source file: mills3.txt Date: Thu, 15 Jan 1998 21:47:32 +0100 Subject: RE: JI approximation to 22ET From: "Paul H. Erlich" Ben Johnston used a 22-tone 7-limit just tuning in his 4th string quartet that was fairly equally spaced: # ratio cents 0: 1/1 0 1: 28/27 63 2: 16/15 112 3: 10/9 182 4: 8/7 231 5: 7/6 267 6: 6/5 316 7: 5/4 386 8: 9/7 435 9: 21/16 471 10: 27/20 520 11: 45/32 590 12: 81/56 639 13: 3/2 702 14: 14/9 765 15: 8/5 814 16: 5/3 884 17: 12/7 933 18: 7/4 969 19: 9/5 1018 20: 15/8 1088 21: 27/14 1137 Kraehenbuehl & Schmidt also proposed a 22-tone 7-limit just tuning, with "inflections" for some of the tones: 0: 1/1 0 1: 49/48 36 36/35 49 25/24 71 2: 21/20 84 16/15 112 15/14 119 3: 35/32 155 4: 9/8 204 8/7 231 5: 7/6 267 25/21 302 6: 6/5 316 128/105 343 7: 49/40 351 5/4 386 8: 9/7 435 9: 21/16 471 4/3 498 75/56 506 10: 27/20 520 48/35 547 11: 7/5 583 45/32 590 10/7 617 12: 35/24 653 13: 3/2 702 32/21 729 14: 49/32 738 54/35* 751 25/16 773 15: 63/40 786 8/5 814 45/28 821 16: 5/3 884 17: 27/16 906 12/7 933 18: 7/4 969 25/14 1004 19: 9/5 1018 175/96 1039 64/35 1045 20: 28/15 1081 15/8 1088 40/21 1116 21: 27/14 1137 *The original text had 56/35, a typo. The number of steps assigned to all these ratios in both tunings agrees with 22TET when displayed on a 7-limit lattice. Right, Manuel? SMTPOriginator: tuning@eartha.mills.edu From: Xou Oxno Subject: Beethoven in the Temperaments article in Village Voice PostedDate: 15-01-98 22:12:01 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: 15-01-98 22:11:27-15-01-98 22:11:28,15-01-98 22:11:14-15-01-98 22:11:14 DeliveredDate: 15-01-98 22:11:14 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 C125658D.00746419; Thu, 15 Jan 1998 22:11:46 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA21884; Thu, 15 Jan 1998 22:12:01 +0100 Date: Thu, 15 Jan 1998 22:12:01 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA21997 Received: (qmail 27387 invoked from network); 15 Jan 1998 13:11:58 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 15 Jan 1998 13:11:58 -0800 Message-Id: <34BEA4D9.1171@virtulink.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu