source file: mills2.txt Date: Tue, 8 Jul 1997 17:49:49 +0200 Subject: RE: Muddy Waters From: "Paul H. Erlich" >I wrote, > >> Marion, I am using geometrical pictures to express my thoughts and your >> LCM idea, as Graham pointed out, is equivalent to a particular >> geometrical picture as well, a rectangular one where 2 is a distinct >> factor that has its own axis, and the log of the LCM is just the >> distance (according to the city-block metric) between the two most >> distant points in the chord. > >I was being a little muddy here. I should have written, the log of the LCM is >just the distance between the two most distant points in the smallest >(hyper-)rectangular region that contains the chord. > >> In other words, the LCM is a measure of the >> longest extent of the ROHS of a chord. > >I think that was correct, using Graham's terminology. > >> Since I feel that a minor triad >> is more consonant than a major seventh chord, I don't like this method >> and would prefer instead to use the triangular lattice. What replaces >> the LCM in that case? If we use the isosceles triangles eluded to above, >> the answer is just the Partch limit! > >That is, the log of the Partch limit will indeed be the distance (according >to a city-block-type metric) between the two most distant notes of a chord in >the isosceles triangular lattice. There is no need to construct anything like >a ROHS. If a certain note appears twice in the lattice, as will happen in the >9-limit, use the closer one to evaluate the distance from any other note. Of >course, the distance between two instances of the same note is zero. Keeping >these rules in mind, the fact that the two recently discussed 6th chords are >merely 9-limit will be clear. > >Marion and Graham, have either of you not yet received TD 1122? If so, I will >repost my posts from there, so we can continue our discussions. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 8 Jul 1997 18:23 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07842; Tue, 8 Jul 1997 18:24:15 +0200 Date: Tue, 8 Jul 1997 18:24:15 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA07879 Received: (qmail 5871 invoked from network); 8 Jul 1997 16:20:56 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 8 Jul 1997 16:20:56 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu