source file: mills2.txt Date: Thu, 16 Jan 1997 02:21:47 -0800 Subject: RE: Comment on Kami's post From: Daniel Wolf <106232.3266@compuserve.com> Paul wrote: ''9-limit constructs are not as pretty geometrically, but the math works out..'' This depends on whether 9 is mapped on the 3 axis (3^2) or given an axis of its own. There are some musical contexts (and some temperaments as well - the tuning of the TX81Z comes to mind) where 9 _has_ a harmonic function distinct from 3^2. Of, course, there are other musical settings -especially long duration sound installations - where distinguishing prime identities is more important. Wilson has graphed his CPSes with factors of 9, 15, and 21 mapped to independent axes. From what I recall of his notes, he has sketched out CPSes with all combinations, including repeated factors, through 15, and tried out a few promising sets with higher factors. The three Eikosany he has worked with most are 3(1,3,5,7,9,11), 3(1,3,7,9,11,15), and 3(1,3,5,7,11,13) and the two Hebdomekontany are 4(1,3,5,7,9,11,13,15) and 4(1,3,5,7,11,13,17,19), the latter of which I have played with on my Rayna. (It can have a Stravinskian quality due to the everpresent quasi-octotonic scales). Perhaps John can persuade Erv to publish his ''Letter to Adrian Fokker'' and ''Letter to John Chalmers'' where all of this material - including the graphing that Paul describes - were first set out. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 16 Jan 1997 20:07 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA30947; Thu, 16 Jan 1997 20:10:48 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA30918 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA13221; Thu, 16 Jan 1997 11:10:45 -0800 Date: Thu, 16 Jan 1997 11:10:45 -0800 Message-Id: <32DE79AA.28F@top.monad.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu