems of adapting these ratios to practical music, has vitiated much of their work. Still their approach is an honorable antidote to the crudities of the dominant 12-tone-equal ethos. SMTPOriginator: tuning@eartha.mills.edu From: Gregg Gibson Subject: Septimal Intervals PostedDate: 17-12-97 02:38:44 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: 17-12-97 02:36:39-17-12-97 02:36:40,17-12-97 02:36:18-17-12-97 02:36:19 DeliveredDate: 17-12-97 02:36:19 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 C1256570.0008D7F4; Wed, 17 Dec 1997 02:38:32 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17517; Wed, 17 Dec 1997 02:38:44 +0100 Date: Wed, 17 Dec 1997 02:38:44 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA17515 Received: (qmail 18905 invoked from network); 16 Dec 1997 17:38:41 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 16 Dec 1997 17:38:41 -0800 Message-Id: <34978F8D.712D@ww-interlink.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu