source file: mills3.txt Date: Wed, 10 Dec 1997 23:04:34 +0100 Subject: RE: repeating patterns From: "Paul H. Erlich" >>Here's something I've wanted to try, maybe someone already has. Suppose I >>took two 12TET scales separated by 80/81. Then one would have both nice >>sounding thirds and a wide open modulation horizon. > >I did this quite some time ago and also posted a question whether anyone else >had. I separated the scales by 15 cents rather than 80/81 to produce better >thirds. > >>One idea I had for a keyboard setup was to use the left hand on one 12TET >>and >>the right hand on the other. Then to play a simple diatonic scale one might >>have a pattern like RRLRRLLR. > >All major triads have the root and fifth in the left hand, the third in the >right hand. All minor triads have the root and fifth in the right hand, and >the third in the left hand. This was about the most sophisticated tuning I >could get out of my Casio CZ-1. Taken to its logical limit, this idea leads >to 72TET (which, besides the nearly pure triads, has unique representations >of all 11-limit intervals and is consistent through the 17-limit). > >>If I understand how the "k-limit" term is used, it might be useful to make a >>finer distinction. Suppose I take a set of notes (2**n)(3**m)(5**p) where n >>and m are unbounded but p is constrained to be 0 or 1. My understanding is >>that this scale would be called 5-limit. The scale where p is also allowed >>unbounded values would also be 5-limit. Perhaps the case of unbounded >>exponents is not of sufficient interest to merit a new term? > >I don't think the case of BOUNDED exponents is of sufficient interest to >merit a new term; someone finding themselves imposing such constraints may be >better served by the odd-limit definition I (and Partch) use rather than the >prime-limit definition you seem to be suggesting above. > >>Jim > >-Paul SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: Reply to Gregg Gibson PostedDate: 11-12-97 00:07:37 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: 11-12-97 00:06:09-11-12-97 00:06:09,11-12-97 00:05:54-11-12-97 00:05:55 DeliveredDate: 11-12-97 00:05:55 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 C1256569.007EE333; Thu, 11 Dec 1997 00:07:53 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12151; Thu, 11 Dec 1997 00:07:37 +0100 Date: Thu, 11 Dec 1997 00:07:37 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA12142 Received: (qmail 14092 invoked from network); 10 Dec 1997 15:07:27 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 10 Dec 1997 15:07:27 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu