source file: mills3.txt Date: Fri, 26 Sep 1997 20:28:13 +0200 Subject: Re: 22tet and 24tet From: "Paul H. Erlich" Many others, including Wendy Carlos, Yunik & Swift, etc. etc. have evaluated tunings on the basis of how well they approximate several just intervals, without bothering to check if these approximations are consistent with each other. So, Peter Blasser, you're in good company. I don't think the consistency idea is published anywhere; I came up with it in 1991, posted some tables based on it to Tuning Digest [7-8]??, John Chalmers presented it at some conference, and Paul Hahn had been independently playing with similar ideas. The idea is useful only for ETs with enough notes to offer accurate approximations (e.g., the fact that 5-tet is 9-limit consistent is not particularly meaningful) but few enough notes so that for any just interval, only one tempered interval is an acceptable approximation of it (e.g., 35-tet has two acceptable approximations of the 3:2, so restricting all chords to contain the better of the two is not really fair). SMTPOriginator: tuning@eartha.mills.edu From: clumma@nni.com Subject: Misc PostedDate: 26-09-97 23:15:34 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $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: 26-09-97 23:15:14-26-09-97 23:15:15,26-09-97 23:14:17-26-09-97 23:14:17 DeliveredDate: 26-09-97 23:14:17 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C125651E.0074BDD1; Fri, 26 Sep 1997 23:15:07 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA32292; Fri, 26 Sep 1997 23:15:34 +0200 Date: Fri, 26 Sep 1997 23:15:34 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA32311 Received: (qmail 10259 invoked from network); 26 Sep 1997 14:15:31 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 26 Sep 1997 14:15:31 -0700 Message-Id: <19970926211725312.AAA410@NIETZSCHE> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu