Still another

Another way of viewing this 9-and-up lattice question is to start by
noticing that the quadratic form for unweighted rms optimization in
the 5 and 7 limits is the dual or mapping form for An*, and that in
this way we can get the symmetrical lattice of 5 and 7 limit notes.
We now can take the dual lattice either of the way Graham and I have
been doing it, or Paul's preferred way, and get a corresponding
lattice in the 9, 11 etc limits. While this works better than the
attempt to find a good Euclidean version of the Tenney norm did, it
doesn't give us something as symmetrical as we might prefer.

By the way, from the above comment rms error is the same as
symmetrical lattice error in the 5 and 7 limits, and I could put that
together with the formula for symmetrical lattice error of 7-limit
linears to do a badness listing for symmetrical error, complexity and
(log flat or other) badness, which could provide a different
perspective on the question of "best". I don't believe in Dave's
quantization of agony theory, and don't think there is one single
notion of "good". This would be another "good", with its own
character and forms of usefulness.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> I don't believe in Dave's
> quantization of agony theory,

That's "quantification", not "quantization". These are very different
things.