Lp temperamental complexity

I laid out an idea for temperamental complexity here:
/tuning-math/message/20836

We can also use Hahn-Banach to prove a theorem about this, which
proceeds exactly like the Lp-TOP theorem we just proved. It turns out
that the thing I mentioned agrees with TE temperamental complexity and
generalizes it to any choice of Lp, so we'll call it Lp temperamental
complexity.

If V is the space of monzos and V* the dual space, and if T* is a
subspace of V* representing a temperament, then T can be identified
with the space of tempered intervals on that temperament. Then, using
Hahn-Banach, an isometric isomorphism exists between T and V/ker(T*).
The norm on V/ker(T*) is the usual quotient norm, which means that
||w|| for any coset w in V/ker(T*) is equal to min ||v|| for v in V
the preimage of w.

Therefore, simply put, the Lp temperamental complexity of any interval
is equal to the Lp norm of the least complex JI monzo mapping to it.
Note that this JI monzo may have fractional or even real coordinates,
however.

-Mike