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Middle Path 11-limit temperaments?

🔗dkeenanuqnetau <d.keenan@...>

12/25/2011 5:11:02 AM

Has anyone done the obvious extension of the work in Paul Erlich's ground-breaking "Middle Path" paper and provided a table of the best ten or twenty 11-limit rank 2 temperaments in the same format, using similar inclusion criteria to the existing 5-limit and 7-limit tables? The same could be done for the other subgroups of the 11-limit.
http://sethares.engr.wisc.edu/paperspdf/Erlich-MiddlePath.pdf

It would also be useful to add a column to the existing tables to give the optimum generator size for those who don't have the option of octaves other than 1200 cents.

-- Dave Keenan

🔗Mike Battaglia <battaglia01@...>

12/25/2011 5:18:29 AM

On Sun, Dec 25, 2011 at 8:11 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> Has anyone done the obvious extension of the work in Paul Erlich's ground-breaking "Middle Path" paper and provided a table of the best ten or twenty 11-limit rank 2 temperaments in the same format, using similar inclusion criteria to the existing 5-limit and 7-limit tables? The same could be done for the other subgroups of the 11-limit.

Graham Breed's temperament finder solves this problem for arbitrary limits

11-limit, 5 cents target error
http://x31eq.com/cgi-bin/pregular.cgi?limit=11&error=5.0

13-limit, 5 cents target error
http://x31eq.com/cgi-bin/pregular.cgi?limit=13&error=5.0

2.3.7-limit, 5 cents target error
http://x31eq.com/cgi-bin/pregular.cgi?limit=2.3.7&error=5.0

2.5.7-limit, 5 cents target error
http://x31eq.com/cgi-bin/pregular.cgi?limit=2.5.7&error=5.0

And my favorite, 2.7.9.11-limit, 5 cents target error
http://x31eq.com/cgi-bin/pregular.cgi?limit=2.7.9.11&error=5.0

Machine temperament, she's a winner. Check out 2 2 1 2 2 2 in 11-EDO.

-Mike

🔗dkeenanuqnetau <d.keenan@...>

12/25/2011 6:20:00 AM

Thanks Mike. Graham's temperament finder is wonderful but I can't reproduce Paul's 5 or 7 limit tables with it, so presumably its 11 limit offerings would not be analogous.

It seems to use different definitions of complexity, error and badness and give different values for the generator and period when compared with Paul's tables.

-- Dave

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Dec 25, 2011 at 8:11 AM, dkeenanuqnetau <d.keenan@...> wrote:
> >
> > Has anyone done the obvious extension of the work in Paul Erlich's ground-breaking "Middle Path" paper and provided a table of the best ten or twenty 11-limit rank 2 temperaments in the same format, using similar inclusion criteria to the existing 5-limit and 7-limit tables? The same could be done for the other subgroups of the 11-limit.
>
> Graham Breed's temperament finder solves this problem for arbitrary limits
>
> 11-limit, 5 cents target error
> http://x31eq.com/cgi-bin/pregular.cgi?limit=11&error=5.0
>
> 13-limit, 5 cents target error
> http://x31eq.com/cgi-bin/pregular.cgi?limit=13&error=5.0
>
> 2.3.7-limit, 5 cents target error
> http://x31eq.com/cgi-bin/pregular.cgi?limit=2.3.7&error=5.0
>
> 2.5.7-limit, 5 cents target error
> http://x31eq.com/cgi-bin/pregular.cgi?limit=2.5.7&error=5.0
>
> And my favorite, 2.7.9.11-limit, 5 cents target error
> http://x31eq.com/cgi-bin/pregular.cgi?limit=2.7.9.11&error=5.0
>
> Machine temperament, she's a winner. Check out 2 2 1 2 2 2 in 11-EDO.
>
> -Mike
>

🔗Mike Battaglia <battaglia01@...>

12/25/2011 6:33:10 AM

I don't have Paul's tables in front of me, nor do I remember what
criteria he used to produce them. If they were in general produced
algorithmically, by sorting temperaments by badness, then Graham's
temperament finder is doing the same basic thing, but the differences
are

1) The 5 cent target error parameter may not be the right setting to
generate comparable results to Paul's
2) Graham's using Tenney-Euclidean measures for temperaments instead
of TOP ones, which are similar but not identical

There might be some other minutia as well, but in general I consider
all of these to be relatively unimportant. In other words, I don't
consider Paul's results to have some deeper sort of validity that
Graham's lack. For the most part, I think that if you're getting a
radically different list from what Paul's got in the 7-limit, some
tweaking of the target error parameter would fix that. If that's not
true then maybe something really is radically different that I don't
know about.

-Mike

On Sun, Dec 25, 2011 at 9:20 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> Thanks Mike. Graham's temperament finder is wonderful but I can't reproduce Paul's 5 or 7 limit tables with it, so presumably its 11 limit offerings would not be analogous.
>
> It seems to use different definitions of complexity, error and badness and give different values for the generator and period when compared with Paul's tables.

🔗Carl Lumma <carl@...>

12/25/2011 8:44:13 AM

Paul used TOP error, wedgie complexity (provided by Gene),
and "moat badness" to make a top-ten list.

Graham uses TE error, TE complexity, Cangwu badness (I think),
and it's never been clear to me how many temperaments he
returns under what circumstances and in what order.

Paul's list is believed to be complete based on a complexity
cutoff (I think). Graham's is proven complete within an
error range or something, assuming you know what the list
is supposed to be of.

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I don't have Paul's tables in front of me, nor do I remember what
> criteria he used to produce them. If they were in general produced
> algorithmically, by sorting temperaments by badness, then Graham's
> temperament finder is doing the same basic thing, but the
> differences are
>
> 1) The 5 cent target error parameter may not be the right setting to
> generate comparable results to Paul's
> 2) Graham's using Tenney-Euclidean measures for temperaments instead
> of TOP ones, which are similar but not identical
>
> There might be some other minutia as well, but in general I consider
> all of these to be relatively unimportant. In other words, I don't
> consider Paul's results to have some deeper sort of validity that
> Graham's lack. For the most part, I think that if you're getting a
> radically different list from what Paul's got in the 7-limit, some
> tweaking of the target error parameter would fix that. If that's not
> true then maybe something really is radically different that I don't
> know about.
>
> -Mike
>

🔗genewardsmith <genewardsmith@...>

12/25/2011 10:32:14 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Paul used TOP error, wedgie complexity (provided by Gene),
> and "moat badness" to make a top-ten list.
>
> Graham uses TE error, TE complexity, Cangwu badness (I think),
> and it's never been clear to me how many temperaments he
> returns under what circumstances and in what order.

Funny this should come up, because just yesterday it occurred to me to wonder if there was some setting for Cangwu badness which closely matched Paul' ad hoc moat.

🔗Graham Breed <gbreed@...>

12/25/2011 12:05:36 PM

"Carl Lumma" <carl@...> wrote:

> Graham uses TE error, TE complexity, Cangwu badness (I
> think), and it's never been clear to me how many
> temperaments he returns under what circumstances and in
> what order.

They're ordered by Cangwu badness. At least the current
ones. The old ones do all kinds of things.

Graham

🔗Graham Breed <gbreed@...>

12/25/2011 12:18:29 PM

"Carl Lumma" <carl@...> wrote:
> Paul used TOP error, wedgie complexity (provided by Gene),
> and "moat badness" to make a top-ten list.

I put tables in primerr.pdf that should duplicate Paul's.
(I think it's http://x31eq.com/primerr.pdf but it may be
different in a subfolder.) There's also an 11-limit table
but I forget how I chose the examples.

There are also tables in http://x31eq.com/badness.pdf that
show Cangwu badness rankings for different parameters. It
looks like you need a range of values to duplicate the
Middle Path list and there's a web app you can play with to
find out. The higher the prime limit, the more focused a
single Cangwu badness list gets.

Graham

🔗Carl Lumma <carl@...>

12/25/2011 2:49:42 PM

Gene wrote:

> Funny this should come up, because just yesterday it occurred
> to me to wonder if there was some setting for Cangwu badness
> which closely matched Paul' ad hoc moat.

The moat was not one of his finer moments. Still, as wonderful
as Cangwu badness is, I can't say I have a working notion of
what the lists it produces mean. I really don't know what was
wrong with logflat error * complexity badness.

-Carl

🔗Carl Lumma <carl@...>

12/25/2011 2:51:22 PM

Graham wrote:

> > Graham uses TE error, TE complexity, Cangwu badness (I
> > think), and it's never been clear to me how many
> > temperaments he returns under what circumstances and in
> > what order.
>
> They're ordered by Cangwu badness. At least the current
> ones. The old ones do all kinds of things.

But what are ordered? How many rank 2 temperaments are
returned for a given search, and what does a "5 cent target"
mean? -Carl

🔗gbreed@...

12/25/2011 3:38:10 PM

The temperaments are ordered. Or things like temperaments that may have conunprino

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Sunday, December 25, 2011 10:51:22 PM GMT-0000
Subject: [tuning] Re: Middle Path 11-limit temperaments?

Graham wrote:

But what are ordered? How many rank 2 temperaments are
returned for a given search, and what does a "5 cent target"
mean? -Carl

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🔗gbreed@...

12/25/2011 3:44:03 PM

The temperaments are ordered. Or things like temperaments that may have contorsion with only the optimal tuning for each class.
I can't remember how many get returned. Maybe you could count them.
The target is explained on the page where you enter it. It's the bad

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Sunday, December 25, 2011 10:51:22 PM GMT-0000
Subject: [tuning] Re: Middle Path 11-limit temperaments?

Graham wrote:

But what are ordered? How many rank 2 temperaments are
returned for a given search, and what does a "5 cent target"
mean? -Carl

------------------------------------

🔗gbreed@...

12/25/2011 3:48:43 PM

The temperaments are ordered. Or things like temperaments that may have contorsion with only the optimal tuning for each class.
I don't remember how many get returned. Maybe you could count them.
The target is explained on the page where you enter it. It's the badness parameter in cents per octave multiplied by the largest prime in octaves.

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Sunday, December 25, 2011 10:51:22 PM GMT-0000
Subject: [tuning] Re: Middle Path 11-limit temperaments?

Graham wrote:

But what are ordered? How many rank 2 temperaments are
returned for a given search, and what does a "5 cent target"
mean? -Carl

------------------------------------

🔗dkeenanuqnetau <d.keenan@...>

12/25/2011 5:25:57 PM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I don't have Paul's tables in front of me, nor do I remember what
> criteria he used to produce them.

You only had to google: Erlich Middle Path
and I gave the link at the start of this thread.
http://sethares.engr.wisc.edu/paperspdf/Erlich-MiddlePath.pdf

His inclusion criteria are on page 20.
His error or "damage" measure is described on pages 12 thru 15.
Sadly his complexity measure is not defined.

I only understand the simple integer complexity measure which is the number of generators required to produce the diamond, multiplied by the number of periods per octave (or other equivalence-interval).

Can someone explain how Paul's complexity relates to this?

I personally prefer MiniMax error measures (as Paul used here) to RMS measures.

> In other words, I don't
> consider Paul's results to have some deeper sort of validity that
> Graham's lack.

Probably not, but call me sentimental, I refer to Paul's two tables all the time and I'd love to have a third page that is like what Paul would have written if he'd written Part 2 soon after.

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

12/26/2011 3:30:24 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> His inclusion criteria are on page 20.
> His error or "damage" measure is described on pages 12 thru 15.
> Sadly his complexity measure is not defined.

It would be nice to have the list sorted by how good the temperaments on it rated by the badness measure Paul used, but I don't know how to do that without the complexity measure. Was there ever a sorted list, and does anyone know what it was?

🔗genewardsmith <genewardsmith@...>

12/26/2011 3:41:23 AM

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> The temperaments are ordered.

If you click on the number in the error (cents) column, the temperaments are reordered--but how? I would have thought a Gold Medal temperament would always come out on top if you do this, a Silver Medal second, and so forth, but that doesn't seem to happen.

🔗gbreed@...

12/26/2011 6:42:19 AM

If you click on an error you get a new search with that target error.

Graham

------Original message------
From: genewardsmith <genewardsmith@...>
To: <tuning@yahoogroups.com>
Date: Monday, December 26, 2011 11:41:23 AM GMT-0000
Subject: [tuning] Re: Middle Path 11-limit temperaments?

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> The temperaments are ordered.

------------------------------------

🔗dkeenanuqnetau <d.keenan@...>

12/26/2011 7:11:36 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> It would be nice to have the list sorted by how good the temperaments on it rated by the badness measure Paul used, but I don't know how to do that without the complexity measure.
>

By searching in Tuning Math I eventually found Paul Erlich's Middle Path complexity measure described in this wonderful paper by Graham Breed.
http://x31eq.com/primerr.pdf
See equation (99) on page 21.

> Was there ever a sorted list, and does anyone know what it was?
>

You could either say he didn't use a badness measure or you could say his badness measure was (complexity/12 + damage/10) for 5-limit and (complexity/24 + damage/10) for 7-limit, in which case his badness cutoff was 1 in both cases.

But perhaps I should just refer to Graham's paper above in future, since it includes list of good 5, 7 and 11-limit temperaments.

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

12/26/2011 10:33:17 AM

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> If you click on an error you get a new search with that target error.

I guessed as much. What I didn't see was why "error" for a temperament is not the optimal choice to produce a high listing for that temperament.

🔗genewardsmith <genewardsmith@...>

12/26/2011 10:58:53 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > It would be nice to have the list sorted by how good the temperaments on it rated by the badness measure Paul used, but I don't know how to do that without the complexity measure.
> >
>
> By searching in Tuning Math I eventually found Paul Erlich's Middle Path complexity measure described in this wonderful paper by Graham Breed.
> http://x31eq.com/primerr.pdf
> See equation (99) on page 21.

In other words, the sum of the absolute values of the coefficients of the wedgie in weighted coordinates. I thought it might be that, since I suggested to Paul something proportional to that is what he seemed to want, but the average of the absolute values is an obvious alternative.

> But perhaps I should just refer to Graham's paper above in future, since it includes list of good 5, 7 and 11-limit temperaments.

If you want something to refer to, that would be an obvious topic for a Xenwiki page--but how would you prefer the temperaments to be rated?

🔗genewardsmith <genewardsmith@...>

12/26/2011 1:36:19 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "gbreed@" <gbreed@> wrote:
> >
> > If you click on an error you get a new search with that target error.
>
> I guessed as much. What I didn't see was why "error" for a temperament is not the optimal choice to produce a high listing for that temperament.

I'm trying to work out how you can find an optimal parameter setting for making a given temperament look good, and I've not seen how as yet. It would be nice to have such a thing.

🔗dkeenanuqnetau <d.keenan@...>

12/26/2011 8:35:48 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> If you want something to refer to, that would be an obvious topic for a Xenwiki page--but how would you prefer the temperaments to be rated?
>

Thanks Gene. It would be great if you could reproduce the 5 and 7 limit tables of Middle Path (or at least their "main sequence") and then generate an analogous 11 limit table.

But no need to list them in the same order as in Paul's paper. I agree that ordering them by increasing Erlich-badness would be useful. Buttons to choose whether to show them sorted by badness, damage or complexity (as in Middle Path) would be great. Or just 3 different versions of each.

For it to be analogous, its badness cutoff would need to be

complexity/k_11 + damage/10 < 1

where k_11 is chosen so that
(a) the number of temperaments is similar to the number of temperaments in the main sequences of the 5 and 7 limit tables (respectively 21 and 28) and
(b) it locally maximises the variation in k_11 that will not change the number of included temperaments. This is the "moat" idea.

And it would be extra-nice if k_11 = 36 happened to satisfy the above (deliberately vague) criteria, as there would then be a sequence k_p = 12, 24, 36.

This Xenwiki page should of course link to Paul's paper, and I suggest Graham's paper, and it should be likely to eventually come on the first page of a google search of: Erlich Middle Path.

-- Dave Keenan

🔗dkeenanuqnetau <d.keenan@...>

12/26/2011 9:07:33 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> I really don't know what was
> wrong with logflat error * complexity badness.

I think we had this discussion about 7 years ago. :-)

It's fine for rating temperaments for their purely mathematical properties, or even for use in things like notation, analysis or algorithmic composition, but IMO when it comes to finding temperaments that are easy to play and good to listen to, i.e. that relate to human limitations, then
(a) it admits temperaments of unplayable complexity merely because they have extremely low error, when in fact, for listening purposes a zero error is really no better than an error of about 0.5 cent, and
(b) it admits temperaments of unlistenable error (*) merely because they have extremly low complexity, when in fact, for playing purposes a zero complexity is really no better than a complexity of about 4 generators per diamond,

(*) or at least, if they _are_ interesting to listen to, this has little to do with approximating simple ratios

-- Dave Keenan

🔗dkeenanuqnetau <d.keenan@...>

12/26/2011 9:31:04 PM

More to the point, the Xenwiki page should be likely to come up on the first page of a google search of: Erlich "Middle Path Part 2".

Here's the only relevant thing that currently comes up on such a search
/tuning/topicId_76488.html#76513

-- Dave

🔗Carl Lumma <carl@...>

12/27/2011 1:14:16 AM

"dkeenanuqnetau" <d.keenan@...> wrote:

> (a) it admits temperaments of unplayable complexity merely
> because they have extremely low error, when in fact, for
> listening purposes a zero error is really no better than an
> error of about 0.5 cent, and

It admits an infinite number of temperaments so one usually
needs a complexity cutoff. If we're making a top-10 list the
cutoff can be increased until it returns 10 temperaments,
while still using the logflat idea to give 'correct' relative
ratings of those 10, and appropriate weights for complexity
between top-10 lists of different ranks.

> (b) it admits temperaments of unlistenable error (*) merely
> because they have extremly low complexity, when in fact, for
> playing purposes a zero complexity is really no better than
> a complexity of about 4 generators per diamond,

With complexity bounds 4 < n < 101 notes/oct, the top-7
11-limit rank 1 temperaments are: 31, 72, 22, 12, 5, 8, 41
in that order (once the octave size is optimized). Seems
reasonable to me. One can always view entries like 5 and 8
as templates for circulating temperaments.

-Carl

🔗Keenan Pepper <keenanpepper@...>

12/27/2011 8:52:39 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
> Thanks Gene. It would be great if you could reproduce the 5 and 7 limit tables of Middle Path (or at least their "main sequence") and then generate an analogous 11 limit table.

Interesting note: I tried to do this with TOP-RMS (aka TE) error in place of TOP, thinking the results might be close enough. They are pretty similar, with all the well-known winners still at the top, but some weird temperaments sneak in. For example, in the 7 limit, "hexe" beats out orwell.

Keenan

🔗Mike Battaglia <battaglia01@...>

12/27/2011 9:01:10 AM

On Tue, Dec 27, 2011 at 11:52 AM, Keenan Pepper <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
> > Thanks Gene. It would be great if you could reproduce the 5 and 7 limit tables of Middle Path (or at least their "main sequence") and then generate an analogous 11 limit table.
>
> Interesting note: I tried to do this with TOP-RMS (aka TE) error in place of TOP, thinking the results might be close enough. They are pretty similar, with all the well-known winners still at the top, but some weird temperaments sneak in. For example, in the 7 limit, "hexe" beats out orwell.

Has some full comparison of the benefits of TE vs TOP ever been done like this?

-Mike

🔗Graham Breed <gbreed@...>

12/27/2011 10:08:03 AM

Mike Battaglia <battaglia01@...> wrote:

> Has some full comparison of the benefits of TE vs TOP
> ever been done like this?

I wrote code to churn out lists given different criteria.
That surely still exists, will probably still run, and
there might be output files somewhere. It's also fairly
easy, if you have the code, to get it to produce, say, a
TOP list showing each entry's place on the TE list. I
don't think anybody's done the high level work of looking
through the lists and talking about the comparisons though.

The differences are more important the higher the prime
limit. Which means the number of primes, not the size of
them, if we're getting into subgroups.

Graham

🔗genewardsmith <genewardsmith@...>

12/27/2011 11:00:44 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> But no need to list them in the same order as in Paul's paper. I agree that ordering them by increasing Erlich-badness would be useful.

What would be most useful to me on Graham's site would be the ability to order by logflat badness. This is because if I see some temperament on the list which doesn't have a write-up on the Xenwiki, I'd like to know if it's worth bothering with.

🔗Carl Lumma <carl@...>

12/27/2011 12:19:08 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> What would be most useful to me on Graham's site would be the
> ability to order by logflat badness.

Seconded. -Carl

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 8:31:14 AM

I started http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments . Probably complete, but there might be one or two temperaments that should be in there but escaped. Independent searches encouraged.

I used 42 as the coefficient there because you need it to be >40 to get miracle (which I think everyone agrees should be in there, right?), and using 42 gets a bunch of other good ones (negri, myna, mothra, octacot) without too much other junk.

Turns out 5 of the temperaments possibly need new names:

Catler+ [<12 19 28 34 42|, <0 0 0 -1 -1|]
This probably shouldn't be called "catler" because I don't think Jon Catler's guitar frettings treat 11/7 as an interval of 12-equal, so 56/55 isn't tempered out. Probably [<12 19 28 34 42|, <0 0 0 -1 -2|] should be "catler", but that was too complex to make the cut.

Lemba+ [<2 2 5 6 5|, <0 3 -1 -1 5|]
I vote that this be called simply "lemba", but others might oppose me because there's a more accurate mapping of 11 as (10,-8) rather than (5,5).

Doublewide+ [<2 1 3 4 2|, <0 4 3 3 9|]
There's already an 11-limit "doublewide" and this ain't it.

Beatles+ [<1 1 5 4 2|, <0 2 -9 -4 5|]
Frankly I was surprised that this didn't have the name "beatles" already. But, as always, there are more accurate mappings of 11, so that might upset some people.

Negri+ [<1 2 2 3 5|, <0 -4 3 -2 -15|]
This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...

Keenan

🔗genewardsmith <genewardsmith@...>

12/29/2011 10:57:29 AM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> Catler+ [<12 19 28 34 42|, <0 0 0 -1 -1|]
> This probably shouldn't be called "catler" because I don't think Jon Catler's guitar frettings treat 11/7 as an interval of 12-equal, so 56/55 isn't tempered out. Probably [<12 19 28 34 42|, <0 0 0 -1 -2|] should be "catler", but that was too complex to make the cut.

Catlat? (Though that's so obscure goggling didn't bring up the reference.)

> Lemba+ [<2 2 5 6 5|, <0 3 -1 -1 5|]
> I vote that this be called simply "lemba", but others might oppose me because there's a more accurate mapping of 11 as (10,-8) rather than (5,5).

My philosophy has always been that when you give something the same name, the tuning should not be too different nor degrade the accuracy too much. The (10, -8) temperament has a POTE generator of 232.235, closer to the 7-limit generator of 232.089 than your less accurate lemba, which has 230.974. How about waybread as a name?

> Doublewide+ [<2 1 3 4 2|, <0 4 3 3 9|]
> There's already an 11-limit "doublewide" and this ain't it.

Can't call it triplewide, alas. Fleetwood?

> Beatles+ [<1 1 5 4 2|, <0 2 -9 -4 5|]
> Frankly I was surprised that this didn't have the name "beatles" already. But, as always, there are more accurate mappings of 11, so that might upset some people.

Your Beatles+ involves a considerable drop in accuracy, making it less like an extension of 7-limit beatles. My vote would be to call it something like ringo and to call the one which tempers out 100/99 rather than 56/55 beatles.

> Negri+ [<1 2 2 3 5|, <0 -4 3 -2 -15|]
> This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...

Negru?

🔗genewardsmith <genewardsmith@...>

12/29/2011 12:00:01 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > Catler+ [<12 19 28 34 42|, <0 0 0 -1 -1|]
> > This probably shouldn't be called "catler" because I don't think Jon Catler's guitar frettings treat 11/7 as an interval of 12-equal, so 56/55 isn't tempered out. Probably [<12 19 28 34 42|, <0 0 0 -1 -2|] should be "catler", but that was too complex to make the cut.
>
> Catlat? (Though that's so obscure goggling didn't bring up the reference.)

Why did you put in [<12 19 28 0 109|, <0 0 0 1 -2|] as "catlat" when you asked about [<12 19 28 34 42|, <0 0 0 -1 -1|]?

🔗genewardsmith <genewardsmith@...>

12/29/2011 12:04:49 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Why did you put in [<12 19 28 0 109|, <0 0 0 1 -2|] as "catlat" when you asked about [<12 19 28 34 42|, <0 0 0 -1 -1|]?
>

Eh, sorry, I guess I did that and then forgot.

🔗genewardsmith <genewardsmith@...>

12/29/2011 12:18:34 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > Why did you put in [<12 19 28 0 109|, <0 0 0 1 -2|] as "catlat" when you asked about [<12 19 28 34 42|, <0 0 0 -1 -1|]?
> >
>
> Eh, sorry, I guess I did that and then forgot.
>

Hoping to contain the confusion to an acceptable level, I've put this on the Pythagorean page:

Catcall
Commas: 56/55, 81/80, 128/125

POTE generator: ~36/35 = 32.776

Map: [<12 19 28 0 8|, <0 0 0 1 1|]
EDOs: 12, 24, 36, 72ce
Badness: 0.0345

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 1:46:30 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Hoping to contain the confusion to an acceptable level, I've put this on the Pythagorean page:
>
> Catcall
> Commas: 56/55, 81/80, 128/125
>
> POTE generator: ~36/35 = 32.776
>
> Map: [<12 19 28 0 8|, <0 0 0 1 1|]
> EDOs: 12, 24, 36, 72ce
> Badness: 0.0345

This one's fine with me.

Keenan

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 2:08:21 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > Lemba+ [<2 2 5 6 5|, <0 3 -1 -1 5|]
> > I vote that this be called simply "lemba", but others might oppose me because there's a more accurate mapping of 11 as (10,-8) rather than (5,5).
>
> My philosophy has always been that when you give something the same name, the tuning should not be too different nor degrade the accuracy too much. The (10, -8) temperament has a POTE generator of 232.235, closer to the 7-limit generator of 232.089 than your less accurate lemba, which has 230.974. How about waybread as a name?

You seemed pretty okay with this one back in 2004: /tuning/topicId_53750.html#53751

> > Doublewide+ [<2 1 3 4 2|, <0 4 3 3 9|]
> > There's already an 11-limit "doublewide" and this ain't it.
>
> Can't call it triplewide, alas. Fleetwood?

I confess I wasn't familiar with either of these terms for mobile homes. Sounds fine though.

> > Beatles+ [<1 1 5 4 2|, <0 2 -9 -4 5|]
> > Frankly I was surprised that this didn't have the name "beatles" already. But, as always, there are more accurate mappings of 11, so that might upset some people.
>
> Your Beatles+ involves a considerable drop in accuracy, making it less like an extension of 7-limit beatles. My vote would be to call it something like ringo and to call the one which tempers out 100/99 rather than 56/55 beatles.

As a reductio ad absurdum, wouldn't it be even better to call http://x31eq.com/cgi-bin/rt.cgi?ets=27e_10eee&limit=11 beatles?

> > Negri+ [<1 2 2 3 5|, <0 -4 3 -2 -15|]
> > This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...
>
> Negru?

Haha, cool.

Also, there's this one I seem to have missed:

Quasisuper+ [<1 2 -3 2 1|, <0 -1 13 2 6|]

The only logical name for this one is "quasisupra". Is that acceptable?

Keenan

🔗Mike Battaglia <battaglia01@...>

12/29/2011 2:29:57 PM

On Thu, Dec 29, 2011 at 5:08 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> > > Negri+ [<1 2 2 3 5|, <0 -4 3 -2 -15|]
> > > This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...
> >
> > Negru?
>
> Haha, cool.

I don't think it's possible for me to talk about this temperament in real life.

-Mike

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 3:59:32 PM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Dec 29, 2011 at 5:08 PM, Keenan Pepper <keenanpepper@...> wrote:
> >
> > > > Negri+ [<1 2 2 3 5|, <0 -4 3 -2 -15|]
> > > > This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...
> > >
> > > Negru?
> >
> > Haha, cool.
>
> I don't think it's possible for me to talk about this temperament in real life.

But it's named in honor of Radu Negru, legendary king of Wallachia!

Keenan

🔗genewardsmith <genewardsmith@...>

12/29/2011 4:05:12 PM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > > Lemba+ [<2 2 5 6 5|, <0 3 -1 -1 5|]
> > > I vote that this be called simply "lemba", but others might oppose me because there's a more accurate mapping of 11 as (10,-8) rather than (5,5).
> >
> > My philosophy has always been that when you give something the same name, the tuning should not be too different nor degrade the accuracy too much. The (10, -8) temperament has a POTE generator of 232.235, closer to the 7-limit generator of 232.089 than your less accurate lemba, which has 230.974. How about waybread as a name?
>
> You seemed pretty okay with this one back in 2004: /tuning/topicId_53750.html#53751

That's because I liked the Fibonacci thing. You could try a Fibonacci name.

> > > Beatles+ [<1 1 5 4 2|, <0 2 -9 -4 5|]
> > > Frankly I was surprised that this didn't have the name "beatles" already. But, as always, there are more accurate mappings of 11, so that might upset some people.
> >
> > Your Beatles+ involves a considerable drop in accuracy, making it less like an extension of 7-limit beatles. My vote would be to call it something like ringo and to call the one which tempers out 100/99 rather than 56/55 beatles.
>
> As a reductio ad absurdum, wouldn't it be even better to call http://x31eq.com/cgi-bin/rt.cgi?ets=27e_10eee&limit=11 beatles?

No, because it's logflat badness is way too high.

> The only logical name for this one is "quasisupra". Is that acceptable?

Fine by me.

🔗genewardsmith <genewardsmith@...>

12/29/2011 4:07:11 PM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> > I don't think it's possible for me to talk about this temperament in real life.
>
> But it's named in honor of Radu Negru, legendary king of Wallachia!

Maybe Mike could talk about it if we named it "dracula".

🔗Mike Battaglia <battaglia01@...>

12/29/2011 4:06:55 PM

What is the name of the 531441/524288 5-limit planar temperament?
"Pythagorean temperament?"

I wonder what Paul's reaction to that will be...

-Mike

On Thu, Dec 29, 2011 at 3:18 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > > Why did you put in [<12 19 28 0 109|, <0 0 0 1 -2|] as "catlat" when you asked about [<12 19 28 34 42|, <0 0 0 -1 -1|]?
> > >
> >
> > Eh, sorry, I guess I did that and then forgot.
> >
>
> Hoping to contain the confusion to an acceptable level, I've put this on the Pythagorean page:
>
> Catcall
> Commas: 56/55, 81/80, 128/125
>
> POTE generator: ~36/35 = 32.776
>
> Map: [<12 19 28 0 8|, <0 0 0 1 1|]
> EDOs: 12, 24, 36, 72ce
> Badness: 0.0345

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 4:19:39 PM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> What is the name of the 531441/524288 5-limit planar temperament?
> "Pythagorean temperament?"
>
> I wonder what Paul's reaction to that will be...

No, that's Compton. Right?

Keenan

🔗Mike Battaglia <battaglia01@...>

12/29/2011 4:23:02 PM

On Thu, Dec 29, 2011 at 6:59 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I don't think it's possible for me to talk about this temperament in real life.
>
> But it's named in honor of Radu Negru, legendary king of Wallachia!

How do I say this? "Nee-groo?"

We may want to stop studying the extensions of negri temperament. As
soon as we find them we have to assign them names. We're one matrix
away from ruination at this point.

-Mike

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 4:39:39 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > You seemed pretty okay with this one back in 2004: /tuning/topicId_53750.html#53751
>
> That's because I liked the Fibonacci thing. You could try a Fibonacci name.

> > As a reductio ad absurdum, wouldn't it be even better to call http://x31eq.com/cgi-bin/rt.cgi?ets=27e_10eee&limit=11 beatles?
>
> No, because it's logflat badness is way too high.

OK, you win with these two. They're "waybread" and "ringo" or whatever.

> > The only logical name for this one is "quasisupra". Is that acceptable?
>
> Fine by me.

All right.

Keenan

🔗Mike Battaglia <battaglia01@...>

12/29/2011 4:41:23 PM

On Thu, Dec 29, 2011 at 7:07 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> > > I don't think it's possible for me to talk about this temperament in real life.
> >
> > But it's named in honor of Radu Negru, legendary king of Wallachia!
>
> Maybe Mike could talk about it if we named it "dracula".

"I like the exotic colors of dracula temperament" is something I could
see myself saying out loud.

-Mike

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 4:43:43 PM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Dec 29, 2011 at 6:59 PM, Keenan Pepper <keenanpepper@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > I don't think it's possible for me to talk about this temperament in real life.
> >
> > But it's named in honor of Radu Negru, legendary king of Wallachia!
>
> How do I say this? "Nee-groo?"

I was thinking negg-roo.

> We may want to stop studying the extensions of negri temperament. As
> soon as we find them we have to assign them names. We're one matrix
> away from ruination at this point.

Hahaha.

Keenan

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 4:46:29 PM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > What is the name of the 531441/524288 5-limit planar temperament?
> > "Pythagorean temperament?"
> >
> > I wonder what Paul's reaction to that will be...
>
> No, that's Compton. Right?

Wait, you said planar... but you also said 5-limit... does not compute...

Keenan

🔗Mike Battaglia <battaglia01@...>

12/29/2011 4:50:08 PM

Sorry, meant 5-limit linear. It looks like Compton is 7-limit though.

Sent from my iPhone

On Dec 29, 2011, at 7:46 PM, Keenan Pepper <keenanpepper@gmail.com> wrote:

Wait, you said planar... but you also said 5-limit... does not compute...

Keenan

🔗Keenan Pepper <keenanpepper@...>

12/29/2011 4:57:54 PM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Sorry, meant 5-limit linear. It looks like Compton is 7-limit though.

It does have a 7-limit version, but the 5-limit temperament where the 3/2s are tuned to 12edo and the generator is 81/80 is also "compton".

Keenan

🔗Herman Miller <hmiller@...>

12/29/2011 7:55:07 PM

On 12/29/2011 11:31 AM, Keenan Pepper wrote:

> Lemba+ [<2 2 5 6 5|,<0 3 -1 -1 5|]
> I vote that this be called simply "lemba", but others might oppose me because there's a more accurate mapping of 11 as (10,-8) rather than (5,5).

This agrees with the 13-limit lemba that I posted back in 2004.

[<2 2 5 6 5 7|, <0 3 -1 -1 5 1|]

> Beatles+ [<1 1 5 4 2|,<0 2 -9 -4 5|]
> Frankly I was surprised that this didn't have the name "beatles" already. But, as always, there are more accurate mappings of 11, so that might upset some people.

Strange that this isn't named yet, since the neutral third generator is one of the features of beatles, and neutral thirds are associated with the 11 limit. If you're using beatles, chances are you care more about low complexity than accuracy.

> Negri+ [<1 2 2 3 5|,<0 -4 3 -2 -15|]
> This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...

I never liked the "change one letter" names anyway. Anagrams might be easier to keep straight.

Some other temperaments you might want to check out to see if they're worth including:

blacksmith [<5 8 12 14 18|, <0 0 -1 0 -2|]
hitchcock [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
unnamed 11-limit tetracot [<1 1 1 4 2|, <0 4 9 -8 10|]
monkey [<1 1 1 5 2|, <0 4 9 -15 10|]
unnamed 11-limit semaphore [<1 2 4 3 2|, <0 -2 -8 -1 7|]
liese [<1 3 8 8 3|, <0 -3 -12 -11 1|]
mosura [<1 1 0 3 -1|, <0 3 12 -1 23|]

(I would've preferred taking advantage of the fact we've got two names for cynder/mothra, instead of just using the Japanese pronunciation of "mothra", but that's what's on the wiki.)

🔗Herman Miller <hmiller@...>

12/29/2011 8:09:33 PM

On 12/29/2011 7:39 PM, Keenan Pepper wrote:
>
>
> --- In tuning@yahoogroups.com, "genewardsmith"<genewardsmith@...> wrote:
>>> You seemed pretty okay with this one back in 2004: /tuning/topicId_53750.html#53751
>>
>> That's because I liked the Fibonacci thing. You could try a Fibonacci name.
>
>>> As a reductio ad absurdum, wouldn't it be even better to call http://x31eq.com/cgi-bin/rt.cgi?ets=27e_10eee&limit=11 beatles?
>>
>> No, because it's logflat badness is way too high.
>
> OK, you win with these two. They're "waybread" and "ringo" or whatever.

Um, "waybread"? No.

🔗genewardsmith <genewardsmith@...>

12/29/2011 8:14:01 PM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> Um, "waybread"? No.

Why not, and what else?

🔗Keenan Pepper <keenanpepper@...>

12/30/2011 6:26:46 AM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> On 12/29/2011 11:31 AM, Keenan Pepper wrote:
>
> > Lemba+ [<2 2 5 6 5|,<0 3 -1 -1 5|]
> > I vote that this be called simply "lemba", but others might oppose me because there's a more accurate mapping of 11 as (10,-8) rather than (5,5).
>
> This agrees with the 13-limit lemba that I posted back in 2004.
>
> [<2 2 5 6 5 7|, <0 3 -1 -1 5 1|]

Yeah, I think this ought to be "lemba" because of that precedent alone.

> > Beatles+ [<1 1 5 4 2|,<0 2 -9 -4 5|]
> > Frankly I was surprised that this didn't have the name "beatles" already. But, as always, there are more accurate mappings of 11, so that might upset some people.
>
> Strange that this isn't named yet, since the neutral third generator is
> one of the features of beatles, and neutral thirds are associated with
> the 11 limit. If you're using beatles, chances are you care more about
> low complexity than accuracy.

This is what I was originally thinking too. However, 49/40 and 64/49 are well known to be the simplest 7-limit "neutral thirds", and they become equal if the comma 2401/2400 is tempered out. If you temper out both 2401/2400 and 64/63, then bam!, you get beatles.

Also, the interval to which 11/8 is being mapped, in the less-accurate beatles+, is already 7/5. Mike Battaglia pointed that out to me as a characteristic feature of beatles temperament. 7/5 / (9/8) is equal to the neutral third generator.

So by tempering out 56/55 what you're doing is taking this neutral thirds structure, which is already pretty simple in 7-limit beatles, and making it even simpler by identifying the generator with 11/9. This is a "good" thing to do in that it gets the resulting temperament onto this list, but it's certainly not the only way to do it. This is quite a different situation from mohajira, where 11/9 is just begging to be mapped to the generator.

> > Negri+ [<1 2 2 3 5|,<0 -4 3 -2 -15|]
> > This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...
>
> I never liked the "change one letter" names anyway. Anagrams might be
> easier to keep straight.
>
> Some other temperaments you might want to check out to see if they're
> worth including:
>
> blacksmith [<5 8 12 14 18|, <0 0 -1 0 -2|]
> hitchcock [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
> unnamed 11-limit tetracot [<1 1 1 4 2|, <0 4 9 -8 10|]
> monkey [<1 1 1 5 2|, <0 4 9 -15 10|]
> unnamed 11-limit semaphore [<1 2 4 3 2|, <0 -2 -8 -1 7|]
> liese [<1 3 8 8 3|, <0 -3 -12 -11 1|]
> mosura [<1 1 0 3 -1|, <0 3 12 -1 23|]
>
> (I would've preferred taking advantage of the fact we've got two names
> for cynder/mothra, instead of just using the Japanese pronunciation of
> "mothra", but that's what's on the wiki.)

These are all pretty close to the badness cutoff, especially liese (which apparently is actually called "liesel"?), and semaphore+, but none actually makes the cut.

Keenan

🔗Herman Miller <hmiller@...>

12/30/2011 8:47:55 AM

On 12/29/2011 11:14 PM, genewardsmith wrote:
>
>
> --- In tuning@yahoogroups.com, Herman Miller<hmiller@...> wrote:
>
>> Um, "waybread"? No.
>
> Why not, and what else?

I've already been calling the 13-limit version "lemba", as I mentioned. Also, the name "waybread" tries to make a connection between "lemba" and "lembas", which doesn't make sense. Lemba temperament is used by Zireen from an island on the planet Rishai, not by Elves of Middle-Earth.

🔗Herman Miller <hmiller@...>

12/30/2011 8:50:57 AM

On 12/30/2011 9:26 AM, Keenan Pepper wrote:
>
>
> --- In tuning@yahoogroups.com, Herman Miller<hmiller@...> wrote:
>> Strange that this isn't named yet, since the neutral third
>> generator is one of the features of beatles, and neutral thirds are
>> associated with the 11 limit. If you're using beatles, chances are
>> you care more about low complexity than accuracy.
>
> This is what I was originally thinking too. However, 49/40 and 64/49
> are well known to be the simplest 7-limit "neutral thirds", and they
> become equal if the comma 2401/2400 is tempered out. If you temper
> out both 2401/2400 and 64/63, then bam!, you get beatles.
>
> Also, the interval to which 11/8 is being mapped, in the
> less-accurate beatles+, is already 7/5. Mike Battaglia pointed that
> out to me as a characteristic feature of beatles temperament. 7/5 /
> (9/8) is equal to the neutral third generator.
>
> So by tempering out 56/55 what you're doing is taking this neutral
> thirds structure, which is already pretty simple in 7-limit beatles,
> and making it even simpler by identifying the generator with 11/9.
> This is a "good" thing to do in that it gets the resulting
> temperament onto this list, but it's certainly not the only way to do
> it. This is quite a different situation from mohajira, where 11/9 is
> just begging to be mapped to the generator.

Certainly in a case like this, since none of the 11-limit temperaments have claimed the name "beatles" yet, and this one comes up in a low badness search, I think that's a good case for just naming it "beatles". On the other hand, considering that beatles got its name from the 19/64 generator (although The Beatles' first album was actually released in 1963), if you're going to use all 64 notes, you could make a case for using the more accurate tuning of 11. So maybe "quarrymen" for the simpler 11-limit one?

>> Some other temperaments you might want to check out to see if
>> they're worth including:
>>
>> blacksmith [<5 8 12 14 18|, <0 0 -1 0 -2|]
>> hitchcock [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
>> unnamed 11-limit tetracot [<1 1 1 4 2|, <0 4 9 -8 10|]
>> monkey [<1 1 1 5 2|, <0 4 9 -15 10|]
>> unnamed 11-limit semaphore [<1 2 4 3 2|, <0 -2 -8 -1 7|]
>> liese [<1 3 8 8 3|, <0 -3 -12 -11 1|]
>> mosura [<1 1 0 3 -1|, <0 3 12 -1 23|]
>>
>>
>> (I would've preferred taking advantage of the fact we've got two
>> names for cynder/mothra, instead of just using the Japanese
>> pronunciation of "mothra", but that's what's on the wiki.)
>
> These are all pretty close to the badness cutoff, especially liese
> (which apparently is actually called "liesel"?), and semaphore+, but
> none actually makes the cut.

Well, the cutoff has to cut off somewhere. Out of curiosity, could you list some of the other temperaments that didn't quite make it?

🔗Keenan Pepper <keenanpepper@...>

12/30/2011 9:11:15 AM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> Well, the cutoff has to cut off somewhere. Out of curiosity, could you
> list some of the other temperaments that didn't quite make it?

Sure. We have:

Superkleismic (the 2.7.11 subgroup version of which goes by the name "orgone")

Maqamic

Domineering (the dominant extension that tempers out 45/44)

The 11-limit extension of semiaug that tempers out 56/55 (should just be called "semiaug" I think...) [<3 5 7 9 11|, <0 -2 0 -5 -5|]

Opossum

Wuerschmidt

Liesel (the liese extension you mentioned)

Diminished

Tetracot++ [<1 1 1 0 2|, <0 4 9 19 10|]

Prajapati (31edo but with extra notes for the prime 11) [<31 49 72 87 107|, <0 0 0 0 1|]

The semaphore extension that tempers out 56/55 [<1 2 4 3 2|, <0 -2 -8 -1 7|]

🔗gbreed@...

12/30/2011 9:39:06 AM

I do have a 2.3.7.11 Beatles. It uses the simpler mapping. 17&10 (optimal mappings or unambiguous without the 5). 243:242 tempered out

Graham

------Original message------
From: Herman Miller <hmiller@...m>
To: <tuning@yahoogroups.com>
Date: Friday, December 30, 2011 11:50:57 AM GMT-0500
Subject: Re: [tuning] Re: Middle Path 11-limit temperaments?

On 12/30/2011 9:26 AM, Keenan Pepper wrote:
>
>
> --- In tuning@...m, Herman Miller<hmiller@...> wrote:
>> Strange that this isn't named yet, since the neutral third
>> generator is one of the features of beatles, and neutral thirds are
>> associated with the 11 limit. If you're using beatles, chances are
>> you care more about low complexity than accuracy.
>
> This is what I was originally thinking too. However, 49/40 and 64/49
> are well known to be the simplest 7-limit "neutral thirds", and they
> become equal if the comma 2401/2400 is tempered out. If you temper
> out both 2401/2400 and 64/63, then bam!, you get beatles.
>
> Also, the interval to which 11/8 is being mapped, in the
> less-accurate beatles+, is already 7/5. Mike Battaglia pointed that
> out to me as a characteristic feature of beatles temperament. 7/5 /
> (9/8) is equal to the neutral third generator.
>
> So by tempering out 56/55 what you're doing is taking this neutral
> thirds structure, which is already pretty simple in 7-limit beatles,
> and making it even simpler by identifying the generator with 11/9.
> This is a "good" thing to do in that it gets the resulting
> temperament onto this list, but it's certainly not the only way to do
> it. This is quite a different situation from mohajira, where 11/9 is
> just begging to be mapped to the generator.

Certainly in a case like this, since none of the 11-limit temperaments
have claimed the name "beatles" yet, and this one comes up in a low
badness search, I think that's a good case for just naming it "beatles".
On the other hand, considering that beatles got its name from the 19/64
generator (although The Beatles' first album was actually released in
1963), if you're going to use all 64 notes, you could make a case for
using the more accurate tuning of 11. So maybe "quarrymen" for the
simpler 11-limit one?

Well, the cutoff has to cut off somewhere. Out of curiosity, could you
list some of the other temperaments that didn't quite make it?

------------------------------------

🔗genewardsmith <genewardsmith@...>

12/30/2011 11:10:30 AM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> Lemba temperament is used by Zireen
> from an island on the planet Rishai, not by Elves of Middle-Earth.

And you know elves don't use lemba how, exactly?

🔗genewardsmith <genewardsmith@...>

12/30/2011 11:13:34 AM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> So maybe "quarrymen" for the
> simpler 11-limit one?

That gets my vote. I don't like the idea of calling clearly different temperaments by the same name; I think the name should go to what can be seen as an extension of the same temperament. Of course, as eg with meantone/meanpop, sometimes you do get two.

🔗dkeenanuqnetau <d.keenan@...>

12/30/2011 6:59:18 PM

Great work Keenan. Thanks.

I think the list is too long, with 45 temperaments in the main sequence as compared with 21 and 28 for 5 and 7 limit main sequences. I'd say it should not have more than 35 temperaments max (linear progression of temperament counts).

And I can't help thinking that with more than 800 temperament names now in Graham's database, if something doesn't have a name by now it can't be very interesting. As usual I'm astonished at how much of the subsequent discussion revolved around naming the new temperaments that popped up, rather than whether they ought to be on this list in the first place.

This list doesn't have to be all things to all people. There can be other 11-limit lists. This one is merely attempting to continue on from "Middle Path". If it is biased toward low complexity, so be it, provided that it has (in some sense) the _same_ bias as the 5 and 7 limit lists from "Middle Path".

So if that means that we have to leave Miracle off the list, then I say so be it. It really is quite complex at the 11 limit. Only Blackjack (Miracle-21) has been used in non-algorithmic composition as far as I know, and that does not include a complete 11-limit diamond. Unless you want to claim Partch's 43 as a detempered modified Miracle-41.

Is it possible that Miracle could be included as a "bonus" 11-limit temperament, without having to also include a whole host of others? The criterion for bonus temperaments seems to be much lower _product_ badness than anything in the main sequence. Where "product badness" is damage _multiplied_by_ complexity, where damage and complexity are as used by Paul Erlich in Middle Path.

I guess at this stage I could actually ask Paul what _he_ thinks.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
>
>
> I started http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments . Probably complete, but there might be one or two temperaments that should be in there but escaped. Independent searches encouraged.
>
> I used 42 as the coefficient there because you need it to be >40 to get miracle (which I think everyone agrees should be in there, right?), and using 42 gets a bunch of other good ones (negri, myna, mothra, octacot) without too much other junk.
>
> Turns out 5 of the temperaments possibly need new names:
>
> Catler+ [<12 19 28 34 42|, <0 0 0 -1 -1|]
> This probably shouldn't be called "catler" because I don't think Jon Catler's guitar frettings treat 11/7 as an interval of 12-equal, so 56/55 isn't tempered out. Probably [<12 19 28 34 42|, <0 0 0 -1 -2|] should be "catler", but that was too complex to make the cut.
>
> Lemba+ [<2 2 5 6 5|, <0 3 -1 -1 5|]
> I vote that this be called simply "lemba", but others might oppose me because there's a more accurate mapping of 11 as (10,-8) rather than (5,5).
>
> Doublewide+ [<2 1 3 4 2|, <0 4 3 3 9|]
> There's already an 11-limit "doublewide" and this ain't it.
>
> Beatles+ [<1 1 5 4 2|, <0 2 -9 -4 5|]
> Frankly I was surprised that this didn't have the name "beatles" already. But, as always, there are more accurate mappings of 11, so that might upset some people.
>
> Negri+ [<1 2 2 3 5|, <0 -4 3 -2 -15|]
> This is neither "negri" nor "negric" nor "negril". We're running out of names that start with "negr-" but are not offensive...
>
> Keenan
>

🔗Mike Battaglia <battaglia01@...>

12/30/2011 7:38:05 PM

On Dec 30, 2011, at 9:59 PM, "dkeenanuqnetau" <d.keenan@...>
wrote:

And I can't help thinking that with more than 800 temperament names now in
Graham's database, if something doesn't have a name by now it can't be very
interesting.

That's probably more true now than it was a few months ago, but there are
some noteworthy reasons why this is not the case:

1) Subgroups. Many of the best subgroup temperaments were discovered
earlier this year, and there is a seemingly limitless supply of them. I
don't just mean subgroup versions of existing things, but rather
temperaments that fly completely under the radar until you take the
subgroup perspective on what's going on. Examples: machine, bleu, a-team,
etc.

2) Many of the most popular 5-limit temperaments are relatively high in
error, ex. mavila, blackwood, etc. I don't think 11-limit temperaments like
these have been fully explored.

3) It seems to be rather often that I'll be playing in some EDO, and play
some MOS and then exploit some tempered relation to get to some prime, and
realize the particular relation I chose corresponds to a temperament that
doesn't have a name. The fact that rank-2 temperaments are codimension 3 in
the 11-limit means that there's a ton of variety in how you design things.
I suspect that as I play more in 22-EDO, many of my "go-to" 11-limit
systems will end up being random obscure 11-limit extensions of
temperaments that people aren't thinking about which have strange names (or
no name yet) but which had some random tempered relationship which was
musically useful in some specific situation.

4) I can already think of temperaments that don't have names. Like the one
in 17-EDO where the generator is the ~7/6. At least I don't think it has a
name.

-Mike

__,_._,__

🔗genewardsmith <genewardsmith@...>

12/30/2011 8:30:11 PM

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

> 4) I can already think of temperaments that don't have names. Like the one
> in 17-EDO where the generator is the ~7/6. At least I don't think it has a
> name.

Should it have? You could always call it 4&17.

🔗Keenan Pepper <keenanpepper@...>

12/30/2011 9:48:11 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
> Great work Keenan. Thanks.
>
> I think the list is too long, with 45 temperaments in the main sequence as compared with 21 and 28 for 5 and 7 limit main sequences. I'd say it should not have more than 35 temperaments max (linear progression of temperament counts).

Yeah, I was sort of thinking this. If I make the coefficient 36 I only get 15 temperaments; if I make it 40 I get 34 of them, which seems about right for this consideration. We do lose a lot of temperaments (besides miracle) that people often talk about, namely cassandra, negri, lemba, myna, mothra, and octacot. But perhaps we should think of that as telling us something, in accord with what you wrote about this not having to be the ultimate 11-limit list.

Here's the "pruned" table: http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments+%28pruned%29

The proposed "catcall", "fleetwood", and "quasisupra" are still in there.

Keenan

🔗gbreed@...

12/31/2011 2:52:20 AM

I've written music in Miracle outside Blackjack. When I Set Out For Lyonnesse is an example. The score's online.

Graham

------Original message------
From: dkeenanuqnetau <d.keenan@...>
To: <tuning@yahoogroups.com>
Date: Saturday, December 31, 2011 2:59:18 AM GMT-0000
Subject: [tuning] Re: Middle Path 11-limit temperaments?

Great work Keenan. Thanks.

I guess at this stage I could actually ask Paul what _he_ thinks.

-- Dave Keenan

------------------------------------

🔗dkeenanuqnetau <d.keenan@...>

12/31/2011 3:52:17 AM

Thanks Keenan.

Now we just need the columns for TOP period and generator.

Is it mathematically justifiable to include only miracle and hemiennealimmal as bonus temperaments?

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

12/31/2011 8:43:14 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
> Thanks Keenan.
>
> Now we just need the columns for TOP period and generator.
>
> Is it mathematically justifiable to include only miracle and hemiennealimmal as bonus temperaments?

You want justification for this absurd list? My complaint is what it's always been--Paul's procedure is tendentious, pushing a particular point of view as to what temperaments ought to interest us.

🔗Mike Battaglia <battaglia01@...>

12/31/2011 9:23:17 AM

Tangential question: have you ever considered writing a more lengthy
formal text on all of this yourself? I would strongly encourage it,
and offer my efforts to help such a task in any way I can.

I mean, let's say I just copied and pasted a ton of random Wiki pages
into a nice journal-style template, and made it look all pretty, and
then just left it lying around somewhere, in case any nearby
mathematician might so happen to just feel like perhaps giving it a
look over and writing an intro and polishing some rough edges...

(And lest people think I'm trying to sneak my way into "helping" for
the sake of gaining a dubious co-author credit or something like that,
I don't want any "credit" at all. I just want this sort of thing to
exist. I would only want credit if we were going to do this as a
larger community venture that involves some of the things I've worked
on, but this particular suggestion was purely to Gene as an analogy to
Paul's "Middle Path" paper.)

-Mike

On Sat, Dec 31, 2011 at 11:43 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
> >
> > Thanks Keenan.
> >
> > Now we just need the columns for TOP period and generator.
> >
> > Is it mathematically justifiable to include only miracle and hemiennealimmal as bonus temperaments?
>
> You want justification for this absurd list? My complaint is what it's always been--Paul's procedure is tendentious, pushing a particular point of view as to what temperaments ought to interest us.

🔗genewardsmith <genewardsmith@...>

12/31/2011 9:48:53 AM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Tangential question: have you ever considered writing a more lengthy
> formal text on all of this yourself? I would strongly encourage it,
> and offer my efforts to help such a task in any way I can.

You've noticed, I suppose, that my contributions to the Xenwiki more or less amount to a book already?

🔗Mike Battaglia <battaglia01@...>

12/31/2011 11:14:31 AM

Yeah, that was why I wrote the whole thing about offering to assemble all
of it into a neater, pretty-printed document. What say you to that?

Sent from my iPhone

On Dec 31, 2011, at 12:48 PM, genewardsmith <genewardsmith@sbcglobal.net>
wrote:

--- In <tuning%40yahoogroups.com>tuning@yahoogroups.com, Mike Battaglia
<battaglia01@...> wrote:
>
> Tangential question: have you ever considered writing a more lengthy
> formal text on all of this yourself? I would strongly encourage it,
> and offer my efforts to help such a task in any way I can.

You've noticed, I suppose, that my contributions to the Xenwiki more or
less amount to a book already?

🔗Herman Miller <hmiller@...>

12/31/2011 11:43:26 AM

On 12/30/2011 9:59 PM, dkeenanuqnetau wrote:
> Great work Keenan. Thanks.
>

> I think the list is too long, with 45 temperaments in the main
sequence as compared with 21 and 28 for 5 and 7 limit main sequences.
I'd say it should not have more than 35 temperaments max (linear
progression of temperament counts).
>
> And I can't help thinking that with more than 800 temperament names
now in Graham's database, if something doesn't have a name by now it
can't be very interesting. As usual I'm astonished at how much of the
subsequent discussion revolved around naming the new temperaments that
popped up, rather than whether they ought to be on this list in the
first place.

I was surprised that I didn't have a name for the 6&9 temperament (triforce) when I ran across it. It seems like such a natural 11-limit extension of augmented temperament, with the neutral second generator. I ran across it back in March when Mike Battaglia was looking for a scale with "consonant chords over as many roots as possible". I probably wasn't the first one to find it, but it seems to have been neglected at any rate. With so many thousands of potential candidates for temperaments, it's perhaps not too surprising that a handful of good ones may have been overlooked. It's worth trying the searches to see what comes up.

But it's a good point that the list is rather long. I haven't played with a lot of 11-limit temperaments, so I don't have a good feel for which ones are worth mentioning. I did play around a bit with that unnamed tetracot I mentioned (7&27e), and I think that one's worth exploring. (Since monkey and bunya already have names, 7&27 looks pretty much useless, and 7d&34 doesn't have much to recommend it either, my preference would be for "tetracot" to be the name of 7&27e.) But I haven't played with all the temperaments on the list, and I probably should.

I do like the numeric names like "6&9", especially when looking over lists of temperaments for evaluation that may or may not be of any interest, but the problem with those is that one temperament may have multiple names in that system. There still are a few temperaments like 7&10, which regularly seem to pop up in searches but never attract enough interest to gain a proper name.

> This list doesn't have to be all things to all people. There can be
other 11-limit lists. This one is merely attempting to continue on from
"Middle Path". If it is biased toward low complexity, so be it, provided
that it has (in some sense) the _same_ bias as the 5 and 7 limit lists
from "Middle Path".

Makes sense.

> So if that means that we have to leave Miracle off the list, then I
say so be it. It really is quite complex at the 11 limit. Only Blackjack
(Miracle-21) has been used in non-algorithmic composition as far as I
know, and that does not include a complete 11-limit diamond. Unless you
want to claim Partch's 43 as a detempered modified Miracle-41.
>
> Is it possible that Miracle could be included as a "bonus" 11-limit
temperament, without having to also include a whole host of others? The
criterion for bonus temperaments seems to be much lower _product_
badness than anything in the main sequence. Where "product badness" is
damage _multiplied_by_ complexity, where damage and complexity are as
used by Paul Erlich in Middle Path.

I think it's worth including miracle as a "bonus" temperament from the circumstances of its discovery (and rediscovery) alone, if it turns out to be not good enough to make the list on its own merits. Is it a good enough improvement in accuracy over orwell to make up for the increase in complexity? I think it does make sense to include hemiennealimmal as a "bonus" temperament because of how dramatic the improvement in accuracy is over the relatively small increase in complexity, but you're looking at a 72-note scale at minimum to do anything at all with hemiennealimmal.

🔗Herman Miller <hmiller@...>

12/31/2011 12:31:59 PM

On 12/31/2011 12:48 AM, Keenan Pepper wrote:
>
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau"<d.keenan@...>
> wrote:
>>
>> Great work Keenan. Thanks.
>>
>> I think the list is too long, with 45 temperaments in the main
>> sequence as compared with 21 and 28 for 5 and 7 limit main
>> sequences. I'd say it should not have more than 35 temperaments max
>> (linear progression of temperament counts).
>
> Yeah, I was sort of thinking this. If I make the coefficient 36 I
> only get 15 temperaments; if I make it 40 I get 34 of them, which
> seems about right for this consideration. We do lose a lot of
> temperaments (besides miracle) that people often talk about, namely
> cassandra, negri, lemba, myna, mothra, and octacot. But perhaps we
> should think of that as telling us something, in accord with what you
> wrote about this not having to be the ultimate 11-limit list.

Cassandra is talked about mainly because it's a schismatic temperament, and those were among the first to be explored. Lemba isn't especially a good 11-limit temperament, and I think it barely made it into Paul's 7-limit list, so it's not much of a loss. I'm a bit surprised myna didn't make the list, but it's a bit on the complex side, so it might pop up again in higher temperament searches where it does well (similarly with mothra and octacot).

Vigintiduo is interesting in that it ranks much higher on this list than I would have expected based on the way I've been ranking temperaments. It looks like a case where the complexity measure gives weird results because of all the zeroes in the wedgie.

> Here's the "pruned" table:
> http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments+%28pruned%29
>
> The proposed "catcall", "fleetwood", and "quasisupra" are still in
> there.
>
> Keenan

🔗Mike Battaglia <battaglia01@...>

12/31/2011 12:58:51 PM

On Sat, Dec 31, 2011 at 2:43 PM, Herman Miller <hmiller@...> wrote:
>
> I was surprised that I didn't have a name for the 6&9 temperament
> (triforce) when I ran across it. It seems like such a natural 11-limit
> extension of augmented temperament, with the neutral second generator. I
> ran across it back in March when Mike Battaglia was looking for a scale
> with "consonant chords over as many roots as possible". I probably
> wasn't the first one to find it, but it seems to have been neglected at
> any rate. With so many thousands of potential candidates for
> temperaments, it's perhaps not too surprising that a handful of good
> ones may have been overlooked. It's worth trying the searches to see
> what comes up.

I don't remember posting about it, but triforce is one of my favorite
temperaments, especially for its melodic properties. The LLsLLsLLs
mode is obviously great, but so are its MODMOS's, such as LsLLsLLLs.

-Mike

🔗Herman Miller <hmiller@...>

12/31/2011 5:24:26 PM

On 12/31/2011 12:48 AM, Keenan Pepper wrote:

> Here's the "pruned" table: http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments+%28pruned%29

I sorted a bunch of temperaments in a spreadsheet and found another one that should be on the list:

http://x31eq.com/cgi-bin/rt.cgi?ets=2%2613p&limit=11

Name: unknown (2&13)
Complexity: 20.50
TOP damage: 4.51
Mapping: [<1 3 0 0 3|, <0 -3 5 6 1|]
Commas: 56/55, 64/63, 77/75, 121/120, 392/375, 441/440...

The generators are 1195.644860 and 559.358949.

🔗genewardsmith <genewardsmith@...>

12/31/2011 6:49:09 PM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Yeah, that was why I wrote the whole thing about offering to assemble all
> of it into a neater, pretty-printed document. What say you to that?

It's fine by me, but such a project should probably be updated from time to time.

🔗Herman Miller <hmiller@...>

12/31/2011 7:14:53 PM

On 12/31/2011 11:43 AM, genewardsmith wrote:
>
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau"<d.keenan@...> wrote:
>>
>> Thanks Keenan.
>>
>> Now we just need the columns for TOP period and generator.
>>
>> Is it mathematically justifiable to include only miracle and hemiennealimmal as bonus temperaments?
>
> You want justification for this absurd list? My complaint is what it's always been--Paul's procedure is tendentious, pushing a particular point of view as to what temperaments ought to interest us.

Absurd? I've always found the Middle Path lists to be a useful starting point. They don't have a lot of extreme temperaments which may be of specialized interest (some of my favorite ones aren't on the lists), but they give you a taste of what's possible, and the ones that do make the list are mostly good ones. My criteria for evaluation are somewhat different, but there's a good deal of overlap with Paul's lists.

My main criticism is that the error and complexity scaling factors are arbitrary. Take the 5-limit list and compare with this list based on complexity / 15 + damage / 5 < 1:

5&7 meantone [<1 2 4|, <0 -1 -4|] <<1 4 4||
3&9 augmented [<3 5 7|, <0 -1 0|] <<3 0 -7||
7&8 porcupine [<1 2 3|, <0 -3 -5|] <<3 5 1||
2&10 srutal [<2 3 5|, <0 1 -2|] <<2 -4 -11||
3&16 magic [<1 0 2|, <0 5 1|] <<5 1 -10||
4&15 hanson [<1 0 1|, <0 6 5|] <<6 5 -6||
1&9 negri [<1 2 2|, <0 -4 3|] <<4 -3 -14||
7&27 tetracot [<1 1 1|, <0 4 9|] <<4 9 5||
5&17 superpyth [<1 2 6|, <0 -1 -9|] <<1 9 12||
12&17 helmholtz [<1 2 -1|, <0 -1 8|] <<1 -8 -15||
8&19 sensi [<1 -1 -1|, <0 7 9|] <<7 9 -2||
1&11 passion [<1 2 2|, <0 -5 4|] <<5 -4 -18||
3&28 wï¿½rschmidt [<1 -1 2|, <0 8 1|] <<8 1 -17||
12&48 compton [<12 19 28|, <0 0 -1|] <<0 12 19||
19&39 alicorn [<1 2 3|, <0 -8 -13|] <<8 13 2||
7&39 amity [<1 3 6|, <0 -5 -13|] <<5 13 9||
5&29 [<1 2 5|, <0 -2 -13|] <<2 13 16||
15&16 valentine [<1 1 2|, <0 9 5|] <<9 5 -13||
9&13 orson [<1 0 3|, <0 7 -3|] <<7 -3 -21||
8&26 [<2 2 3|, <0 5 7|] <<10 14 -1||

Less complex temperaments like dicot and mavila are absent, but new temperaments with lower error have been added to the list. Compare this with a list of "grade A" or "gold medal" temperaments, which gives better results if you're looking for high accuracy temperaments:

1&2 father [<1 2 2|, <0 -1 1|] <<1 -1 -4||
3&4 dicot [<1 1 2|, <0 2 1|] <<2 1 -3||
5&7 meantone [<1 2 4|, <0 -1 -4|] <<1 4 4||
2&10 srutal [<2 3 5|, <0 1 -2|] <<2 -4 -11||
4&15 hanson [<1 0 1|, <0 6 5|] <<6 5 -6||
12&17 helmholtz [<1 2 -1|, <0 -1 8|] <<1 -8 -15||
16&18 vishnu [<2 4 5|, <0 -7 -3|] <<14 6 -23||
25&31 luna [<1 4 2|, <0 -15 2|] <<15 -2 -38||
27&45 ennealimmal [<9 15 22|, <0 -2 -3|] <<18 27 1||
22&52 kwazy [<2 1 6|, <0 8 -5|] <<16 -10 -53||
53&188 monzismic [<1 2 10|, <0 -2 -37|] <<2 37 54||
26&145 senior [<1 11 19|, <0 -35 -62|] <<35 62 17||
71&84 pirate [<1 -6 0|, <0 49 15|] <<49 15 -90||
7&381 raider [<1 -9 -26|, <0 37 99|] <<37 99 71||
12&576 atomic [<12 19 28|, <0 1 -7|] <<12 -84 -161||

This misses out on a lot of useful temperaments, but most of the "good" ones are in the first 5 grades (A-E) if you rank them by comparing temperaments against each other. (I use different measures of error and complexity for ranking, but my 5-limit list is similar to this, omitting ennealimmal and senior.)

So we may have better ways to evaluate temperaments now, but I don't see any harm in following the Middle Path and seeing where it leads. We could end up finding things we missed, like that 2&13 which looks pretty nice.

🔗genewardsmith <genewardsmith@...>

12/31/2011 8:31:04 PM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> > You want justification for this absurd list? My complaint is what it's always been--Paul's procedure is tendentious, pushing a particular point of view as to what temperaments ought to interest us.
>
> Absurd? I've always found the Middle Path lists to be a useful starting
> point.

I have not. It pushes a particular point of view, that temperaments should be low in complexity, which is useless to me. I pointed out at the time, and it remains true, that if you want a list for *all of us*, a better way is to use logflat badness with error and complexity cutoffs.

> Less complex temperaments like dicot and mavila are absent, but new
> temperaments with lower error have been added to the list. Compare this
> with a list of "grade A" or "gold medal" temperaments, which gives
> better results if you're looking for high accuracy temperaments:

Simply listing gold, silver and bronze over a range defined by cutoffs for complexity and error gives better results, period.

> So we may have better ways to evaluate temperaments now, but I don't see
> any harm in following the Middle Path and seeing where it leads. We
> could end up finding things we missed, like that 2&13 which looks pretty
> nice.

I think that's fine, but I object to it being promoted as the One True Way.

🔗dkeenanuqnetau <d.keenan@...>

12/31/2011 9:32:53 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@> wrote:
> > Absurd? I've always found the Middle Path lists to be a useful starting
> > point.
>
> I have not. It pushes a particular point of view, that temperaments should be low in complexity, which is useless to me.

So if a point of view is useless to you, it's absurd?

> I pointed out at the time, and it remains true, that if you want a list for *all of us*, a better way is to use logflat badness with error and complexity cutoffs.
>

What's absurd is your failure to recognise that you are merely pushing another "particular point of view". And a fine one it is too.

> > So we may have better ways to evaluate temperaments now, but I don't see
> > any harm in following the Middle Path and seeing where it leads. We
> > could end up finding things we missed, like that 2&13 which looks pretty
> > nice.

> I think that's fine, but I object to it being promoted as the One True Way.
>

Please point us to where in this thread the evaluation method of the Middle Path paper was promoted as the "One True Way".

Could it be you're just annoyed that we don't all bow down and worship logflat badness with error and complexity cutoffs as the One True way? Fine though it is.

-- Dave Keenan

🔗Keenan Pepper <keenanpepper@...>

12/31/2011 10:00:45 PM

My impression was that the bonus temperaments needed no mathematical justification at all. They're simply other really good temperaments that didn't make the list because nothing that low in error could possibly make the list, and are deemed worth mentioning.

Miracle and hemiennealimmal seem to fit this to a T. Any other *uniquely* efficient temperaments worth mentioning?

Keenan

🔗Keenan Pepper <keenanpepper@...>

12/31/2011 10:07:53 PM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> I sorted a bunch of temperaments in a spreadsheet and found another one
> that should be on the list:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=2%2613p&limit=11
>
> Name: unknown (2&13)
> Complexity: 20.50
> TOP damage: 4.51
> Mapping: [<1 3 0 0 3|, <0 -3 5 6 1|]
> Commas: 56/55, 64/63, 77/75, 121/120, 392/375, 441/440...
>
> The generators are 1195.644860 and 559.358949.

You're right, this should even be in the pruned list. I have referred to this by the stupid throwaway name "notliese". It deserves a better one.

Like liese, this temperament has an omnitetrachordal scale, LssLsssss, that's quite reminiscent of ancient Greek enharmonic scales (but with the 9/8 divided in three parts).

Keenan

🔗genewardsmith <genewardsmith@...>

12/31/2011 11:03:27 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> So if a point of view is useless to you, it's absurd?

I objected then and I object now to having my point of view dismissed.
It's not a one-size-fits-all tuning universe, or at least I don't think it should be. And any list which says the best temperament around is hedgehog strikes me as fairly absurd. Do we really want to say hedgehog is all that special? When Paul did this, I thought he made a point of saying his badness metric wasn't really supposed to measure badness, but was just a way of coming up with a list.

🔗dkeenanuqnetau <d.keenan@...>

12/31/2011 11:03:31 PM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> My impression was that the bonus temperaments needed no mathematical justification at all. They're simply other really good temperaments that didn't make the list because nothing that low in error could possibly make the list, and are deemed worth mentioning.
>

That's fine by me.

🔗genewardsmith <genewardsmith@...>

12/31/2011 11:05:11 PM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> You're right, this should even be in the pruned list. I have referred to this by the stupid throwaway name "notliese". It deserves a better one.

Suggestions?

🔗genewardsmith <genewardsmith@...>

12/31/2011 11:16:30 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> I objected then and I object now to having my point of view dismissed.

To clarify, I think it should be made clear this isn't a "best" list, it's just a list. The criteria are not designed to single out the "best" according to any defintion which makes sense to me.

🔗dkeenanuqnetau <d.keenan@...>

12/31/2011 11:25:01 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
>
> > So if a point of view is useless to you, it's absurd?
>
> I objected then and I object now to having my point of view dismissed.

You poor dear. That must be awful. Tell me who dismissed your point of view and I'll give them a stern talking to.

> Do we really want to say hedgehog is all that special? When Paul did this, I thought he made a point of saying his badness metric wasn't really supposed to measure badness, but was just a way of coming up with a list.
>

Now _that's_ a good point. It was in fact _you_ who wrote:

"It would be nice to have the list sorted by how good the temperaments on it rated by the badness measure Paul used ..."
/tuning/topicId_102092.html#102108

I replied:

"You could either say he didn't use a badness measure or ..."
/tuning/topicId_102092.html#102111

I'd be quite happy if we only showed it sorted on complexity as in Middle Path.

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

12/31/2011 11:33:04 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
> >
> > > So if a point of view is useless to you, it's absurd?
> >
> > I objected then and I object now to having my point of view dismissed.

You and Paul, with your plan to first decide on what you think should be on such a list and to hell with anyone else, and then to cook up something so you could make your personal preferences look objective and scientific. Now, since it's published on actual paper, it's a far better, more canonical list than any other.

🔗Carl Lumma <carl@...>

12/31/2011 11:54:16 PM

Gene wrote:
> You and Paul, with your plan to first decide on what you think
> should be on such a list and to hell with anyone else, and then
> to cook up something so you could make your personal preferences
> look objective and scientific. Now, since it's published on
> actual paper, it's a far better, more canonical list than
> any other.

Paul published a paper, it's his business what list it
contains. Dave likes the list and wants it extended to
the 11-limit, Keenan volunteers. So far so good.

What goes off the rails is the idea that logflat badness
with cutoffs is somehow just as ad hoc as a moat. In fact,
logflat badness is a simpler model and therefore has less
of an agenda than moats, which contain two cherry-picked
constants while adding incommensurate units. It also
happens that logflat badness gives better results, in my
subjective opinion.

-Carl

🔗genewardsmith <genewardsmith@...>

1/1/2012 12:15:28 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Paul published a paper, it's his business what list it
> contains.

I think he should have at least listened to and responded to my comments, and my attempts to formulate a way of doing what he seemed to want to do which would be less ad hoc. But that's past history. I note, however, that the sneering dismissal Dave just made is along the same lines as from years past.

> What goes off the rails is the idea that logflat badness
> with cutoffs is somehow just as ad hoc as a moat. In fact,
> logflat badness is a simpler model and therefore has less
> of an agenda than moats, which contain two cherry-picked
> constants while adding incommensurate units. It also
> happens that logflat badness gives better results, in my
> subjective opinion.

Mine too, but I spend a lot of time trying to modify things so as to bring it more into line with what Paul wanted, and got no response at all. And I think there's something flawed in a procedure which brings hedgehog to the top--it lacks all plausibility as an objective look at the question of making a list. And why, for instance, sum weighted complexity and error and not their logs?

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 12:16:37 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> You and Paul, with your plan to first decide on what you think should be on such a list and to hell with anyone else, and then to cook up something so you could make your personal preferences look objective and scientific.
>

The truth is in the archives of the tuning-math list for 2005 for anyone to see for themselves. Your views were respected and carefully considered. They just didn't happen to be chosen by the author, and it's no use stamping your feet about that now.

> Now, since it's published on actual paper, it's a far better, more canonical list than any other.
>

I have to disagree with you there. I'm really looking forward to seeing _your_ best-of 5, 7 and 11-limit lists using logflat badness with error and complexity cutoffs. I'm keen to see how you make _your_ personal preferences for those _three_ cutoffs look objective and scientific.

I have removed all reference to badness from
http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments+%28pruned%29
And BTW, it never did claim to be a "best-of".

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

1/1/2012 12:27:44 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> And why, for instance, sum weighted complexity and error and not their logs?

Not that I don't know why. But I think something more defensible could have been managed, had the will to do so been there.

🔗genewardsmith <genewardsmith@...>

1/1/2012 12:29:19 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> The truth is in the archives of the tuning-math list for 2005 for anyone to see for themselves. Your views were respected and carefully considered.

Bah. I kept making postings which were not responded to at all.

🔗genewardsmith <genewardsmith@...>

1/1/2012 12:32:31 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> I have to disagree with you there. I'm really looking forward to seeing _your_ best-of 5, 7 and 11-limit lists using logflat badness with error and complexity cutoffs. I'm keen to see how you make _your_ personal preferences for those _three_ cutoffs look objective and scientific.

It's not that hard--just check if anyone seems interested in that range of complexity or error. I've not seen a lot of interest in nanotemperaments more accurate than ennealimmal, or "temperaments" less accurate than father--have you?

> I have removed all reference to badness from
> http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments+%28pruned%29

Good.

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 12:39:23 AM

Carl,

I've been meaning to point out that the concept of a "moat" is completely independent of what functions are used to draw the boundary on the complexity vs error scatter-plot that determines inclusion in the list. It is equally applicable to a 3-piece boundary composed of logflat badness (hyperbola), error (vertical straight line) and complexity (horizontal straight line) limits as it is to the one-piece (oblique straight line) boundary used in Middle Path.

The idea is simply to choose the boundary so the content of the list is not sensitive to the exact values of the parameters.

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

1/1/2012 12:44:09 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> It's not that hard--just check if anyone seems interested in that range of complexity or error. I've not seen a lot of interest in nanotemperaments more accurate than ennealimmal, or "temperaments" less accurate than father--have you?

Actually, what I was thinking of doing was putting up some olympic lists--gold, silver, bronze. That would need a cutoff also, however.

🔗Carl Lumma <carl@...>

1/1/2012 12:50:00 AM

Dave wrote:

> I've been meaning to point out that the concept of a "moat" is
> completely independent of what functions are used to draw the
> boundary on the complexity vs error scatter-plot that determines
> inclusion in the list. It is equally applicable to a 3-piece
> boundary composed of logflat badness (hyperbola), error
> (vertical straight line) and complexity (horizontal straight
> line) limits as it is to the one-piece (oblique straight line)
> boundary used in Middle Path.

I don't know what you mean. A complexity cutoff is all
that's needed to produce a finite list, and logflat badness
can order it.

I've been meaning to point out that your moat formula lacks
the exponent to normalize complexity to just intonation, so
that lists made at different prime limits can be directly
compared. And so you get the right answer. :)

-Carl

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 2:32:33 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Dave wrote:
>
> > I've been meaning to point out that the concept of a "moat" is
> > completely independent of what functions are used to draw the
> > boundary on the complexity vs error scatter-plot that determines
> > inclusion in the list. It is equally applicable to a 3-piece
> > boundary composed of logflat badness (hyperbola), error
> > (vertical straight line) and complexity (horizontal straight
> > line) limits as it is to the one-piece (oblique straight line)
> > boundary used in Middle Path.
>
> I don't know what you mean. A complexity cutoff is all
> that's needed to produce a finite list,

I'll let Gene set you straight about that one.

> I've been meaning to point out that your moat formula

The fact that you're still using terms like "moat formula" suggests that you didn't understand what I wrote above.

There's no such thing as a moat formula. There are however boundary formulas (aka limit formulas, cutoff formulas). If the content of the list is not sensitive to small changes in the parameters of the boundary formulas then plotting them on a complexity/error plot would give the visual appearance of the boundary falling within a "moat", in other words there would be no dots representing temperaments for some distance either side of the boundary. The "moat" is a fuzzy concept intended to make use of our spatial intuition.

If you want to characterise the particular kind of boundary formula used in Middle Path, you could call it "linear", or "triangular" since it delimits a triangular region of complexity x error space, when considered with the (usually implied) boundaries of complexity > 0 and error > 0.

> lacks
> the exponent to normalize complexity to just intonation, so
> that lists made at different prime limits can be directly
> compared.

That is certainly a valid objection.

I suggest that what we need is a nice big inclusive scatter plot for each prime limit (or subset thereof), with hundreds of temperaments on each, and with logflat badness contours shown on it, and each point labelled with the temperament's name, which is also a link to its wiki page if it has one. For those without trivial names or pages it could show Graham Breed's twin-ET-mapping style of name.

Incidentally that system of letters after the ET number, for alternative prime mappings is great! Who came up with that?

Then no one has to throw a hissy fit because they don't like where someone else draws the boundaries of what is interesting to them.

-- Dave

🔗Carl Lumma <carl@...>

1/1/2012 3:08:11 AM

--- "dkeenanuqnetau" <d.keenan@...> wrote:

> > I don't know what you mean. A complexity cutoff is all
> > that's needed to produce a finite list,
>
> I'll let Gene set you straight about that one.

That ought to be good!

> There's no such thing as a moat formula.

You coined the term, not me. You can call

complexity/40 + damage/10 < 1

anything you like and remain guiltless of producing correct
temperament rankings.

-Carl

🔗Carl Lumma <carl@...>

1/1/2012 3:43:04 AM

I wrote:
> > > I don't know what you mean. A complexity cutoff is all
> > > that's needed to produce a finite list,
> >
> > I'll let Gene set you straight about that one.
>
> That ought to be good!

For example:
/tuning-math/message/17927

-C.

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 5:20:12 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> I suggest that what we need is a nice big inclusive scatter plot for each prime limit (or subset thereof), with hundreds of temperaments on each, and with logflat badness contours shown on it, and each point labelled with the temperament's name, which is also a link to its wiki page if it has one. For those without trivial names or pages it could show Graham Breed's twin-ET-mapping style of name.
>

They would be an updated version of this kind of plot:
/tuning/files/Erlich/dave3.gif
with Gene-approved error, complexity and badness measures, and modern names.

-- Dave Keenan

🔗Keenan Pepper <keenanpepper@...>

1/1/2012 5:40:14 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > You're right, this should even be in the pruned list. I have referred to this by the stupid throwaway name "notliese". It deserves a better one.
>
> Suggestions?

I hereby dub this temperament "pycnic", after the Greek word "pyknon" which I understand to mean "dense cluster of notes". Also, it sounds like "picnic", which makes me happy.

Also, I think nobody is any more upset by the "pruned" version than the original version, so it seems like the final version of this list should use 40 as that constant, and also be ordered only by complexity, like the Middle Path lists.

Keenan

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 6:08:25 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
> The truth is in the archives of the tuning-math list for 2005 for anyone to see for themselves.
>

Correction: That should have been 2004 (beginning in late January), not 2005.

-- Dave Keenan

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 6:38:46 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
I note, however, that the sneering dismissal Dave just made is along the same lines as from years past.
>

Gene, either email me a link to an example of this or stop wasting our time with false ad homenims.

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

1/1/2012 7:08:37 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> > I don't know what you mean. A complexity cutoff is all
> > that's needed to produce a finite list,
>
> I'll let Gene set you straight about that one.

Carl is entirely correct. The problem in practice is that you get junk not even the people who like junk can like.

A loglog plot would be much better.

> Incidentally that system of letters after the ET number, for alternative prime mappings is great! Who came up with that?

Herman, I think.

> Then no one has to throw a hissy fit because they don't like where someone else draws the boundaries of what is interesting to them.

When there is an implicit claim it was the result of an objective process?

🔗genewardsmith <genewardsmith@...>

1/1/2012 7:12:40 AM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> Also, I think nobody is any more upset by the "pruned" version than the original version, so it seems like the final version of this list should use 40 as that constant, and also be ordered only by complexity, like the Middle Path lists.

Plus, let's not forget, bonus temperaments.

🔗genewardsmith <genewardsmith@...>

1/1/2012 7:14:37 AM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> I note, however, that the sneering dismissal Dave just made is along the same lines as from years past.
> >
>
> Gene, either email me a link to an example of this or stop wasting our time with false ad homenims.

"Poor baby" doesn't count? They have some strange standards for these things Down Under.

🔗Herman Miller <hmiller@...>

1/1/2012 7:59:53 AM

On 1/1/2012 1:00 AM, Keenan Pepper wrote:
> --- In tuning@yahoogroups.com, "dkeenanuqnetau"<d.keenan@...>
> wrote:
>>
>> Thanks Keenan.
>>
>> Now we just need the columns for TOP period and generator.
>>
>> Is it mathematically justifiable to include only miracle and
>> hemiennealimmal as bonus temperaments?
>
> My impression was that the bonus temperaments needed no mathematical
> justification at all. They're simply other really good temperaments
> that didn't make the list because nothing that low in error could
> possibly make the list, and are deemed worth mentioning.
>
> Miracle and hemiennealimmal seem to fit this to a T. Any other
> *uniquely* efficient temperaments worth mentioning?

Octoid and hemienneadecal are the only two that might even come close that I can find, but nothing is as outstanding as hemiennealimmal. Even miracle isn't all that outstanding, but it's good to include for historical reasons. My "grade A" temperament list goes like this:

...

9&22 orwell [<1 0 3 1 3|, <0 7 -3 8 2|]
<<7 -3 8 2 -21 -7 -21 27 15 -22||
7&39 hitchcock [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
<<5 13 -17 9 9 -41 -3 -76 -24 84||
10&31 miracle [<1 1 3 3 2|, <0 6 -7 -2 15|]
<<6 -7 -2 15 -25 -20 3 15 59 49||
19&53 catakleismic [<1 0 1 -3 9|, <0 6 5 22 -21|]
<<6 5 22 -21 -6 18 -54 37 -66 -135||
22&50 wizard [<2 1 5 2 8|, <0 6 -1 10 -3|]
<<12 -2 20 -6 -31 -2 -51 52 -7 -86||
26&46 unidec [<2 5 8 5 6|, <0 -6 -11 2 3|]
<<12 22 -4 -6 7 -40 -51 -71 -90 -3||
58&72 harry [<2 4 7 7 9|, <0 -6 -17 -10 -15|]
<<12 34 20 30 26 -2 6 -49 -48 15||
58&94 [<2 4 11 7 13|, <0 -3 -23 -5 -22|]
<<6 46 10 44 59 -1 49 -106 -57 89||
72&80 octoid [<8 13 19 23 28|, <0 -3 -4 -5 -3|]
<<24 32 40 24 -5 -4 -45 3 -55 -71||
36&94 [<2 4 -2 7 0|, <0 -3 24 -5 25|]
<<6 -48 10 -50 -90 -1 -100 158 50 -175||
72&126 hemiennealimmal [<18 28 41 50 62|, <0 2 3 2 1|]
<<36 54 36 18 2 -44 -96 -68 -145 -74||
46&132 abigail [<2 7 13 -1 1|, <0 -11 -24 19 17|]
<<22 48 -38 -34 25 -122 -130 -223 -245 36||
152&190 hemienneadecal [<38 60 88 106 131|, <0 1 1 3 2|]
<<38 38 114 76 -28 74 -11 158 45 -181||

...

My ranking isn't the same as the error and complexity measures that Paul used, but the lists tend to be similar. I'll have to make another list using TOP-max error and wedgie complexity and see how it comes out.

🔗Keenan Pepper <keenanpepper@...>

1/1/2012 8:17:33 AM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> I hereby dub this temperament "pycnic", after the Greek word "pyknon" which I understand to mean "dense cluster of notes". Also, it sounds like "picnic", which makes me happy.

Whoops, strike this from the record. It looks like this is already named "progress" on the wiki (see "Archytas clan"), and also on second thought I want to reserve the name "pycnic" for a different temperament.

Keenan

🔗genewardsmith <genewardsmith@...>

1/1/2012 10:23:25 AM

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> 36&94 [<2 4 -2 7 0|, <0 -3 24 -5 25|]
> <<6 -48 10 -50 -90 -1 -100 158 50 -175||

Care to name it? It tempers out 540/539, so it has essentially tempered chords and therefore must be good. Thought its badness figure doesn't seem to be anything special.

🔗genewardsmith <genewardsmith@...>

1/1/2012 10:39:40 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@> wrote:
>
> > 36&94 [<2 4 -2 7 0|, <0 -3 24 -5 25|]
> > <<6 -48 10 -50 -90 -1 -100 158 50 -175||
>
> Care to name it? It tempers out 540/539, so it has essentially tempered chords and therefore must be good. Thought its badness figure doesn't seem to be anything special.
>

Actually, one this has been pogo for a while. I'll check if it's listed on a page Graham scrapes.

🔗Carl Lumma <carl@...>

1/1/2012 2:10:59 PM

Dave wrote:

> They would be an updated version of this kind of plot:
> /tuning/files/Erlich/dave3.gif
> with Gene-approved error, complexity and badness measures, and
> modern names.

My first question about such plots is why they aren't black.
Presumably they already reflect a complexity cutoff.

These days it's the general consensus that either TOP error
(aka TOP damage) or TE (Tenney-Euclidean) error (aka TOP-RMS)
are acceptable. The latter is more common because Graham
figured out how to compute it easily.

For complexity, there are scalar complexity (aka Graham
complexity) and TE complexity, which is like weighted
scalar complexity and is very close if not identical to what
got used in Middle Path.

For badness, there's logflat badness, which is the product
of any error and complexity you want to use, normalized to
what you'd expect in just intonation. It also happens to
give the same number of results in each complexity range on
a log scale, which strikes me as a property that any unbiased
badness ought to have
http://en.wikipedia.org/wiki/St._Petersburg_paradox#Expected_utility_theory

Which brings me to my second question about the plot: why
isn't complexity on a log scale?

The other badness is Cangwu badness (aka parametric badness).
It's a quadratic form for the product of error and complexity
with an additive term for error, which pads the error so
the distinction between temperaments below a chosen error
threshold is softened, as you often say is desirable.
However, so far as I know it doesn't have logflatness, so
I think it ought to be modified or rejected.

-Carl

🔗Carl Lumma <carl@...>

1/1/2012 2:15:15 PM

Gene wrote:
> Carl is entirely correct. The problem in practice is that you
> get junk not even the people who like junk can like.

That depends on the tightness of the complexity cutoff.
I'm happy using badness to cut a list by a factor as small
as 2. I can't say I've tried it in all cases, but I'm
perfectly happy with the results for rank 1 cutting by a
factor of 10.

> A loglog plot would be much better.

Looks like we see eye to eye on that.

>> Incidentally that system of letters after the ET number, for
>> alternative prime mappings is great! Who came up with that?
>
> Herman, I think.

Correct. Well, Mike B. and others were involved in the thread.

-Carl

🔗Carl Lumma <carl@...>

1/1/2012 2:16:01 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Plus, let's not forget, bonus temperaments.

...A sure sign your list-making procedure didn't do
what you wanted. -C.

🔗Carl Lumma <carl@...>

1/1/2012 2:26:24 PM

> For example:
> /tuning-math/message/17927

Gene, I'd like to encourage you to update this list with names
and post it on the wiki. The 7-limit one upthread from it, too.

-C.

🔗gbreed@...

1/1/2012 2:32:36 PM

Scalar complexity is the old name for TE complexity. Odd limit complexity is what people call Graham complexity.
Cangwu badness favors temperaments with an error close to the free parameter. That's what it's supposed to do and it can't also be logflat. The gold medalists by Cangwu badness do seem to shadow logflat badness though.
Cangwu badness is only a combination of complexity and complexity times error as an operator equation. The result is a new quadratic form. That makes it easy to calculate and also easy to find the best mappings for any given parameter.

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Sunday, January 1, 2012 10:10:59 PM GMT-0000
Subject: [tuning] Re: Middle Path 11-limit temperaments?

Dave wrote:

> They would be an updated version of this kind of plot:
> /tuning/files/Erlich/dave3.gif
> with Gene-approved error, complexity and badness measures, and
> modern names.

My first question about such plots is why they aren't black.
Presumably they already reflect a complexity cutoff.

For complexity, there are scalar complexity (aka Graham
complexity) and TE complexity, which is like weighted
scalar complexity and is very close if not identical to what
got used in Middle Path.

Which brings me to my second question about the plot: why
isn't complexity on a log scale?

-Carl

------------------------------------

🔗Carl Lumma <carl@...>

1/1/2012 3:01:45 PM

Graham wrote:
> Scalar complexity is the old name for TE complexity.
> Odd limit complexity is what people call Graham complexity.

I must be confused about scalar complexity - I thought
it was unweighted. -C.

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 3:42:59 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
>
>> --- Carl wrote:
> > > I don't know what you mean. A complexity cutoff is all
> > > that's needed to produce a finite list,
> >
> > I'll let Gene set you straight about that one.
>
> Carl is entirely correct. The problem in practice is that you get junk not even the people who like junk can like.
>

I'm not surprised that a lone complexity cutoff includes complete junk. I am surprised it gives a finite list. Can you provide a proof? I would have assumed it would also need either an error cutoff (giving a rectangular region) or badness and error cutoffs, or a badness cutoff and a second complexity cutoff.

The example Carl gave, apparently thinking it had only a complexity cutoff, clearly also has a badness cutoff.
/tuning-math/message/17927

> When there is an implicit claim it was the result of an objective process?
>

Neither Paul nor I made claim of objectivity, implicit or otherwise. I've been over the discussion from 2004. How could there ever be such a thing as a list of "objectively-best" temperaments? All Paul (or anyone) could ever hope to do is generate a list that folks didn't disagree too wildly about.

Paul was very conscious of his responsibility in bringing this stuff we'd _all_ been working on, to a wider audience. He bent over backwards to find a compromise between our various points of view. The only folks that seemed to be claiming any sort of objectivity for their point of view were you and Carl.

🔗Carl Lumma <carl@...>

1/1/2012 3:54:28 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
> I'm not surprised that a lone complexity cutoff includes
> complete junk. I am surprised it gives a finite list. Can you
> provide a proof?

You can brute force check all wedgies. QED

-Carl

🔗Carl Lumma <carl@...>

1/1/2012 4:02:00 PM

What I meant of course is that the number of wedgies
<<n_1 n_2... n_i]] with |n_i| < k is finite. -C.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
> >
> > I'm not surprised that a lone complexity cutoff includes
> > complete junk. I am surprised it gives a finite list. Can you
> > provide a proof?
>
> You can brute force check all wedgies. QED
>
> -Carl
>

🔗genewardsmith <genewardsmith@...>

1/1/2012 4:09:40 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > For example:
> > /tuning-math/message/17927
>
> Gene, I'd like to encourage you to update this list with names
> and post it on the wiki. The 7-limit one upthread from it, too.

Not a bad idea. I wonder what such a list should be called?

🔗genewardsmith <genewardsmith@...>

1/1/2012 4:12:24 PM

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:

> Cangwu badness is only a combination of complexity and complexity times error as an operator equation. The result is a new quadratic form. That makes it easy to calculate and also easy to find the best mappings for any given parameter.

Drawing plots of temperaments on a loglog chart with a line drawn for a Cangwu badness value for a certain parameter might be interesting re this whole moat business.

🔗genewardsmith <genewardsmith@...>

1/1/2012 4:15:38 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> The example Carl gave, apparently thinking it had only a complexity cutoff, clearly also has a badness cutoff.
> /tuning-math/message/17927

No badness cutoff--I simply listed the complete and total trash separately.

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 4:19:17 PM

You claimed that your ideas were sneeringly dismissed "in years past", implying that Paul or I did so back in 2004 re Middle Path list cutoffs. Show us an example or drop this slanderous nonsense.

I did however come across this amusing post by you from back then, which contains the clearly objective terms "goofy ad-hoc weirdness" and "utterly looney" as possible descriptions of boundary setting methods other than your own.
/tuning-math/message/9131

And regarding more recent times, it was "You poor dear", not "Poor baby". Please get my sneering dismissals right. I expect better from the master of the sneering dismissal. :-)

-- Dave Keenan

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
>
> > I note, however, that the sneering dismissal Dave just made is along the same lines as from years past.
> > >
> >
> > Gene, either email me a link to an example of this or stop wasting our time with false ad homenims.
>
> "Poor baby" doesn't count? They have some strange standards for these things Down Under.
>

🔗genewardsmith <genewardsmith@...>

1/1/2012 4:32:40 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> I did however come across this amusing post by you from back then, which contains the clearly objective terms "goofy ad-hoc weirdness" and "utterly looney" as possible descriptions of boundary setting methods other than your own.
> /tuning-math/message/9131

Which was a suggestion that no looney method be adopted, not a characterization of anything which had.

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 5:12:15 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
>
> > The example Carl gave, apparently thinking it had only a complexity cutoff, clearly also has a badness cutoff.
> > /tuning-math/message/17927
>
> No badness cutoff--I simply listed the complete and total trash separately.
>

You write, "The number after the wedgie is wedgie logflat badness, for which I used a cutoff of 1/30." And neither list contains anything with badness over 1/30.

It appears to be a second complexity cutoff that separates the two lists.

But I do understand now that a complexity limit is enough to ensure finiteness. Thanks for the proof sketch Carl. And thanks for confirming that a single complexity limit alone isn't sufficient for practical purposes, Gene.

🔗dkeenanuqnetau <d.keenan@...>

1/1/2012 5:17:40 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Plus, let's not forget, bonus temperaments.
>
> ...A sure sign your list-making procedure didn't do
> what you wanted. -C.
>

Or evidence of Paul's caring nature and generosity in trying to keep everyone happy.

-- Dave Keenan

🔗genewardsmith <genewardsmith@...>

1/1/2012 5:43:10 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> You write, "The number after the wedgie is wedgie logflat badness, for which I used a cutoff of 1/30." And neither list contains anything with badness over 1/30.

Sorry, I misstated. Had no badness cutoff been employed, the list would have been huge and mostly worthless. What I was thinking was that there was no error cutoff.

🔗Carl Lumma <carl@...>

1/1/2012 7:28:26 PM

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> And thanks for confirming that a single complexity limit alone
> isn't sufficient for practical purposes, Gene.

I strongly disagree with this statement. At least, it has
hardly been established yet. -Carl

🔗Carl Lumma <carl@...>

1/1/2012 7:35:58 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> > You write, "The number after the wedgie is wedgie logflat
> > badness, for which I used a cutoff of 1/30." And neither list
> > contains anything with badness over 1/30.
>
> Sorry, I misstated. Had no badness cutoff been employed, the
> list would have been huge and mostly worthless. What I was
> thinking was that there was no error cutoff.

I think you're both confused. To generate the *initial*
list only a complexity cutoff was used. That entire list
was obviously not reported by Gene in the post because it
was huge. So a badness cutoff was used to generate a
top-n list. In other words, he did exactly what I've been
advocating here. Right, Gene?

It may be worth pointing out that a complexity cutoff does
bound error too. At least for rank 1, since it bounds
the step size, and I reckon for rank 2 also.

-Carl

🔗Carl Lumma <carl@...>

1/1/2012 7:42:21 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> > > For example:
> > > /tuning-math/message/17927
> >
> > Gene, I'd like to encourage you to update this list with names
> > and post it on the wiki. The 7-limit one upthread from it, too.
>
> Not a bad idea. I wonder what such a list should be called?

Howabout "meantone-median lists", since you'll no doubt take
my suggestion and adjust the logflat badness threshold until
you have an odd number of temperaments with meantone as the
median. And then adjust the complexity cutoff until that
odd number is approximately 9.

-Carl

🔗Carl Lumma <carl@...>

1/1/2012 8:06:13 PM

Here's the algorithm

- generate all wedgies below complexity cutoff k
- sort by logflat badness
- check if the first extended meantone on the list is in
the 5th position
- if not, increase k and repeat; if so, return the first
11 entries

Before I joined this thread I wondered if it was really
about the color of a bike shed. Now that I'm participating
I must resolve this question in the negative, and here's
how I do that:

The regular mapping paradigm is broadly useful, but one of
its uses is to generalize Western polyphonic music under
the assumption that it required a specialized tuning system
and, through cultural evolution, found one. For composers
interested in writing polyphonic music with melody, harmony,
motivic structure, etc. but a different tuning system, the
theory ought to be able reduce the number of systems they
need to try before finding one. That would be useful since
trying novel systems is apparently hard (maybe even requiring
generations of effort). If we can furnish a top-9 list
guaranteed to contain at least one viable meantone successor,
it would be a good thing. In fact we can answer the question
"Why hasn't this been done yet?" by saying that the evolution
f music was stuck in a local minimum and only deliberate
theory (not a random walk) could get it out.

So I think the question of top-n lists and how to make them
is potentially important and that the details might matter.

-Carl

I wrote:

> Howabout "meantone-median lists", since you'll no doubt take
> my suggestion and adjust the logflat badness threshold until
> you have an odd number of temperaments with meantone as the
> median. And then adjust the complexity cutoff until that
> odd number is approximately 9.
> -Carl

🔗Mike Battaglia <battaglia01@...>

1/1/2012 9:14:50 PM

I hope mavila makes the list.

-Mike

On Jan 1, 2012, at 11:06 PM, Carl Lumma <carl@...> wrote:

Here's the algorithm

Before I joined this thread I wondered if it was really
about the color of a bike shed. Now that I'm participating
I must resolve this question in the negative, and here's
how I do that:

So I think the question of top-n lists and how to make them
is potentially important and that the details might matter.

-Carl

I wrote:

🔗genewardsmith <genewardsmith@...>

1/1/2012 11:58:29 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> I think you're both confused. To generate the *initial*
> list only a complexity cutoff was used. That entire list
> was obviously not reported by Gene in the post because it
> was huge. So a badness cutoff was used to generate a
> top-n list. In other words, he did exactly what I've been
> advocating here. Right, Gene?

Right, and then I listed 27 junk temperaments separately. The remaining 162 I'm working on putting into table form to go on the Xenwiki. Since "Catalog" has been taken, I'm thinking of "Gallery", though it would seem to make more sense the other way around.

🔗Keenan Pepper <keenanpepper@...>

1/2/2012 5:28:11 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Right, and then I listed 27 junk temperaments separately. The remaining 162 I'm working on putting into table form to go on the Xenwiki. Since "Catalog" has been taken, I'm thinking of "Gallery", though it would seem to make more sense the other way around.

We can also rename articles to have more specific and descriptive titles. It's no big deal to rename something and repair any incoming links.

Keenan

🔗genewardsmith <genewardsmith@...>

1/2/2012 6:54:29 AM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Right, and then I listed 27 junk temperaments separately. The remaining 162 I'm working on putting into table form to go on the Xenwiki. Since "Catalog" has been taken, I'm thinking of "Gallery", though it would seem to make more sense the other way around.
>
> We can also rename articles to have more specific and descriptive titles. It's no big deal to rename something and repair any incoming links.

Want to switch Gallery with catalog?

🔗Mike Battaglia <battaglia01@...>

1/2/2012 9:03:24 AM

I just threw a ton of names on for some temperaments that already have
names but were not listed; you might want to double check my most recent
commit to make sure it all looks good.

Sent from my iPhone

On Jan 2, 2012, at 9:54 AM, genewardsmith <genewardsmith@...>
wrote:

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Right, and then I listed 27 junk temperaments separately. The remaining
162 I'm working on putting into table form to go on the Xenwiki. Since
"Catalog" has been taken, I'm thinking of "Gallery", though it would seem
to make more sense the other way around.
>
> We can also rename articles to have more specific and descriptive titles.
It's no big deal to rename something and repair any incoming links.

Want to switch Gallery with catalog?

🔗Keenan Pepper <keenanpepper@...>

1/2/2012 9:51:05 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> > We can also rename articles to have more specific and descriptive titles. It's no big deal to rename something and repair any incoming links.
>
> Want to switch Gallery with catalog?

I was thinking it would be better to put "Middle Path" explicitly in the title, to be specific about where the criteria come from. If I were a newcomer to the wiki, I would assume that anything with a name like "catalog" or "gallery" is something comprehensive to which I could add anything I wanted, rather than a finite list with well-defined criteria.

Keenan

🔗genewardsmith <genewardsmith@...>

1/2/2012 10:05:31 AM

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I just threw a ton of names on for some temperaments that already have
> names but were not listed; you might want to double check my most recent
> commit to make sure it all looks good.

I only saw two, but we were editing at the same time and I think if the edits don't conflict it just gets saved. Anyway, all I saw was armodue and progression, and I've updated for those.

🔗genewardsmith <genewardsmith@...>

1/2/2012 10:11:42 AM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> I was thinking it would be better to put "Middle Path" explicitly in the title, to be specific about where the criteria come from. If I were a newcomer to the wiki, I would assume that anything with a name like "catalog" or "gallery" is something comprehensive to which I could add anything I wanted, rather than a finite list with well-defined criteria.

I think catalog sounds like it's more comprehensive and is a good name for what's now a "gallery". I also think putting Middle Path into the title is an excellent idea. If you compare this

Gallery+of+eleven-limit+rank+two+temperaments

with this

http://xenharmonic.wikispaces.com/Catalog+of+eleven-limit+rank+two+temperaments

I think it's clear why I claim Paul's method entails a point of view on temperaments which a survey like the "Gallery" really doesn't have, despite claims to the contrary.

🔗dkeenanuqnetau <d.keenan@...>

1/2/2012 3:33:23 PM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> I was thinking it would be better to put "Middle Path" explicitly in the title, to be specific about where the criteria come from. If I were a newcomer to the wiki, I would assume that anything with a name like "catalog" or "gallery" is something comprehensive to which I could add anything I wanted, rather than a finite list with well-defined criteria.
>

I agree with putting "Middle Path" in the title, and suggest calling them what Paul calls them, "Table". A gallery is usually a collection of images.

-- Dave Keenan