Reducing to the ennealimmal band

If we take the matrix defined by the three vals

[<1 1 2 0|, <0 1 1 3|, <0 0 -1 4|]

then we may use the value derived from the first val as the exponent
of 2, for the second val as the exponent of 3/2, and for the third val
as the exponent of 6/5, giving the 4375/4374 temperament in terms of
generators 2, 3/2, 6/5. In this temperament, the ennealimma is
2^10 (3/2)^(-9) (6/5)^(-18), and 2400/2401 is the same. We may reduce
a 7-limit interval to the ennealimmal band by first finding the three
exponents [a b c], then define n = round(b/9), where "round" means to
round to the nearest integer. Then the reduction to the ennealimmal
band is given by [a b c] + n*[10 -9 -18]. If we reduce 32805/32768 to
the ennealimmal band, we get [5 0 -19], from which we see that adding
this as a comma closes the circle of minor thirds. And indeed, adding
32805/32768 to ennealimmal gives 7-limit 171-et.