EDOs pop out of Riemann zeta function???

http://www.research.att.com/~njas/sequences/A117536

Whoa, whoa, whoa. Whoa. My head just exploded. Is it possible to
explain why these pop out of the Riemann zeta function while sticking
to undergrad math?

I was going to ask why they're equal divisions of the octave rather
than some other interval, but then I realized that's because they're
scaled by ln(2)/2pi. If they were scaled by ln(3)/2pi they'd be equal
divisions of the 3/1 instead, right? And those would also tend to be
integers... exactly because they're good EDOs... whoa.

Keenan

--- In tuning-math@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> http://www.research.att.com/~njas/sequences/A117536
>
> Whoa, whoa, whoa. Whoa. My head just exploded. Is it possible to
> explain why these pop out of the Riemann zeta function while sticking
> to undergrad math?

I guess the Riemann-Siegal formula for Z(t) would be a good place to
start. Or simply take the zeta function in the half-plane with real
part greater than 1, and you see it has to have peaks, as you go up a
line with fixed real part, near scale divisions. As the real part gets
smsmaller, higher-limit primes are considered more and more.

It's a little more complicated than this but this is where to start to
see the basic idea.

By the way, Dave Keenan is *very* interested in getting in touch with
you. Check the tuning list.