source file: mills2.txt Date: Fri, 4 Jul 1997 11:44:53 +0200 Subject: Muddy waters From: Daniel Wolf Marion wrote: ''Gosh, I thought Pythagorus started the whole thing (at least in the west) with his famous 3 limit. I certainly was working with prime limits before I ever heard of Partch.'' This is a twofold misunderstanding. The tradition is muddy enough, but evidently Pythagoras (or better: the Pythagoreans) was (were) not workingwith a conscious ''limit'' of three, but with the hypothesis that the numbers 1 and 2 alone yielded musically insufficient materials, and that the addition of some number of factors of 3 would yield the rational resources to construct the known scales. This is subtly but vitally different from the notion of _limit_. Although an obvious enough concept, the term _limit_ appears to be Partch's innovation in musical terminology. His late romantic harmonic view was based upon a ''stacked thirds'' model, frequently found in American theory texts of the time, and used by Partch in terms of odd, not prime chordal components. (Interestingly, Partch's viewpoint leads - to my ears - to a better explaination of the lowered ninth (as the 17th) than the conventional treatment as an ''altered tone''.) In view of Partch's priority and importance, I think it is due respect to use ''limit'' as ''odd limit'' and explicitly say ''prime limit'' when that is the case. The leading alternative to the limit classification is that of Euler, which lists the set of generative factors. This has the advantage in that factors left out in a given system that would otherwise be implied by a limit labeling are not falsely incorporated. (Example: Sometimes I use the Eikosany with (1,3,7,9,11,15) as factors in preference to (1,3,5,7,9,11);a limit notation would not make the distinction clear). This discussed really repeats a discussion from last fall (and probably from earlier than that!). Are the archives to the list available and indexed in such a way that we can easily direct new members to earlier messages? Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 4 Jul 1997 11:45 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04347; Fri, 4 Jul 1997 11:46:05 +0200 Date: Fri, 4 Jul 1997 11:46:05 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA04795 Received: (qmail 24007 invoked from network); 4 Jul 1997 09:45:20 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 4 Jul 1997 09:45:20 -0000 Message-Id: <199707040509_MC2-19CC-B67@compuserve.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu