I thought I'd work a more elaborate example, to see if any problems

arose--one did, but one easily dealt with.

I started from the 8539-et in the 19-limit, to put the method to a

more difficult test. Doing the lattice reduction and inverting gives

a basis <10830/10829,50578/50575,28900/28899,12376/12375,

314721/314678,5928/5929,14364/14365,4914/4913>. On the grounds they

were the three largest, I kept the 5th, 6th and 8th commas, and did a

lattice reduction on the corresponding vals, which were the 581,742

and 954 ets. This gave me the following matrix:

[-3 -3 2]

[ 1 -5 -4]

[-3 -2 2]

[-1 1 7]

[ 2 -4 1]

[-2 -6 -1]

[ 7 -6 -1]

[ 4 0 8]

I ran into difficulties with my trick of finding an invertible

submatrix, but this is not really necessary. I simply fitted to the

three generators (in a rough and ready way, using just the primes,

which could be improved on in an example intended for use) and

obtained generators of size 51.6, -859.188, 611.382; of course the

negative cents can be replaced by positive cents and everything taken

inside an octave. This resulted in a planar temperament all of whose

19-limit prime approximations were within a fraction of a cent (1/17

or less) of being just.