source file: mills3.txt Date: Thu, 20 Nov 1997 22:38:11 +0100 Subject: RE: Xenharmonic? From: "Paul H. Erlich" While I personally am in favor of as diverse as possible a plurality of tunings, polymicrotonality, omnimicrotonality, etc., as long as the results are musical, there is a history of attempts to identify "the next step" in Western tuning after 12-equal; here are some equal-tempered examples: 8.2021: Bohlen, Pierce 16: Goldsmith 19: Salinas, Yasser 20: Balzano 24: Wychnegradsky 31: Huygens, Fokker 36: Gawel 41: von Janko 53: Mercator (did he strictly look at 3-limit? Who was the first to note the applicability of 53 to 5-limit?) 72: Richter-Herf (Partch missed this in his list -- it would have disturbed him that an ET could come so close to 11-limit JI!) My paper is just another proposition along these lines, but it is, I feel, the strongest one. I do believe that composers must be given an alternate set of tools than 12-tone keyboards, guitars, etc. for xenharmonic music to have a chance to naturally evolve. If the goal is to ditch diatonicism but preserve the principles behind Western tonality with minimal alteration, I believe 22 is the best way to go. And harmonically, if JI is your goal, and if you believe the basic harmonies of the diatonic scale in classical compositions can be "bent" by variable-pitch instrumentalists to achieve just 5-limit triads, then the basic harmonies of my 10-tone scales in 22 can be bent by about the same amount to achieve just 7-limit tetrads. 22 also happens to be an important number in describing ancient Indian tuning and if modern accounts of that tuning (basically 5-limit JI) are correct, a 22-tone "well-temperament" can be constructed which combines very close approximations of the ancient Indian scales with a few keys of my 7-limit decatonic scales. This is analogous to a 12-tone well-temperament with 6 pure fifths in a row and 6 fifths diminished by 1/6 pyth. comma, which contains both a pythagorean scale (in 1 key) and a meantone scale (in 1 key). SMTPOriginator: tuning@eartha.mills.edu From: Johnny Reinhard Subject: Re: Woodwind etc PostedDate: 21-11-97 03:15:17 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: 21-11-97 03:13:52-21-11-97 03:13:52,21-11-97 03:13:58-21-11-97 03:13:59 DeliveredDate: 21-11-97 03:13:59 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 C1256556.000C3E4F; Fri, 21 Nov 1997 03:13:43 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04535; Fri, 21 Nov 1997 03:15:17 +0100 Date: Fri, 21 Nov 1997 03:15:17 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA04532 Received: (qmail 26967 invoked from network); 20 Nov 1997 18:15:08 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 20 Nov 1997 18:15:08 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu