Reply-To: jhchalmers@UCSD.Edu
To: Joe Monzo
Subject: New lattice type
Date: Mon, 29 Mar 1999 16:50:40 +0000
Joe: I've sent these to juno as well. This type of lattice has the following characteristics:
1. the length of the vector from the center (1/1) to each tone is proportional to the cents value of the interval from 1/1 to the tone.
2. The angle each tone makes with the horizontal axis is determined by the prime factors (+ and -) of each tone on a rectilinear, isotropic lattice. In other words, all powers of 3 are on the horizontal axis, but where they fall depends upon their cents value (octave reduced, of course). 3/2 is to the right, 4/3 to the left and their powers. Fives are on the vertical axis and 7's are 30 degrees to the horizontal.
3. The 3's axis is red, the 5's green, the 7's blue.
4. I have still to work out the equations for your plots where the axis angles are proportional to the cents values of the prime factors, octave reduced.
5. The plots are mostly PICT files, but I included a couple of GIF in case the former don't work. I've plotted a 1.3.5.7 hexany (1/3 is tonic), a 3.5.7 Euler Genus, a 7 and 9 limit diamond and Ellis's duodene (3x5 only). I've stopped at 7 here, but one could obviously move on to 11, 13 and higher primes.
--John
Ellis, 3x5 Duodene
.jpg)
Euler, 3 * 5 * 7 Euler Genus
Wilson, 1 * 3 * 5 * 7 Hexany
Partch, 7-Limit Tonality Diamond
Partch, 9-Limit Tonality Diamond
created 1999-3-29, last updated 1999-4-6
|
or try some definitions. |
