Here is a plot of the Z function around 30

http://xenharmonic.wikispaces.com/file/view/plot30.png/220060356/plot30.png

WTF? That's actually how it works? Peak values of the Z function just
mean good EDOs?

Is this the unmodified Z-function we're talking about? And by the Z
function, we're talking just about |zeta(0.5+ix)|? Am I missing
something? It's been this simple the whole time?

Once again I am unsure if numbers mean things.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> http://xenharmonic.wikispaces.com/file/view/plot30.png/220060356/plot30.png
>
> WTF? That's actually how it works? Peak values of the Z function just
> mean good EDOs?

High peal values of |Z(x)| mean good scale divisions, but the integral between adjacent zeros works even better.

> Is this the unmodified Z-function we're talking about? And by the Z
> function, we're talking just about |zeta(0.5+ix)|?

|Z(x)| = |zeta(1/2+ix)|, modulo the fact that I've renormalized so that we are using zeta(1/2 + 2 pi i x/ln(2)) really. So actually, I'm plotting Z(2 pi x/ln(2)), not Z(x).

Am I missing
> something? It's been this simple the whole time?

There are more fun facts I am planning to add to the zeta function article.

I was just thinking about this the other day!

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > http://xenharmonic.wikispaces.com/file/view/plot30.png/220060356/plot30.png
> >
> > WTF? That's actually how it works? Peak values of the Z function just
> > mean good EDOs?

I know right???

> High peal values of |Z(x)| mean good scale divisions, but the integral between adjacent zeros works even better.
>
> > Is this the unmodified Z-function we're talking about? And by the Z
> > function, we're talking just about |zeta(0.5+ix)|?
>
> |Z(x)| = |zeta(1/2+ix)|, modulo the fact that I've renormalized so that we are using zeta(1/2 + 2 pi i x/ln(2)) really. So actually, I'm plotting Z(2 pi x/ln(2)), not Z(x).

Right, the unscaled zeta function doesn't give you the equal divisions of the 2/1, or 3/1 or any other prime, but instead gives the equal divisions of the "natural" unit exp(2*pi). (If a factor of e is one radian, then exp(2*pi) is a whole cycle.)

> Am I missing
> > something? It's been this simple the whole time?
>
> There are more fun facts I am planning to add to the zeta function article.

Here's something I was just thinking about when I saw this thread: Are there any published sources (articles, books...) that even mention this connection? If not, let's write a short paper on it and submit it to some journal! I'm sure, e.g. Journal of Mathematics and Music would publish it.

Keenan

--- In tuning-math@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> Here's something I was just thinking about when I saw this thread: Are there any published sources (articles, books...) that even mention this connection?

Naah. I gave a talk about it at Berkeley. I've long thought it would make a good Math Monthly article which I never wrote.

>If not, let's write a short paper on it and submit it to some journal! I'm sure, e.g. Journal of Mathematics and Music would publish it.

Yeah, if it's not on a dead tree it means nothing.