One way of doing something along the lines Dan suggested would be to
use the Osmium versions of the orwell and the secor, together with
the octave, to express notes. These are pretty far off their usual
values, but looking at the 9-note scale I gave we find a lot of 16/15
(secor) and some 75/64 (orwell) relationships, so it might be just
the ticket. If we invert the matrix for <2,16/15,75/64> we get

[1 0 0]
[2 -1 -2]
[2 1 1]

From this we see we can express notes in the Osmium system by
q ~ 2^f1(q) * o^f2(q) * s^f3(q), where f1=v2+2v3+2v5,f2=-v3+v5,
f3=-2v3+v5. Here o is the Osmium orwell, (40-11z-14z^2)/241, of
268.1254776 cents, and s is the Osmium secor, (43-11z-3z^2)/241, of
115.3367774 cents. Of course given our 225/224~1 and 385/384~1 we
have the 11-limit expressed in these terms. In these terms, we have

3 ~ 2^2 o^(-1) s^(-2)
5 ~ 2^2 o s
7 ~ 2^3 s^(-2)
11 ~ 2^4 o^(-2) s^(-1)