source file: mills3.txt Date: Mon, 8 Dec 1997 22:24:01 +0100 Subject: repeating patterns From: James Kukula 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. 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. Equal tempered scales have the property that each note has the same set of intervals available. With other scales, notes will fall into some set of classes based on what precise intervals are available. Most non-ET scales repeat on an octave cycle, so a typical 12 note per octave scale would have 12 distinct classes of notes. The scale I propose above would have 24 notes per octave, but break into just two classes. Conventional ET is not the only system with interval symmetry. One can have multiple generating intervals instead of just one. For example if one takes the set of pitches (2**n)(3**m) then every note has the same intervals available. 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? Jim SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: Reply to Gregg Gibson PostedDate: 08-12-97 23:35:10 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: 08-12-97 23:33:24-08-12-97 23:33:25,08-12-97 23:33:12-08-12-97 23:33:12 DeliveredDate: 08-12-97 23:33:12 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 C1256567.007BE3EF; Mon, 8 Dec 1997 23:33:12 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10006; Mon, 8 Dec 1997 23:35:10 +0100 Date: Mon, 8 Dec 1997 23:35:10 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA09922 Received: (qmail 13460 invoked from network); 8 Dec 1997 14:35:07 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 8 Dec 1997 14:35:07 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu