source file: mills3.txt Date: Tue, 16 Dec 1997 18:45:20 +0100 Subject: series of improving equal temperaments From: "Paul H. Erlich" In each series below, each term represents the number of notes in the simplest equal temperament that improves upon the accuracy of the previous one. Tunings in parentheses are the second-best for up to that many notes. I don't go beyond 200TET. Accuracy is defined with respect to JI in the indicated odd limit; equal temperaments not consistent within the given limit are excluded. 3-limit: 1 2 3 5 7 12 (17) (24) 29 41 53 (65) (94) (106) 200 5-limit: 3 (4) 5 7 (8) (9) (10) 12 (15) 19 (22) 31 34 (46) 53 (65) (87) 118 (137) (152) 171 7-limit: 4 (5) 6 9 10 12 15 (16) 19 22 (26) 27 31 (37) (41) (53) (62) 68 72 99 (103) (130) 140 171 9-limit: 5 12 19 22 27 31 41 (46) 53 (58) 72 (77) (94) 99 (118) (130) 171 11-limit: 22 (26) (29) 31 41 (46) 58 72 (80) (87) (94) (111) 118 (130) 152 (159) (176) (183) (198) 13-limit: 26 29 41 46 58 72 (80) 87 111 130 (149) (159) 166 183 190 198 15-limit: 29 41 58 72 (80) 87 (94) 111 121 130 (149) (159) 183 190 17-limit: 58 72 (80) 94 111 121 149 159 183 19-limit: 80 94 111 121 21-limit: 94 111 23-limit: 94 SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: 19-tone ruminations and 22-tone exhortations PostedDate: 16-12-97 18:47:57 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: 16-12-97 18:45:58-16-12-97 18:45:58,16-12-97 18:45:37-16-12-97 18:45:37 DeliveredDate: 16-12-97 18:45:37 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 C125656F.0061942A; Tue, 16 Dec 1997 18:47:45 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17131; Tue, 16 Dec 1997 18:47:57 +0100 Date: Tue, 16 Dec 1997 18:47:57 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA17127 Received: (qmail 6964 invoked from network); 16 Dec 1997 09:47:52 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 16 Dec 1997 09:47:52 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu