Locomotive

Here is a 2.9.11.13 subgroup scale, using the sval <2 38 41 44|. The name comes from the fact that 91113 is one of the British Rail Class 91 high speed electric locomotives. It's known as the County of North Yorkshire, but formerly the Sir Michael Faraday.

http://www.geograph.org.uk/photo/840003

Tempering out 144/143 would reduce it to a nine-note scale, which would not help my plan of presenting this as a 12-note JI scale but which might be a pretty good idea.

! locomotive.scl
A 2.9.11.13 subgroup scale
12
!
88/81
9/8
11/9
16/13
11/8
13/9
16/11
13/8
18/11
16/9
81/44
2/1

This sparked an idea - perhaps a good way to search for useful scales
would be to look for scales of a certain size, without respect to any
type of prime limit. That way we can cover all kinds of subgroups at
once. Would it be possible to work some magic with the zeta function
to get zeta rank 2 tunings?

-Mike

On Wed, Mar 2, 2011 at 10:58 PM, genewardsmith
<genewardsmith@...> wrote:
>
>
>
> Here is a 2.9.11.13 subgroup scale, using the sval <2 38 41 44|. The name comes from the fact that 91113 is one of the British Rail Class 91 high speed electric locomotives. It's known as the County of North Yorkshire, but formerly the Sir Michael Faraday.
>
> http://www.geograph.org.uk/photo/840003
>
> Tempering out 144/143 would reduce it to a nine-note scale, which would not help my plan of presenting this as a 12-note JI scale but which might be a pretty good idea.
>
> ! locomotive.scl
> A 2.9.11.13 subgroup scale
> 12
> !
> 88/81
> 9/8
> 11/9
> 16/13
> 11/8
> 13/9
> 16/11
> 13/8
> 18/11
> 16/9
> 81/44
> 2/1
>
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> This sparked an idea - perhaps a good way to search for useful scales
> would be to look for scales of a certain size, without respect to any
> type of prime limit. That way we can cover all kinds of subgroups at
> once. Would it be possible to work some magic with the zeta function
> to get zeta rank 2 tunings?

You could stick two zeta-derived vals together for what that would be worth.

On Thu, Mar 3, 2011 at 12:40 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > This sparked an idea - perhaps a good way to search for useful scales
> > would be to look for scales of a certain size, without respect to any
> > type of prime limit. That way we can cover all kinds of subgroups at
> > once. Would it be possible to work some magic with the zeta function
> > to get zeta rank 2 tunings?
>
> You could stick two zeta-derived vals together for what that would be worth.

I thought about that, but is that optimal? If we could somehow derive
from it a non-octave ET, we could also throw the octave in and get a
linear temperament that way too.

For example, one of the entries on the list is 7-equal. Is it actually
7-equal, though, or is that rounded? Is the actual number closer to
7.2, for instance? If so, that's the porcupine generator.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Mar 3, 2011 at 12:40 AM, genewardsmith
> <genewardsmith@...> wrote:

> For example, one of the entries on the list is 7-equal. Is it actually
> 7-equal, though, or is that rounded? Is the actual number closer to
> 7.2, for instance? If so, that's the porcupine generator.

I consider the canonical zeta tuning to be at the local maxima or minima, or in other words at the corresponding zero of Z'(t). Which means, it would be some number near to 7, but not 7; kind of like a TOP/TE tuning, only without specifying a prime limit.

On Thu, Mar 3, 2011 at 12:56 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Thu, Mar 3, 2011 at 12:40 AM, genewardsmith
> > <genewardsmith@...> wrote:
>
> > For example, one of the entries on the list is 7-equal. Is it actually
> > 7-equal, though, or is that rounded? Is the actual number closer to
> > 7.2, for instance? If so, that's the porcupine generator.
>
> I consider the canonical zeta tuning to be at the local maxima or minima, or in other words at the corresponding zero of Z'(t). Which means, it would be some number near to 7, but not 7; kind of like a TOP/TE tuning, only without specifying a prime limit.

a) I thought the zeta tuning involved taking the integral between two zeros?
b) I also thought the zeta tuning involved doing (t+s)/2, where t and
s are two successive renormalized zeroes?
c) Is there any way, if you ever have a sec, I could get a list of the
first few zeta zeroes unrounded? I'd appreciate it and it would be
useful for me to figure out what the heck is going on.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> a) I thought the zeta tuning involved taking the integral between two zeros?

That seems to be the zeta goodness figure which works the best.

> b) I also thought the zeta tuning involved doing (t+s)/2, where t and
> s are two successive renormalized zeroes?

That can also be done, and is a lot easier.

> c) Is there any way, if you ever have a sec, I could get a list of the
> first few zeta zeroes unrounded? I'd appreciate it and it would be
> useful for me to figure out what the heck is going on.

I'll email it. Do you want the actual zeros, or the zeros normalized so as to correspond to equal divisions?

On Thu, Mar 3, 2011 at 1:28 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > a) I thought the zeta tuning involved taking the integral between two zeros?
>
> That seems to be the zeta goodness figure which works the best.

But now you're saying we just take the location of the minimum or maximum?

> > c) Is there any way, if you ever have a sec, I could get a list of the
> > first few zeta zeroes unrounded? I'd appreciate it and it would be
> > useful for me to figure out what the heck is going on.
>
> I'll email it. Do you want the actual zeros, or the zeros normalized so as to correspond to equal divisions?

Can you send the normalized ones for equal divisions, just unrounded?
I'd much appreciate it.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> But now you're saying we just take the location of the minimum or maximum?

Computing a figure of merit and computing an octave retuning are two completely different problems. For the latter, there's another method which is lightening fast but which isn't as easy to justify, by the way.