2401/2400 lattice diagrams

Using 225/224, we can convert the 5-limit lattice of note classes into
a representation of 7-limit classes, marvel tempered; here we use
225/32 in the place of 7. For more accuracy we could use 4374/625
instead, but an alternative is to make use of 2401/2400.

If we use the Hermite reduction mapping for 2401/2400, we find that it
is generated by 2, 49/40, and 10/7; hence pitch classes can be
represented by u=49/5 and v=5/7. From the mapping, we get

3 = u^2/32 * 2400/2401
5 = u*v^2
7 = u*v

and we can find the [u,v] coordinates of any 7-limit pitch class
w = |* a b c> by [h1(w), h2(w)], where h1 = <0 2 1 1| and
h2 = <0 0 2 1|. This gives a form of the no-threes projection using
the breed temperament I think I've mentioned before.

The 32 note chord cube, which boils down to a 31 note scale in breed,
which Bodacious Breed was written in, contains the following notes:

{[3, -2], [3, 2], [-2, 3], [1, -3], [1, -1], [1, 2], [3, 1], [0, 0],
[0, 1], [0, 2], [2, 1], [2, 2], [0, 3], [1, 1], [1, 0], [0, 4], [4,
3], [2, -1], [1, 3], [2, 3], [-1, -1], [4, 0], [-1, 1], [1, -2], [3,
-1], [-2, 0], [0, -1], [2, 0], [2, 4], [-1, -2], [-1, 2]}

If I could figure out how to get Maple to draw stuff like this again,
I could get a plot of it; it looks like it might be instructive.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

Sorry, this was supposed to go to tuning-math. Now you know why you
avid tuning-math.