The space of vals vs "tuning space"

These seem to be two different concepts. The notation <1200 1902
2786|, for example, means something very different depending on which
one you're looking at.

What is the name for the space that vals live in, and what is the name
for the space of things that tell you the tuning of a temperament's
primes? By the latter I refer to the thing that we're supposed to be
bringing as close as possible to the JIP when working with things like
TOP and so on.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> These seem to be two different concepts. The notation <1200 1902
> 2786|, for example, means something very different depending on which
> one you're looking at.
>
> What is the name for the space that vals live in, and what is the name
> for the space of things that tell you the tuning of a temperament's
> primes? By the latter I refer to the thing that we're supposed to be
> bringing as close as possible to the JIP when working with things like
> TOP and so on.

Both are tuning space. If you normalize <1200.0 1902.0 2786.0|, you get <1.0 1.585 2.322|, which is obviously not the same as <1200 1902 2786|. If you val weight them, you get <1.0 1.0000237 0.9998874| and <1200.000000 1200.0283913 1199.864891|.

So what does <24 38 58| refer to? A stupid crappy tuning for 12-EDO in
which the octave is mapped to 2400 cents, or the contorted 5-limit val
for 24-EDO?

-Mike

On Sat, Dec 24, 2011 at 12:32 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
>
>
>
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > These seem to be two different concepts. The notation <1200 1902
> > 2786|, for example, means something very different depending on which
> > one you're looking at.
> >
> > What is the name for the space that vals live in, and what is the name
> > for the space of things that tell you the tuning of a temperament's
> > primes? By the latter I refer to the thing that we're supposed to be
> > bringing as close as possible to the JIP when working with things like
> > TOP and so on.
>
> Both are tuning space. If you normalize <1200.0 1902.0 2786.0|, you get <1.0 1.585 2.322|, which is obviously not the same as <1200 1902 2786|. If you val weight them, you get <1.0 1.0000237 0.9998874| and <1200.000000 1200.0283913 1199.864891|.
>
>

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> So what does <24 38 58| refer to? A stupid crappy tuning for 12-EDO in
> which the octave is mapped to 2400 cents, or the contorted 5-limit val
> for 24-EDO?

The latter.

On Sun, Dec 25, 2011 at 1:24 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > So what does <24 38 58| refer to? A stupid crappy tuning for 12-EDO in
> > which the octave is mapped to 2400 cents, or the contorted 5-limit val
> > for 24-EDO?
>
> The latter.

I don't get it. What did you mean by this?

> If you normalize <1200.0 1902.0 2786.0|, you get <1.0 1.585 2.322|, which is obviously not the same as <1200 1902 2786|.

-Mike