source file: mills2.txt Date: Mon, 14 Jul 1997 23:04:57 +0200 Subject: RE: Muddy Waters From: "Paul H. Erlich" >>>i.e., a major seventh is just as dissonant/complex as a major >>>sixth. Gary Morrison wrote >Although I certainly respect that as an opinion, I'm amazed that anybody >would feel that way. I don't know if anybody actually does feel that way, though I'm glad to have Gary on my side in this. I was simply pointing out that if the rectangular matrix (Euler-Fokker, Tenney, Rapoport) view is applied to questions of consonance and dissonance, and octave equivalence is assumed, the above comes out as a consequence. I know that certain applications of Euler-Fokker theory have assumed octave equivalence, for example using the genera as scales for compositions (I recently pointed out that in a triangular latice, there are many structures as compact or more compact than the E-F genera). I also know that James Tenney examines the lattice along with a city block metric to give a measure of harmonic complexity, but I don't know whether he assumes octave equivalence. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 14 Jul 1997 23:07 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14061; Mon, 14 Jul 1997 23:07:52 +0200 Date: Mon, 14 Jul 1997 23:07:52 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA14146 Received: (qmail 9167 invoked from network); 14 Jul 1997 19:37:23 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 14 Jul 1997 19:37:23 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu