A spin on Hofstadter's MU-puzzle from G.E.B.

I am rereading Goedel Escher Bach by Douglas R. Hofstadter (BTW, a
new edition has been published, I think the major change is a new
Forward).

Anyway, I think a spin on the MU-puzzle could be applied to tuning-
math. For example:

Rule I: Any 9 in the denominator can be replaced by 7 in the
numerator. Also, any 9 in the numerator can be replaced by 7 in the
denominator (However, this is a one-way rule, replacing 7 by 9 is not
allowed).

Rule II: Any two 5's in the numerator can be replaced by a 5 in the
denominator, and any two 5's in the denominator can be replaced by
a 5 in the numerator. This rule is two-way.

Rule III: Any three 5's can be eliminated. (Diesis).

Rule IV: Two 7's in the numerator can be replaced by one 5 in the
denominator, and vice-versa. One-way rule.

Okay, it's not exactly the MU-puzzle, for example the Mxx rule
would cause torsion...but just an idea. Still under development.
The idea is to end up with a term with: no more than 1 "3", 1 "5" and
1 "7". This is basically for use with 12-tET. (I know - boring...)

It's part of my shoebox idea which uses (3,5,7) for x,y,z <->
6/5, 5/4, 7/5 (or 10/7) for x,y,z (2^1/4, 2^1/3, 2^1/2)

Paul Hj.