I decided to start from arbitary 7-limit wedgies, and investigate the

conditions that lead to a good temperament. To start with, for a

wedgie [u1,u2,u3,v1,v2,v3] we should have u1^2+u2^2+u3^2!=0,

v1^2+v2^2+v3^2!=0, and u1*v1+u2*v2+u3*v3=0, but this is far from

enough to give a good temperament, though it will defined one.

In requiring the error to be small, I was led to the condition that

the wedgie be the product of [0,u1,u2,u3] and [g(2),g(3),g(5),g(7)]

for a good et val g. Then to get the number of generator steps small,

one may want to have a factor of g(2) one can divide out, and so are

led to u1 = g(3)*t mod m, u2 = g(5)*t mod m, u3 = g(7)*t mod m,

where m divides g(2) and gcd(t,m)=1. This, however, is just a form of

finding good temperaments from the et-and-generator system, so I

conclude that if done correctly, this method should be exhaustive for

good temperaments.