Yahoo Tuning Groups Ultimate Backup tuning When can two different temperaments share the same name?

See http://xenharmonic.wikispaces.com/message/view/Porcupine/45348918 for the conversation that started this.

I remember the days when we had "negripent" and "negrisept" to distinguish between the 5-limit and 7-limit versions of negri temperament.

Currently, I think everyone supports calling these both "negri". Why is it acceptable for them to share the same name? AFAIK the precise conditions have never been spelled out anywhere, so I'm going to give it a shot:

1. Temperaments with the same name must have the same rank. (It might be tempting to call both the 2.3.7 64/63 linear temperament and the 2.3.5.7 64/63 planar temperament "archytas", for example, but I don't think this is currently done.)

2. Temperaments with the same name must agree perfectly on their common subgroup. That is, the mappings for all primes (or other basis elements) must be identical.

3. The common subgroup temperament must not be contorted or reduced in rank, and it must also share the same name.

These conditions guarantee that temperaments with the same name can always be derived, from some simplest possible version of that temperament, by mapping new primes to intervals that *already exist* in the temperament.

When I go from 5-limit meantone to 7-limit meantone, I'm not adding any new notes or intervals to 5-limit meantone. I'm just saying that the previously existing interval of an augmented sixth is now going to represent 7/4 in addition to all the 5-limit intervals it represented before.

Here are some examples of things this *disallows*:

* Consider Bohlen-Pierce (the rank-2 one) and bohpier. Bohlen-Pierce is 3.5.7 and bohpier is 2.3.5.7, so their common subgroup is 3.5.7. But bohpier is rank-1 if restricted to the 3.5.7 subgroup, while Bohlen-Pierce is still rank-2 on that subgroup. This violates condition 2, so they must have different names.

* Consider tutone, a 2.9.5.7.11 temperament with the same commas as meantone. In meantone, 9 is mapped to -2 generators plus some octaves, but in tutone, 9 is mapped to 1 generator plus some octaves. This violates condition 2, so they must have different names.

* Consider bridgetown (a 2.3.11/5.13/5 temperament) and semiphore (a 2.3.7 temperament). These *do* agree perfectly on their common subgroup of 2.3, satisfying condition 2, but the common subgroup temperament is contorted Pythagorean, so this fails condition 3.

Note that according to these conditions, some familiar temperaments would be allowed to share names even though they currently don't. For example, slendric is not forbidden from being called "2.3.7 rodan", or "2.3.7 mothra" or even "2.3.7 gorgo". That it currently has the unique name "slendric" is totally fine - these conditions only say when two temperaments are *allowed* to have the same name. It's never *required*.

If these conditions are acceptable to everybody, then that's great because the name of the 2.3.5.11 temperament tempering out 55/54 and 100/99 can be simply "porcupine", which is the only name that ever made sense for it.

Keenan

🔗genewardsmith <genewardsmith@...>

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

> If these conditions are acceptable to everybody, then that's great because the name of the 2.3.5.11 temperament tempering out 55/54 and 100/99 can be simply "porcupine", which is the only name that ever made sense for it.

I think it's very confusing to call it simply "porcupine" rather than "2.3.5.11 porcupine". My way of proceeding has been to always introduce a new name for subgroup temperaments, which means I would have called it "porkupine" or something of the sort. But if the Keenan Conditions are adhered to, and either the context or explicitly as above the subgroup is made clear, perhaps we could keep the naming system from descending into chaos, which is what I've been concerned about. Of course, we could do both--call it either 2.3.5.11 porcupine, or porkupine, your choice. I think "porkupine" would make searching and labeling easier, whereas "2.3.5.11 porcupine" tells you what the temperament is up-front.

🔗genewardsmith <genewardsmith@...>

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

> * Consider bridgetown (a 2.3.11/5.13/5 temperament) and semiphore (a 2.3.7 temperament). These *do* agree perfectly on their common subgroup of 2.3, satisfying condition 2, but the common subgroup temperament is contorted Pythagorean, so this fails condition 3.

It seems to me you ought at least to insist that there is some temperament, with the proposed name, that your two temperaments (eg bridgetown and semiphore) are subgroups of with infinite index, with the quotient group free.

> Note that according to these conditions, some familiar temperaments would be allowed to share names even though they currently don't. For example, slendric is not forbidden from being called "2.3.7 rodan", or "2.3.7 mothra" or even "2.3.7 gorgo".

This completely ignores the question of tuning, which has always figured when going from one prime limit to another and considering a name. I prefer to be pretty strict about that; when Graham and I had our hecate-marvel confusion, I had initially picked hecate to be 13-limit marvel on the grounds the tuning was closer to 11-limit marvel, whereas Graham went for a 13-limit version where the tuning was quite close, but not quite so close. It's not something with an agreed-on system, but I don't like the idea of calling slendric 2.3.7 gorgo.

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > If these conditions are acceptable to everybody, then that's great because the name of the 2.3.5.11 temperament tempering out 55/54 and 100/99 can be simply "porcupine", which is the only name that ever made sense for it.
>
> I think it's very confusing to call it simply "porcupine" rather than "2.3.5.11 porcupine".

Yeah, of course the full name of that specific temperament would be "2.3.5.11 porcupine". This is analogous to the way "5-limit meantone" is different from "7-limit meantone", and the way "2.9.7 machine" is different from "2.9.7.11 machine".

There are many occasions when people want to talk about some set of closely related temperaments as a single object, and do not care about making such distinctions. It's very useful to be able to say "meantone" or "machine" and not have to specify which subgroup, unless you want to.

> My way of proceeding has been to always introduce a new name for subgroup temperaments, which means I would have called it "porkupine" or something of the sort. But if the Keenan Conditions are adhered to, and either the context or explicitly as above the subgroup is made clear, perhaps we could keep the naming system from descending into chaos, which is what I've been concerned about.

Better call them Pepper Conditions if anything, to avoid confusion with Dave Keenan.

> Of course, we could do both--call it either 2.3.5.11 porcupine, or porkupine, your choice. I think "porkupine" would make searching and labeling easier, whereas "2.3.5.11 porcupine" tells you what the temperament is up-front.

I definitely prefer "2.3.5.11 porcupine", for the same reason that I like the name "7-limit meantone" rather than "smeantone" or "meanntone" or whatever. A slightly different spelling would create confusion and make searching and labeling more difficult, in my opinion.

People are going to be using these names who only care what the intervals, chords, etc. of the temperament sound like, and couldn't care less which specific subgroup of Q (the rational numbers) it's mapping.

Keenan

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> It seems to me you ought at least to insist that there is some temperament, with the proposed name, that your two temperaments (eg bridgetown and semiphore) are subgroups of with infinite index, with the quotient group free.

This is actually a really great idea - to look at the combination of the two subgroups (smallest common extension) rather than the largest common subgroup. My condition 3 is thus totally wrong and backwards - I'll post revised conditions later.

> This completely ignores the question of tuning, which has always figured when going from one prime limit to another and considering a name. I prefer to be pretty strict about that; when Graham and I had our hecate-marvel confusion, I had initially picked hecate to be 13-limit marvel on the grounds the tuning was closer to 11-limit marvel, whereas Graham went for a 13-limit version where the tuning was quite close, but not quite so close. It's not something with an agreed-on system, but I don't like the idea of calling slendric 2.3.7 gorgo.

Yes, of course. Calling slendric "gorgo" seems crazy to me too; I'm not advocating that.

There are always going to be multiple possible extensions of a temperament to a new prime. My conditions don't forbid any of them from having the same name as the original, but they do insist that only one of them has that name. Which particular one gets that honor will have to be decided on an individual basis - I don't pretend to have an algorithm that always produces the "best" extension most deserving of the name.

The 2.3.5.11 porcupine case is a different situation - it's not like any other 2.3.5.11 temperaments are contenders for the "porcupine" name. There is no disambiguation to make. The only question is whether *any* 2.3.5.11 temperament should bear the name "porcupine".

Keenan

🔗Carl Lumma <carl@...>

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

> There are many occasions when people want to talk about some
> set of closely related temperaments as a single object, and do
> not care about making such distinctions. It's very useful to be
> able to say "meantone" or "machine" and not have to specify
> which subgroup, unless you want to.

I agree.

> Better call them Pepper Conditions if anything, to avoid
> confusion with Dave Keenan.

I agree.

> I definitely prefer "2.3.5.11 porcupine", for the same reason
> that I like the name "7-limit meantone" rather than "smeantone"
> or "meanntone" or whatever. A slightly different spelling would
> create confusion and make searching and labeling more difficult,
> in my opinion.

I especially agree.

> People are going to be using these names who only care what the
> intervals, chords, etc. of the temperament sound like, and
> couldn't care less which specific subgroup of Q (the rational
> numbers) it's mapping.

I think 'most people' really care about commas, most of the
time. At least I think a naming scheme based on commas is
bound to be more intuitive than one based on generator size.

-Carl

🔗Carl Lumma <carl@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> I wrote:
> > At least I think a naming scheme based on commas is
> > bound to be more intuitive than one based on generator size.
>
> Or anything to do with tuning space. For instance, I don't
> place a high priority on a
>
> Keenan wrote:
> >> guarantee that temperaments with the same name can always
> >> be derived, from some simplest possible version of that
> >> temperament, by mapping new primes to intervals that
> >> *already exist* in the temperament.
>
> Though perhaps you can explain what's you mean by "already
> exist". Already exist... with what complexity?

I wasn't thinking of complexity, I was thinking of the more obvious fact that some extensions keep all the generators and mappings of the "original" primes the same, whereas others split generators into smaller parts (or otherwise mangle them) and change all the mappings.

For example, let's say I want to extend 5-limit meantone to include the prime 7. There are many different ways to do this, but they fall into two categories.

In the first category we have 7-limit temperaments that coincide perfectly with meantone in the 5-limit. This means they take some interval that already exists in meantone and call it the 7th harmonic. Examples:

* If 7/4 is represented as a minor seventh (an interval which already exists in 5-limit meantone), then you get dominant.
* If 7/4 is represented as an augmented sixth, you get 7-limit meantone.
* If 7/4 is represented as a diminished seventh, you get flattone.

In the second category we have 7-limit temperaments that, when restricted to the 5 limit, are contorted versions of meantone rather than meantone itself. This means they add new intervals to 5-limit meantone that didn't originally belong to it and cannot be described in meantone-based nomenclature (e.g. "augmented sixth"). Examples:

* Godzilla splits the perfect fourth into two equal parts. Any interval that's an odd number of these parts is not an ordinary meantone interval, it's something new.
* Cynder splits the perfect fifth into three equal parts. Now only one out of every three intervals is a familiar meantone one.
* Injera splits the octave into two equal parts.

I think it's pretty darn important that the name "meantone" be bestowed only on an extension in the first category, never the second category.

You seem to be making the argument that since all the extensions in both categories temper out 81/80, they're all equally valid candidates for the name "meantone" because they're compatible with it. I can think of three good reasons to insist on extensions in the first category, though:

* Equal temperaments: Many people like to perform in equal temperaments. If an equal temperament supports meantone, then it's guaranteed to support all extensions in the first category to some extent, but not those in the second category. For example, 12edo supports meantone, therefore it also supports dominant, 7-limit meantone, and flattone (albeit with the second-best mapping for 7). In contrast, it does not support godzilla or cynder at all (unless you use a worse mapping for 3, which is insane).

* Notation and nomenclature: If you have a notation system worked out for some rank-2 temperament, that system automatically works for all extensions in the first category, but not the second. Dominant, 7-limit meantone, and flattone can all be notated with standard meantone-based notation. But how can you use standard notation to notate godzilla? The generator is neither a major second nor a minor third, nor any other meantone interval.

* MOS scales: The cardinalities of MOS (and MODMOS!) scales of extensions in the first category are closely related to those of 5-limit meantone (only changing for higher numbers of notes if the optimum tuning changes too much), but the cardinalities of those in the second category are totally different.

Keenan

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > > I definitely prefer "2.3.5.11 porcupine", for the same reason
> > > that I like the name "7-limit meantone" rather than "smeantone"
> > > or "meanntone" or whatever. A slightly different spelling would
> > > create confusion and make searching and labeling more difficult,
> > > in my opinion.
> >
> > I especially agree.
>
> Yes, but you aren't thinking about adding an entry for "2.3.5.11 porcupine" to the Chromatic pairs page, where it is important it not be confused with 2.3.5.7.11 porcupine, since that might appear on the same page. The naming system isn't perfect from that point of view.

I guess I just don't see how this is any different from having both 2.3.5 meantone and 2.3.5.7 meantone. Why is it important to make the distinction in one case but not the other?

Keenan

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > > I definitely prefer "2.3.5.11 porcupine", for the same reason
> > > > that I like the name "7-limit meantone" rather than "smeantone"
> > > > or "meanntone" or whatever. A slightly different spelling would
> > > > create confusion and make searching and labeling more difficult,
> > > > in my opinion.
> > >
> > > I especially agree.
> >
> > Yes, but you aren't thinking about adding an entry for "2.3.5.11 porcupine" to the Chromatic pairs page, where it is important it not be confused with 2.3.5.7.11 porcupine, since that might appear on the same page. The naming system isn't perfect from that point of view.
>
> I guess I just don't see how this is any different from having both 2.3.5 meantone and 2.3.5.7 meantone. Why is it important to make the distinction in one case but not the other?

Because 7-limit meantone is not floating off on a separate page from 5-limit meantone, so it's easy to do the nomenclature thing. If you call something "porcupine" which is a 2.3.5.11 temperament, which is on a page with no reference to any other porcupine, it gives entirely the wrong impression that porcupine is a no-sevens temperament, which it is n ot.

🔗Carl Lumma <carl@...>

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

> > > I definitely prefer "2.3.5.11 porcupine", for the same reason
> > > that I like the name "7-limit meantone" rather than "smeantone"
> > > or "meanntone" or whatever. A slightly different spelling would
> > > create confusion and make searching and labeling more difficult,
> > > in my opinion.
> >
> > I especially agree.
>
> Yes, but you aren't thinking about adding an entry for "2.3.5.11
> porcupine" to the Chromatic pairs page, where it is important it
> not be confused with 2.3.5.7.11 porcupine, since that might appear
> on the same page. The naming system isn't perfect from that point
> of view.

Not sure what you mean, or why xenwiki page structure should
influence naming. Both your and Keenans pairs of names are
differentiated by a single character change. But your changing
character conveys no meaning, and is much easier to miss in
the middle of a word that the eye wants to read. In contrast,
the subgroup contains information, and is easier to parse
by eye.

-Carl

🔗Jake Freivald <jdfreivald@...>

I'm sure I don't understand some of the subtleties here, but I really
like the idea of having the subgroup instead of a single character
change. Despite some potential for confusion, I instantly understand
the major difference between "2.3.5.11 Porcupine" and "2.3.5.7
Porcupine", whereas I have no idea about the difference between
"Porkupine" vs. "Porcupine". I suggest, further, that people who would
understand the difference between "Porkupine" and "Porcupine" would be
able to remember that seeing a "2.3.5.11" in front of "Porcupine"
doesn't automatically mean that the 7 is not possible.

The sheer quantity of temperament names can be pretty intimidating.
Unless I'm missing something, this move would reduce the complexity of
the naming scheme(s) without reducing clarity.

For what it's worth.

Regards,
Jake

On 11/2/11, Carl Lumma <carl@...> wrote:
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>> > > I definitely prefer "2.3.5.11 porcupine", for the same reason
>> > > that I like the name "7-limit meantone" rather than "smeantone"
>> > > or "meanntone" or whatever. A slightly different spelling would
>> > > create confusion and make searching and labeling more difficult,
>> > > in my opinion.
>> >
>> > I especially agree.
>>
>> Yes, but you aren't thinking about adding an entry for "2.3.5.11
>> porcupine" to the Chromatic pairs page, where it is important it
>> not be confused with 2.3.5.7.11 porcupine, since that might appear
>> on the same page. The naming system isn't perfect from that point
>> of view.
>
> Not sure what you mean, or why xenwiki page structure should
> influence naming. Both your and Keenans pairs of names are
> differentiated by a single character change. But your changing
> character conveys no meaning, and is much easier to miss in
> the middle of a word that the eye wants to read. In contrast,
> the subgroup contains information, and is easier to parse
> by eye.
>
> -Carl
>
>
>
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🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > If an equal temperament supports meantone, then
> > it's guaranteed to support all extensions in the first category
> > to some extent, but not those in the second category.
> > If you have a notation system worked out for some rank-2
> > temperament, that system automatically works for all
> > extensions in the first category, but not the second.
>
> It's definitely a meaningful distinction (for keyboard
> layouts too) but if it conflicted with some property of
> the tree of comma sequences I would prefer a naming
> scheme that respected the latter.

I'm having trouble imagining how this is possible. Can you concoct an example?

Keenan

🔗Carl Lumma <carl@...>

Keenan wrote:

> > > If an equal temperament supports meantone, then
> > > it's guaranteed to support all extensions in the first category
> > > to some extent, but not those in the second category.
> > > If you have a notation system worked out for some rank-2
> > > temperament, that system automatically works for all
> > > extensions in the first category, but not the second.
> >
> > It's definitely a meaningful distinction (for keyboard
> > layouts too) but if it conflicted with some property of
> > the tree of comma sequences I would prefer a naming
> > scheme that respected the latter.
>
> I'm having trouble imagining how this is possible. Can you
> concoct an example?

I'm not sure how comma sequences would work with nonstandard
subgroups. It seems Gene was using your distinction years
ago under the rubric of legitimate/illegitimate family
members.

-Carl

🔗Carl Lumma <carl@...>

"Keenan Pepper" <keenanpepper@...> wrote:

> > It's definitely a meaningful distinction (for keyboard
> > layouts too) but if it conflicted with some property of
> > the tree of comma sequences I would prefer a naming
> > scheme that respected the latter.
>
> I'm having trouble imagining how this is possible. Can you
> concoct an example?

You seem to want to use the same name only for temperaments
of the same rank, whereas I'm happier using the same name
for temperaments that share a kernel. For example, I'm happy
calling anything with a kernel of 81/80 "meantone". Two
temperaments might have the same name under your proposal,
when under Gene's comma sequence scheme (as I understand it),
they would be sisters.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 4, 2011 at 5:12 AM, Carl Lumma <carl@...> wrote:
>
> You seem to want to use the same name only for temperaments
> of the same rank, whereas I'm happier using the same name
> for temperaments that share a kernel. For example, I'm happy
> calling anything with a kernel of 81/80 "meantone". Two
> temperaments might have the same name under your proposal,
> when under Gene's comma sequence scheme (as I understand it),
> they would be sisters.

I was thinking about this exact subject earlier, as it pertains to
infinite-limit temperaments.

In the infinite-limit, you can specify a temperament in one of two
ways: as a finite codimension (e.g. a handful of commas being tempered
out), or as a finite rank (e.g. a handful of vals). All of the
temperaments in the middle, which are of countably infinite dimension
as well as countably infinite codimension, are lost to us, at least
for now (and I'm not sure what point they'd serve anyway).

So one question is, will the name "meantone" end up being assigned to
the codimension-1 temperament tempering out 81/80? Or will it end up
being assigned to one of the rank-2 infinite variants eliminating
81/80, perhaps the lowest in badness? Both of these are higher-limit
extensions of the 2.3.5-limit meantone temperament, but in different
ways.

Another way to frame the question is, should "meantone" be assigned to
the 7-limit 81/80 planar temperament, the 11-limit 81/80 3D
temperament, etc? Or, should those names go to the lowest-badness
rank-2 extensions of the 5-limit 81/80 linear temperament? I note that
the 2.3.5.7 81/80 and 126/125 temperament is called "meantone," but
the 2.3.5.7 81/80 planar temperament usually is not. Same-rank
higher-limit extensions of some temperament are usually the ones that
get the same name, whereas higher-rank extensions don't.

It might be done on a case by case basis: I hear lots of talk about
"marvel tempering" meantone to get septimal meantone, but I haven't
heard much reference to "meantone-tempering" slendric to get mothra.

-Mike

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Nov 4, 2011 at 5:12 AM, Carl Lumma <carl@...> wrote:
> >
> > You seem to want to use the same name only for temperaments
> > of the same rank, whereas I'm happier using the same name
> > for temperaments that share a kernel. For example, I'm happy
> > calling anything with a kernel of 81/80 "meantone". Two
> > temperaments might have the same name under your proposal,
> > when under Gene's comma sequence scheme (as I understand it),
> > they would be sisters.

Carl, I was trying to stick to current practice as much as possible. What you're suggesting (using the same name only for temperaments of the same *codimension*, a.k.a. number of independent commas) also makes sense, but AFAIK there are no examples of people using this convention.

> I was thinking about this exact subject earlier, as it pertains to
> infinite-limit temperaments.
>
> In the infinite-limit, you can specify a temperament in one of two
> ways: as a finite codimension (e.g. a handful of commas being tempered
> out), or as a finite rank (e.g. a handful of vals). All of the
> temperaments in the middle, which are of countably infinite dimension
> as well as countably infinite codimension, are lost to us, at least
> for now (and I'm not sure what point they'd serve anyway).
>
> So one question is, will the name "meantone" end up being assigned to
> the codimension-1 temperament tempering out 81/80? Or will it end up
> being assigned to one of the rank-2 infinite variants eliminating
> 81/80, perhaps the lowest in badness? Both of these are higher-limit
> extensions of the 2.3.5-limit meantone temperament, but in different
> ways.
>
> Another way to frame the question is, should "meantone" be assigned to
> the 7-limit 81/80 planar temperament, the 11-limit 81/80 3D
> temperament, etc? Or, should those names go to the lowest-badness
> rank-2 extensions of the 5-limit 81/80 linear temperament? I note that
> the 2.3.5.7 81/80 and 126/125 temperament is called "meantone," but
> the 2.3.5.7 81/80 planar temperament usually is not. Same-rank
> higher-limit extensions of some temperament are usually the ones that
> get the same name, whereas higher-rank extensions don't.

Right. So the current practice is to name them according to the vals, not the commas.

> It might be done on a case by case basis: I hear lots of talk about
> "marvel tempering" meantone to get septimal meantone, but I haven't
> heard much reference to "meantone-tempering" slendric to get mothra.

That's exactly the way I think of mothra though. Mothra tempers out 81/80 so it's meantone-tempered slendric, guiron tempers out 32805/32768 so it's schismatic-tempered slendric, and gorgo tempers out 36/35 so it's dominant-tempered slendric.

Keenan

🔗Carl Lumma <carl@...>

Mike wrote:

> In the infinite-limit, you can specify a temperament in one of
> two ways: as a finite codimension (e.g. a handful of commas
> being tempered out), or as a finite rank (e.g. a handful
> of vals). All of the temperaments in the middle, which are of
> countably infinite dimension as well as countably infinite
> codimension, are lost to us, at least for now (and I'm not
> sure what point they'd serve anyway).

Yup. Feasible searching for commas depends on an error
weighting that essentially lets us ignore primes above
some number, like 31. Feasibly searching for mappings
(handfuls of vals) depends on a complexity weighting
that lets us effectively ignore temperaments with more
than number of notes. If we choose the relative steepness
of these two weighting functions to align with typical
work in the field that uses hard cutoffs (prime limits
and hard complexity cutoffs), a comma will be easier to
find than a val. Now, putting two good commas together
doesn't always produce a good temperament, so that's
where it gets hairy. By the way: How are people writing
wedgies for subgroup temperaments?

> So one question is, will the name "meantone" end up being
> assigned to the codimension-1 temperament tempering out 81/80?
> Or will it end up being assigned to one of the rank-2 infinite
> variants eliminating 81/80, perhaps the lowest in badness?
> Both of these are higher-limit extensions of the 2.3.5-limit
> meantone temperament, but in different ways.

As far as naming schemes are concerned, the kernel method
(pun intended) is a lot simpler. I've suggested assigning
phonemes to the best 50 infinite-limit commas, and then
sticking them together into Lojban-like temperament names
from the comma sequences.

> Another way to frame the question is, should "meantone" be
> assigned to the 7-limit 81/80 planar temperament, the 11-limit
> 81/80 3D temperament, etc?

Yes. :)

That's how things evolve sometimes - messy. I have no
desire to change it, actually. I'm only interested in the
naming question as a thought experiment to make discoveries
about temperaments in general.

-Carl