Zeta Tunings

Hi,

From what Gene has written on the subject I've understood that local
maxima of |zeta(z)| (in the critical line?) somehow correspond to good
equal divisions. I have no idea why this is so but am interested about
zeta versions of equal tunings because I would like to have only one
version of e.g. 12-equal without having to specify a prime limit as in
TOP tuning paradigm.

Is there any kind of list of calculated zeta tunings in existence?

Kalle

--- In tuning-math@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:

> Is there any kind of list of calculated zeta tunings in existence?

I don't think so. However, there *are* lists of zeros of the zeta
function in existence; Andy Odlyzko has them listed in greater numbers
and accuracy than any musical use could require. The zeta peaks will
occur between two zeros, and taking the midpoint gets you very close
to the peak, and could be used for your purpose instead of the actual
peak. Moreover, it is an excellent starting point for finding the peak
by Newton's method.

I may calculate some of these when I have the time. Which zeta tunings
do you think are of interest?

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

> However, there *are* lists of zeros of the zeta
> function in existence; Andy Odlyzko has them listed in greater
numbers
> and accuracy than any musical use could require. The zeta peaks will
> occur between two zeros, and taking the midpoint gets you very close
> to the peak, and could be used for your purpose instead of the actual
> peak. Moreover, it is an excellent starting point for finding the
peak
> by Newton's method.
>
> I may calculate some of these when I have the time.

I would also like to try to do this myself. I've read about Riemann
Siegel formula. Should I try to use this to compute values of Zeta
along the critical line or are there easier ways to numerically
calculate them with computer?

> Which zeta tunings do you think are of interest?

All of them!