source file: mills2.txt Date: Sun, 6 Jul 1997 15:06:10 +0200 Subject: Scale Dimensionality From: Daniel Wolf David Finnamore wrote: >BTW, I like a concept that Graham Breed introduced me to: harmonic >dimensionality using prime limits. As I understand it, using all octaves >(like P. D. Q. Bach's Don Octave) would be 1-dimensional, Pythagorean scales >(3-limit in practice) would be 2-dimensional, 5-limit would be 3-dimensional. Although this is the most familar scheme (Riemann, Tanaka, Johnston, Tenney), it is often useful not to lock in the identity of a given dimension with a given generating element. For example, I might - like LaMonte Young - want to use sevens but no fives. Why should I have to speakin terms of four dimensions when I am only using three? Or, in the other direction, I might choose to treat nine as a separate dimension from three, in which case, Partch's diamond is viewed as six-dimensional rather than the five yielded by counting primes. Let's reserve ''dimension'' for thenumber of dimensions on the graph independent of the particular intervalsto which they are assigned. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 6 Jul 1997 15:07 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05700; Sun, 6 Jul 1997 15:07:33 +0200 Date: Sun, 6 Jul 1997 15:07:33 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05695 Received: (qmail 8220 invoked from network); 6 Jul 1997 13:07:13 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 6 Jul 1997 13:07:13 -0000 Message-Id: <199707060902_MC2-1A52-E589@compuserve.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu