source file: mills3.txt Date: Tue, 30 Dec 1997 20:30:16 +0100 Subject: RE: Wilson scale From: "Paul H. Erlich" >}I have a tape McLaren sent me years ago. It has a killer piece that >}is in a 1-3-5-7 Stellated Hexany tuning that Erv Wilson invented. It is a >}14 tone just scale. Does anyone have info about just what this is? Is it >}possible for someone to write out the scale, with both ratios and cents >}intervals? It sounds like something I'd be interested in >}investigating...thanks...Hstick > >I'm glad you like it -- it's 7-limit! > >The hexany by itself is the CPS 2)4 [1,3,5,7], or, if we choose 1*5 as the >tonic (an arbitrary but convenient choice), the tones > >1/1 21/20 6/5 7/5 3/2 7/4 > >It might be a good idea to play around with this scale first. This scale has >eight triads that are consonant within the 7-limit. "Stellation" refers to >the process of adding one note to each triad to form a complete 7-limit >tetrad: > >Triad Completion >1/1 6/5 7/5 8/5 (1 Odentity) >6/5 3/2 21/20 9/5 (3 Odentity) >1/1 3/2 7/4 5/4 (5 Odentity) >7/5 7/4 21/20 49/40 (7 Odentity) >7/4 21/20 3/2 21/16 (1 Udentity) >7/5 7/4 1/1 7/6 (3 Udentity) >7/5 21/20 6/5 42/25 (5 Udentity) >1/1 6/5 3/2 12/7 (7 Udentity) > >Each of the original six tones serves four tetradic functions, while each of >the eight new tones serves only one. > >Here is the entire scale, in just ratios, cents, and degrees of 31TET (the >best of your axes for 7-limit): > >Ratio cents 31TET >1/1 0 0 >21/20 84 2 >7/6 267 7 >6/5 316 8 >49/40 351 9 >5/4 386 10 >21/16 471 12 >7/5 583 15 >3/2 702 18 >8/5 814 21 >42/25 898 23 >12/7 933 24 >7/4 969 25 >9/5 1018 26 > >Of course, McLaren may have chosen a different "tonic," so it really may be a >particular mode of this scale you are interested in. I suspect his tonic was >the note called "8/5" above. SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: RE: PLANCK CONSTANT PostedDate: 30-12-97 22:41:14 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: 30-12-97 22:38:57-30-12-97 22:38:58,30-12-97 22:38:21-30-12-97 22:38:21 DeliveredDate: 30-12-97 22:38:21 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 C125657D.0076EABC; Tue, 30 Dec 1997 22:40:49 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA28317; Tue, 30 Dec 1997 22:41:14 +0100 Date: Tue, 30 Dec 1997 22:41:14 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA28332 Received: (qmail 23693 invoked from network); 30 Dec 1997 13:41:11 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 30 Dec 1997 13:41:11 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu