source file: mills2.txt Date: Thu, 16 Jan 1997 11:22:27 -0800 Subject: Reply to Paul Erlich From: Daniel Wolf <106232.3266@compuserve.com> Paul wrote: '' I don't dispute the musical validity of this construct. In fact it supports everything I've been saying about odd numbers and about including a factor of 1 in the CPS. It's just that in graphing this along with 2(1,3,5,7,9,11), you'd have no idea that 1*9 is the same pitch as 1*3*3, if you have a separate axis for 9. '' I find that an attractive part of the discipline of working in a (non-stellated) CPS is not using compound factors as supplementary tones - as in your example, using 1*9 as 1*3*3. It may sometimes be handy to have ''extra identities'' in this way, but in fact, placing compound factors on their own axes makes the whole structure of the set more transparent, and makes a whole range of operations upon the set considerably more clear. I enjoy, for example, composing a bit of music and then reassigning the factors, to generate a variation where the contours and intervals are totally different, but the set properties maintained. (By the way, Erv Wilson's elegant graphs of some CPSes - some are abstract, those with numbers assign compound factors to separate axes - are found on the covers of Xenharmonikon 1, 4, IX, XV. For the cover of Xenharmonikon XII, Wilson has assigned tones to the vertices of a Penrose tiling.) I wrote: There are some musical contexts (and some temperaments as well - >the tuning of the TX81Z comes to mind) You asked: ''What's this?'' A resolution of 1.56 cents. So that a 3/2 is approximated by an offset of 1 unit, but a 9/8 by 3 units. So for the TX81Z the best 9/8 is not equal to the sum of 3/2s. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 16 Jan 1997 20:50 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07439; Thu, 16 Jan 1997 20:53:34 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA07458 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA16540; Thu, 16 Jan 1997 11:53:12 -0800 Date: Thu, 16 Jan 1997 11:53:12 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu