Linear temperament search question

Why does 4&5, in the 11-limit, turn up "Beep" and "Pentoid" over the
superior and almighty Orwell temperament? Surely it's lower in badness
than both of those?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Why does 4&5, in the 11-limit, turn up "Beep" and "Pentoid" over the
> superior and almighty Orwell temperament? Surely it's lower in badness
> than both of those?

I suspect that the relevant vals, 4bd and 5bdd, are too far down on the list of good vals for 4 and 5. You can't expect it to search every possible val (of which there are infinitely many).

http://x31eq.com/cgi-bin/rt.cgi?ets=4bd+5bdd&limit=11

Keenan

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Why does 4&5, in the 11-limit, turn up "Beep" and "Pentoid" over the
> superior and almighty Orwell temperament? Surely it's lower in badness
> than both of those?

If you're using patent vals you don't get Orwell. Anyway, I don't know what you mean by "turn up">

On Sat, Aug 27, 2011 at 1:10 AM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Why does 4&5, in the 11-limit, turn up "Beep" and "Pentoid" over the
> > superior and almighty Orwell temperament? Surely it's lower in badness
> > than both of those?
>
> If you're using patent vals you don't get Orwell. Anyway, I don't know what you mean by "turn up">

I meant in Graham's temperament finder. See here:

http://x31eq.com/cgi-bin/rt.cgi?ets=4%2C5&limit=11

It doesn't turn up Orwell at all. It's returned an ambiguous result
between various Beep and Pentoid extensions, both of which are
competing for the "canonical" 4&5 result, but Orwell, which is better
than both, doesn't appear. I assume this is because it first finds the
best 4's and the best 5's and just uses those, rather than finding the
best 4&5 temperament in general. Keenan said the same thing, perhaps
Graham can confirm?

-Mike

Mike Battaglia <battaglia01@gmail.com> wrote:
> On Sat, Aug 27, 2011 at 1:10 AM, genewardsmith
> <genewardsmith@sbcglobal.net> wrote:
> >
> > --- In tuning-math@yahoogroups.com, Mike Battaglia
> > <battaglia01@...> wrote:
> > >
> > > Why does 4&5, in the 11-limit, turn up "Beep" and
> > > "Pentoid" over the superior and almighty Orwell
> > > temperament? Surely it's lower in badness than both
> > > of those?
> >
> > If you're using patent vals you don't get Orwell.
> > Anyway, I don't know what you mean by "turn up">
>
> I meant in Graham's temperament finder. See here:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=4%2C5&limit=11
>
> It doesn't turn up Orwell at all. It's returned an
> ambiguous result between various Beep and Pentoid
> extensions, both of which are competing for the
> "canonical" 4&5 result, but Orwell, which is better than
> both, doesn't appear. I assume this is because it first
> finds the best 4's and the best 5's and just uses those,
> rather than finding the best 4&5 temperament in general.
> Keenan said the same thing, perhaps Graham can confirm?

Something like that, but how would it decide which 4&5
temperament is best? You're asking for around 4 or 5 notes
to the octave. Orwell's useless for that. It's too
complicated.

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> Something like that, but how would it decide which 4&5
> temperament is best? You're asking for around 4 or 5 notes
> to the octave. Orwell's useless for that. It's too
> complicated.

Right, exactly. I mean, there also have to be 0.001-cent microtemperaments whose MOS series also happens to begin (4,5,...). They're better in accuracy but worse in complexity.

If you say Orwell is the best, that's assuming some desired trade-off of accuracy versus complexity. But Graham's temperament finder is more universal than that, because it doesn't just assume one specific trade-off for everything - instead it bases the trade-off on the size of the numbers you put in.

That's why 4&5 turns up beep/pentoid/whatever, rather than Orwell.

It's also why 84&137 doesn't turn up Orwell either (try it), but some more accurate yet more complex temperaments (e.g. different mappings of 11).

Keenan

On Sat, Aug 27, 2011 at 7:37 AM, Graham Breed <gbreed@gmail.com> wrote:
>
> Mike Battaglia <battaglia01@gmail.com> wrote:
>
> Something like that, but how would it decide which 4&5
> temperament is best? You're asking for around 4 or 5 notes
> to the octave. Orwell's useless for that. It's too
> complicated.

-and also-

On Sat, Aug 27, 2011 at 10:07 PM, Keenan Pepper <keenanpepper@gmail.com> wrote:
>
> Right, exactly. I mean, there also have to be 0.001-cent microtemperaments whose MOS series also happens to begin (4,5,...). They're better in accuracy but worse in complexity.
>
> If you say Orwell is the best, that's assuming some desired trade-off of accuracy versus complexity. But Graham's temperament finder is more universal than that, because it doesn't just assume one specific trade-off for everything - instead it bases the trade-off on the size of the numbers you put in.

OK, thanks. I didn't realize that the badness measure it uses takes a
cues from the numbers you put in to weight complexity. That's pretty
neat.

-Mike