L infinity TOP complexity and Kees complexity

When these aren't exactly the same, which itself is pretty often, they
usually seem to be the same to three decimal places. I didn't findd an
example differing by more than 1% in my old faithful list of 45
seven-limit temperaments.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> When these aren't exactly the same, which itself is pretty often, they
> usually seem to be the same to three decimal places. I didn't findd an
> example differing by more than 1% in my old faithful list of 45
> seven-limit temperaments.

How about Kees complexity vs. L1 TOP complexity (if you throw in an
appropriate multiplicative constant)?

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > When these aren't exactly the same, which itself is pretty often,
they
> > usually seem to be the same to three decimal places. I didn't findd
an
> > example differing by more than 1% in my old faithful list of 45
> > seven-limit temperaments.
>
> How about Kees complexity vs. L1 TOP complexity (if you throw in an
> appropriate multiplicative constant)?

And more importantly, any proofs or arguments that connect *generation*
complexity to these, since you confirmed my hunch that in the 5-limit
Kees case, complexity as you originally defined it (the complexity of
*generating* the important intervals in the scale?) is proportional to
the Kees complexity (=expressibility) of the vanishing comma.