Consistent kleismic ets

Since its 7-limit temperaments are also consistent in the 9-limit, it
appears 53&72 wins the Keenan Prize.

15&19

7-limit: 4, 15, 19
9-limit: 19

53&72

7-limit: 19, 53, 72, 91, 125, 144, 197
9-limit: 19, 53, 72, 91, 125, 144, 197

53&87

7-limit: 53, 87, 140, 193, 227, 280, 333
9-limit: 53, 87, 140, 193

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Since its 7-limit temperaments are also consistent in the 9-limit, it
> appears 53&72 wins the Keenan Prize.

I counted both 72 and 144 for 53&72 and 140 and 280 for 53&87, which
are contorted tunings; I presume this should count?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Since its 7-limit temperaments are also consistent in the 9-limit,
it
> appears 53&72 wins the Keenan Prize.

Er. What does this mean exactly?

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > Since its 7-limit temperaments are also consistent in the 9-limit,
> it
> > appears 53&72 wins the Keenan Prize.
>
> Er. What does this mean exactly?

It's got the most consistent ets in the 9-limit; since of course these
are also consistent in the 5-limit, it also has the most consistent
ets in common with 5-limit kleismic. Wasn't this your system for
picking which tuning gets to keep the same name, leaving off the whole
undefined "simple" business?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> > > Since its 7-limit temperaments are also consistent in the 9-
limit,
> > it
> > > appears 53&72 wins the Keenan Prize.
> >
> > Er. What does this mean exactly?
>
> It's got the most consistent ets in the 9-limit; since of course
these
> are also consistent in the 5-limit, it also has the most consistent
> ets in common with 5-limit kleismic. Wasn't this your system for
> picking which tuning gets to keep the same name, leaving off the
whole
> undefined "simple" business?

Um. I might have mentioned something like that as one possibility.
Sounds reasonable. But I don't have a strong attachment to it.

I'd prefer that the "complex"/"inaccurate" business got better
defined. I thought the "best" i.e. "least bad" one should get the
unqualified name and then all the others, since they are more bad,
must be either more complex or more inaccurate. But that might
require us to agree on a badness metric, a notoriously difficult
thing. Still, we might find we can agree on which is the best of the
family, in some individual cases.