source file: m1431.txt Date: Fri, 29 May 1998 13:29:29 -0400 Subject: RE: 9-limit lattices From: "Paul H. Erlich" >I've been reviewing saturated chords for my website. Although >Paul Erlich used these as an argument for giving 9 a separate >direction Did I really argue that way? I thought my reasons for sometimes giving 9 a separate direction had nothing to do with saturated chords. Although I may have used a saturated chord as an example of a 9-limit harmony. >As there are no 7s, we can use a tetrahedral lattice with 9 at >the apex. The chords then become: > > 5 5----15 > / \ \ / > / 9 \ 9 \ / > 1-----3 3 > >Which doesn't look as clear to me. I would have to disagree with the way you drew those pictures. The 3-limit connection between 3 and 9 is very important, so I would include an additional 9 to the right of 3 in both chords. As I have said before, the disadvantage of giving composites their own axes is that certain notes often have to appear in more than one place in the lattice. >The reason is that these >anomalous suspensions work because of the compositeness of 9. True. >A lattice that treats 9 as prime can't show that. Unless you put 9 in two places. >I can understand why 9 is a separate axis in Erv Wilson's >diagrams. In all of his diagrams that I've seen, 9 is NOT a separate axis. >The way the scales are generated, there's no confusion. I'm confused. >For general lattices, though, why? If you want the otonality >to look like a primary unit, how about a double linkage? > 5 > / \ > / 7 \ > 1=====3-----9 Something along those lines might be the best solution, although (I'm assuming you have invisible lines connecting 7 to the other identities) I would still want to have 9 directly connected to 5 and to 7. The advantage of giving 9 its own axis is that such connections can be easily made without a messy tangle of lines. >Now, a curved >structure in 5-dimensional space, that might work... Right, one where the two occurences of 9 would coincide due to the curvature.