72 et 11-limit linear temperaments

I did the same thing as before, only this time calculating the
11-limit wedgie. I then calculated gens^(5/3) cents for the
corresponding 11-limit temperaments. The reason for the 5/3 is best
left to the argument about this by the Mullahs of Mathematics on the
math list.

1 1133.376037
2 565.8424250
3 432.2032507
4 440.3356274
5 358.2243782
6 --
7 125.5016755
8 803.0229838
9 304.3374043
10 803.0229838
11 1088.157186
12 --
13 1138.079494
14 440.3356740
15 304.3374043
16 565.8423914
17 467.9306241
18 --
19 271.0589693
20 565.8423914
21 432.2032624
22 440.3356274
23 942.0084789
24 false
25 1186.609159
26 803.0229838
27 432.2032364
28 803.0229988
29 314.4089813
30 --
31 353.9145617
32 440.3356274
33 304.3374043
34 565.8423914
35 371.7076477

Ennealimmal gets beaten up badly and now Miracle rules the roost.
This is not because there isn't a highly accurate extension to the
11-limit, but because this one isn't it. Second place is now held by
kleismic (19/72), Enneamiracle is closing in at third, and 29/72 is
not far behind in fourth place. Some new entries now appear: 31/72,
the 65+7 system, in fifth, and 5/72, the 43+29 system, in sixth,
trailed by 35/72, the 37+35 system, in seventh. Now I leave it to
Dave Keenan to explain why these rankings are a bunch of nonsense;
however I think once again the method proves its worth as a
temperament-finder.

If Joe wants to try something new, he might consider Enneamiracle, in
a scale of 27 notes consisting of three rows of 9-ets separated by
secors. He might also look at kleismic if he hasn't already.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> I did the same thing as before, only this time calculating the
> 11-limit wedgie.

I'm not going to be able to take this very seriously until you
address the concern I had with your 7-limit results.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Now I leave it to
> Dave Keenan to explain why these rankings are a bunch of nonsense;
> however I think once again the method proves its worth as a
> temperament-finder.

I don't know whether it _is_ nonsense. It's certainly way better than
random. If you give us the number of generators required and the error
for each one (and explain what the numbers mean), then folks have a
chance to make up their own minds.

But one obvious bit of nonsense is the 10 significant digits in your
badness numbers. I'd say 2 is all we need.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_31245.html#31245

>
> If Joe wants to try something new, he might consider Enneamiracle,
in a scale of 27 notes consisting of three rows of 9-ets separated by
> secors. He might also look at kleismic if he hasn't already.

I'm game, Gene! Please keep this stuff on tap for me for the day
when "miracles" are no longer happening! Thanks for the
investigations!!!

Joe

how about a diamond made out of miracle :) or a cross set with Enneamiracle :)

jpehrson2 wrote:

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> /tuning/topicId_31245.html#31245
>
> >
> > If Joe wants to try something new, he might consider Enneamiracle,
> in a scale of 27 notes consisting of three rows of 9-ets separated by
> > secors. He might also look at kleismic if he hasn't already.
>
> I'm game, Gene! Please keep this stuff on tap for me for the day
> when "miracles" are no longer happening! Thanks for the
> investigations!!!
>
> Joe
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_31245.html#31301

> how about a diamond made out of miracle :) or a cross set with
Enneamiracle :)
>

Now *that's* getting into *your* world, Kraig. It *definitely*
should be done, even if it's a limited set of "pure" ratios!

JP

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> But one obvious bit of nonsense is the 10 significant digits in
your
> badness numbers. I'd say 2 is all we need.

It's computer output, so rounding off would mean a little more work,
for no apparent gain.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> > I did the same thing as before, only this time calculating the
> > 11-limit wedgie.
>
> I'm not going to be able to take this very seriously until you
> address the concern I had with your 7-limit results.

I saw a posting about 13/72, which I answered, but that is all.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> how about a diamond made out of miracle :)

Graham Breed detailed that for us -- the 11-limit diamond in MIRACLE
requires a chain of 45 generators, and happens to pick up one of
Partch's 43-tone scales (within 3 cents, as George Secor pointed out).

> or a cross set with Enneamiracle :)

The planar temperament resulting from taking the Cartesian or direct
product of Miracle with Ennealimmal is exactly along the lines of
something Gene would be interested in . . . Gene?

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> > > I did the same thing as before, only this time calculating the
> > > 11-limit wedgie.
> >
> > I'm not going to be able to take this very seriously until you
> > address the concern I had with your 7-limit results.
>
> I saw a posting about 13/72, which I answered, but that is all.

That was it. I was misled by your misleading table.