Artemis and friends

I decided to do a 31-limit search for Marvel extensions.
What I found was this:

http://x31eq.com/cgi-bin/uv.cgi?limit=31&uvs=225:224

Most of those are rank 2 temperaments with one or two
primes pushed out to an independent generator. But there
is an Artemis variant in there. This may be interesting,
depending on how you feel about the 31-limit. There's
something to be said for using temperaments that work in
lower limits, but attaching higher primes to them where you
think it makes sense. Artemis isn't that good lower down,
but it's interesting that it is a way of making sense of
the 31-limit.

I didn't add a 31-limit name, but I hased Artemis back to
the 23-limit, where it comes at the top of the relatively
arbitrary Marvel list:

http://x31eq.com/cgi-bin/uv.cgi?limit=23&uvs=225:224

So there you go, that's now 23-limit Artemis, and it
determines the lower limits. Out in the big wide world, it
doesn't count for much, but it doesn't do much harm to
extend the name. Now that's established, there's an
obvious Diana:

http://x31eq.com/cgi-bin/rt.cgi?ets=29_31_22p&limit=13

It might not be much good, but it is obvious.

Artemis is still one of the optimal marvels in the 19-limit.
But something else comes close, and tops some of the lists,
so I called it Hestia after another virgin Greek goddess.
See it here:

http://x31eq.com/cgi-bin/uv.cgi?uvs=225%3A224&limit=19

There are also Prodigy extensions that follow 11-limit
Prodigy directly instead of the 13-limit Prodigy I assigned
some time or other. So why did I make the simpler mapping
the standard? Well, there are two different mappings that
give around the same error and complexity, but one that
stands out as being simpler, so I named that one. So there.

For a target error of 3 cents, Hestia comes out number 6 of
all distinct 19-limit rank 3 temperaments:

http://x31eq.com/cgi-bin/pregular.cgi?limit=19&error=3

But hey, what's that optimal 19-limit R3 temperament from 3
to 5 cents? I decided to call it Demeter because that
name's still going. As the 19-limit goes, it seems to be
outstanding. And still gold in the 17-limit.

One of Demeter's notable followers is this Sensus extension:

http://x31eq.com/cgi-bin/rt.cgi?ets=27eg_19egh&limit=19

I don't know much about Sensus so I don't know how to
extend the name. But this looks like one way of tackling
the higher limits.

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> There are also Prodigy extensions that follow 11-limit
> Prodigy directly instead of the 13-limit Prodigy I assigned
> some time or other. So why did I make the simpler mapping
> the standard? Well, there are two different mappings that
> give around the same error and complexity, but one that
> stands out as being simpler, so I named that one. So there.

You went for a low-complexity, high error version so far as I can see.

"genewardsmith" <genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Graham Breed
> <gbreed@...> wrote:
>
> > There are also Prodigy extensions that follow 11-limit
> > Prodigy directly instead of the 13-limit Prodigy I
> > assigned some time or other. So why did I make the
> > simpler mapping the standard? Well, there are two
> > different mappings that give around the same error and
> > complexity, but one that stands out as being simpler,
> > so I named that one. So there.
>
> You went for a low-complexity, high error version so far
> as I can see.

I went for a gold medalist:

http://x31eq.com/cgi-bin/pregular.cgi?limit=13&error=5

The low error versions are also-rans in the same limit. You
can see them near the bottom here:

http://x31eq.com/cgi-bin/more.cgi?r=3&limit=13&error=2.2

They do better in the 17-limit but aren't outstanding.

Graham