source file: mills3.txt Date: Thu, 26 Feb 1998 22:00:00 +0100 Subject: Ten equal tunings From: "Paul H. Erlich" }PS...where is everybody? I miss the action.. I've been thinking hard about which tunings I would have if I had unlimited resources for guitars and generalized keyboards. As I mention in my paper, I don't like equal temperaments with more than 34 notes per octave, since it becomes possible to approximate the same interval in more than one way (assuming the ear has a 1% tolerance), which is more confusion than I want to deal with. So I came up with the following symmetrical scheme: 7, 10, 12, 15, 19, 22, 26, 29, 31, 34 Notice that subtracting any of the numbers above from 41 gives another one of these numbers. A brief summary: 7: The Thai tuning. 10: Fun with neutral triads and 5tET subsets (there was an article in Ear Magazine East on 10tET). 12: For all those paid gigs. 15: Read Blackwood, "Modes and Chord Progressions in Equal Tunings", Perspectives of New Music Vol. 29 No. 2 (1991) pp. 166-200. 19: Read Mandelbaum, Haverstick, Yasser, Yunik & Swift, etc. 22: Read my paper (a slightly messed up version is at http://www-math.cudenver.edu/~jstarret/microtone.html under "Notes on Microtonality"). It describes 10-note scales that are 7-limit analogues to the 5-limit diatonic scale. Also the first ET consistent through the 11-limit. 26: A meantone tuning that commits all the errors of 12 in the opposite direction. Amazingly, two diatonic scales a half-octave apart contain all the septimal completions of each other's consonant triads. Also the first ET consistent through the 13-limit. 29: The purest 3-limit intervals of any ET below 53. Also the first ET consistent through the 15-limit. 31: Read Fokker, etc. Approximates 7-limit JI and 1/4-comma meantone very well. 34: Approximates 5-limit JI very well, perhaps the best of these tunings for Indian music. Also contains 17tET which contains Arabic scales. SMTPOriginator: tuning@eartha.mills.edu From: Aline Surman Subject: 34 in the news PostedDate: 27-02-98 00:15:29 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: 27-02-98 00:14:08-27-02-98 00:14:09,27-02-98 00:14:10-27-02-98 00:14:10 DeliveredDate: 27-02-98 00:14:10 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 C12565B7.007FA200; Fri, 27 Feb 1998 00:14:19 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12744; Fri, 27 Feb 1998 00:15:29 +0100 Date: Fri, 27 Feb 1998 00:15:29 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA12748 Received: (qmail 22983 invoked from network); 26 Feb 1998 15:14:22 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 26 Feb 1998 15:14:22 -0800 Message-Id: <34F5FD57.37EE@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu