Some proposed names for important subgroup temperaments

We've sorted out 2.3.7 49/48, which is now "semaphore." Two others
which really badly need sorting out are 2.3.7 12&17 and 2.3.11 7&17,
which are arguably even more important. We currently have naming
confusion surrounding those just like we did with semaphore. I think
we should do again what we did with semaphore and try to organize
things in a nice clean way.

These are things which should define their own familes just like
meantone 2.3.5 81/80 does, or semaphore 2.3.7 49/48 does, and which
ought to have extensions in extension groups of the subgroup just like
any other good rank-2 temperament does.

As you know, these temperaments already have a plethora of possible
names due to Keenan's naming scheme. 2.3.7 12&17 is 2.3.7 superpyth,
2.3.7 dominant, and so on. Likewise, 2.3.5 meantone is also 2.3.5
dominant, 2.3.5 meanenneadecal, etc. However, 2.3.5 meantone also has
one main name, which is "meantone." Below I propose what the main name
for each temperament should be to make everything as clear as
possible.

=2.3.7 12&17 64/63 - SUPERPYTH=
Sometimes I think that this is the most conceptually important rank-2
temperament after meantone, if not the most exotic. It's gone through
a few different names. At one point I think "septipyth" was being
floated around, and now it's called "archy" on the wiki. Almost
everyone calls this "superpyth," and it is indeed 2.3.7 superpyth.
Much like how we swapped "semiphore" with "semaphore," I think it
would be nice to call this "superpyth" and leave the "archy" to the
2.3.5.7 64/63 rank-3 temperament. Then the 2.3.5.7 temperament is just
an extension of superpyth, which it is, and then superpyth and
suprapyth are two 11-limit extensions, etc.

A wrinkle arises in this case that didn't with semaphore. In this
case, Graham's temperament finder also calls this "superpyth":
http://x31eq.com/cgi-bin/rt.cgi?ets=22_5&limit=5

This name is not on the wiki, so I'm not sure if there's a conflict or
if it's supposed to be that way. However, note that this superpyth is
indeed 2.3.5 superpyth using Keenan's naming scheme, so it's not a
false name. However, note that 2.3.5 superpyth is not in the 2.3.7
superpyth family, so it might be wise to call this something else.

One solution presents itself from that I note Erv Wilson and John
Chalmers are both talking about it in Xenharmonikon 1 (!!), which
means they might have precedence anyway. Maybe John Chalmers can weigh
in on who first worked it out. This could be Chalmers or Wilson
temperament. I dunno. Point is, 2.3.7 64/63 should definitely be
superpyth too.

=2.3.11 7&17 1029/1024 - MOHAJIRA=
This temperament is so damn important it needs to have its own page
and family and everything. This temperament is one of the most damn
important things in the entire regular temperament paradigm. In fact,
2.3.5.7.11 mohajira should be a proper extension of THIS guy, and get
off the page which has it as some weird secondary 11-limit extension
of meantone.

The two most popular unofficial names for this are "mohajira" and
"maqamic," both higher-limit temperaments that this is a valid
restriction of. This is important enough that it needs a single valid
name. It's unfortunately going by the name of
"mohajira/maqamic/beatles/hemififths/neutralthirds/oh to hell with it"
temperament though, because nobody knows what to call it. I've
proposed "mohajira" above because it's the oldest as per Graham's
request, and it also makes sense.

This one lends itself immediately to a great family structure that
should be taken advantage of. For instance, it branches off right away
to 2.3.5.11, adding 81/80, and 2.3.7.11, adding 64/63. This is
obviously the "mohajira" branch of the family. The 2.3.5.11
temperament as it stands is currently called "mohajira," but there's
really no reason it shouldn't just be the 2.3.5.11 extension of
"mohajira", especially since its best 2.3.5.7.11-limit extension is
also called "mohajira"!

The other main branch is the 2.3.7.11 extension adding 64/63. Since
the other common name for this neutral thirds temperament is maqamic,
and since 2.3.5.7.11 maqamic is an extension of this adding 36/35,
then this might as well be maqamic.

There are other extensions as well, like the 2.3.11.13 branch adding
144/143, and maybe other 2.3.7.11 branches. They should all be in this
family!

Any objections? I think that this would be pretty huge to clear up.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> These are things which should define their own familes just like
> meantone 2.3.5 81/80 does, or semaphore 2.3.7 49/48 does, and which
> ought to have extensions in extension groups of the subgroup just like
> any other good rank-2 temperament does.
>
> As you know, these temperaments already have a plethora of possible
> names due to Keenan's naming scheme. 2.3.7 12&17 is 2.3.7 superpyth,
> 2.3.7 dominant, and so on. Likewise, 2.3.5 meantone is also 2.3.5
> dominant, 2.3.5 meanenneadecal, etc. However, 2.3.5 meantone also has
> one main name, which is "meantone." Below I propose what the main name
> for each temperament should be to make everything as clear as
> possible.

Hear, hear!

> =2.3.11 7&17 1029/1024 - MOHAJIRA=

Should be 243/242, not 1029/1024.

(2.3.7 1029/1024 seems like it's in a good situation already, because the parent 2.3.7 temperament is "slendric", a name most people seem to like and be comfortable using, and some 2.3.5.7 extensions are rodan, cynder/mothra, gorgo, and guiron. The rank-3 2.3.5.7 temperament shows up as "gamelan" which is an extremely bad name, but nobody seems to talk about that one anyway.)

Keenan

On Jun 4, 2012, at 12:31 PM, keenan_pepper <keenanpepper@...> wrote:

> =2.3.11 7&17 1029/1024 - MOHAJIRA=

Should be 243/242, not 1029/1024.

(2.3.7 1029/1024 seems like it's in a good situation already, because the
parent 2.3.7 temperament is "slendric", a name most people seem to like and
be comfortable using, and some 2.3.5.7 extensions are rodan, cynder/mothra,
gorgo, and guiron. The rank-3 2.3.5.7 temperament shows up as "gamelan"
which is an extremely bad name, but nobody seems to talk about that one
anyway.)

Yeah, 243/242. The other thing was left over from an earlier revision of
the post.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> As you know, these temperaments already have a plethora of possible
> names due to Keenan's naming scheme. 2.3.7 12&17 is 2.3.7 superpyth,
> 2.3.7 dominant, and so on.

Dave Kennan or Keenan Pepper? Those aren't Dave K. names.

> Point is, 2.3.7 64/63 should definitely be superpyth too.

Eh? Why??

> Any objections? I think that this would be pretty huge to clear up.

Aside from equating 64/63 with superpyth, if we're going
to change the Graham list, I think it should be done
algorithmically (not by hand).

-Carl

On Mon, Jun 4, 2012 at 3:57 PM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > As you know, these temperaments already have a plethora of possible
> > names due to Keenan's naming scheme. 2.3.7 12&17 is 2.3.7 superpyth,
> > 2.3.7 dominant, and so on.
>
> Dave Kennan or Keenan Pepper? Those aren't Dave K. names.

Keenan Pepper.

> > Point is, 2.3.7 64/63 should definitely be superpyth too.
>
> Eh? Why??

Graham's list calls this "dominant." The wiki calls it "archy." But
most people, I note, are just calling it "superpyth." I think Igs has
posted a few times that he thinks this should be superpyth "because
nobody cares about the crappy mapping for 5 anyway." So it already has
an unofficial name. If we're going to give it an official name from
which a multitude of options exist, there's no reason we shouldn't
make it the one that's already the unofficial name.

All these lists ought to be changed as little as possible, but where
subgroup temperaments are involved there are often no consistent names
at all. In this cases, I think we should set it up so that there are
consistent and sensible names. Doing so might mean that one of the
names making it inconsistent will have to change. As it stands, Graham
and Gene have both gone ahead and assigned systematic names to
subgroup temperaments in a completely different way.

> > Any objections? I think that this would be pretty huge to clear up.
>
> Aside from equating 64/63 with superpyth, if we're going
> to change the Graham list, I think it should be done
> algorithmically (not by hand).

I think it would be good to do algorithmically in general, save for a
few serious trouble spots which should probably be finessed to make
the whole thing sensible overall. The two above are two examples of
that.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> > > As you know, these temperaments already have a plethora of
> > > possible names due to Keenan's naming scheme. 2.3.7 12&17
> > > is 2.3.7 superpyth, 2.3.7 dominant, and so on.
> >
> > Dave Kennan or Keenan Pepper? Those aren't Dave K. names.
>
> Keenan Pepper.

Is there a link? (I wasn't aware he proposed a naming scheme)

> > > Point is, 2.3.7 64/63 should definitely be superpyth too.
> >
> > Eh? Why??
>
> Graham's list calls this "dominant." The wiki calls it "archy."
> But most people, I note, are just calling it "superpyth."

Why do they do that (and who are they)?
I call it 2.3.7 dominant. The comma I associate with
superpythagorean is 36/35.

> I think Igs has
> posted a few times that he thinks this should be superpyth
> "because nobody cares about the crappy mapping for 5 anyway."

Uh...

> All these lists ought to be changed as little as possible, but
> where subgroup temperaments are involved there are often no
> consistent names at all. In this cases, I think we should set
> it up so that there are consistent and sensible names. Doing so
> might mean that one of the names making it inconsistent will
> have to change. As it stands, Graham and Gene have both gone
> ahead and assigned systematic names to subgroup temperaments
> in a completely different way.

Sounds like a good move to me, but again, it would be
good to do it with an algorithm everyone can understand
and comment on.

Graham and Gene use systematic names?? Gene's the
godfather of trivial names, and Graham pulls from him.

> > Aside from equating 64/63 with superpyth, if we're going
> > to change the Graham list, I think it should be done
> > algorithmically (not by hand).
>
> I think it would be good to do algorithmically in general,

Great! Any proposals?

-Carl

On Mon, Jun 4, 2012 at 4:41 PM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > > Dave Kennan or Keenan Pepper? Those aren't Dave K. names.
> >
> > Keenan Pepper.
>
> Is there a link? (I wasn't aware he proposed a naming scheme)

Yes, it was in these two threads:
/tuning/topicId_101888.html#101888
/tuning-math/message/19938

> > > > Point is, 2.3.7 64/63 should definitely be superpyth too.
> > >
> > > Eh? Why??
> >
> > Graham's list calls this "dominant." The wiki calls it "archy."
> > But most people, I note, are just calling it "superpyth."
>
> Why do they do that (and who are they)?
> I call it 2.3.7 dominant. The comma I associate with
> superpythagorean is 36/35.

36/35 for superpyth? 7-limit superpyth doesn't temper out 36/35;
that's tempered out by armodue and dominant and such. Did you mean
something else?

As for why people call it superpyth - if you play around with
superpyth in 22-EDO or 27-EDO, the mapping for 5, or 5/3, or 7/5, or
any simple ratio involving 5 doesn't appear in the diatonic scale at
all, so it's quite natural to think of it as a 2.3.7 temperament "with
some other mapping for 5 that doesn't turn up much." So it's common to
hear people talk about superpyth in 17-EDO and such too, despite that
superpyth is only in 17p and not 17c, because people aren't thinking
of the mapping for 5 at all. On the other hand, dominant[7] does have
both 5 and 7 turn up, so there's no reason to think of it as a
subgroup temperament and that name didn't catch on.

"They" are the usual group of newer theorists/composers who also like
regular mapping theory. I'll list Keenan, Ryan, John M, Andrew
Heathwaite, Jacob Barton, Igs, and myself as people I can remember
calling it "superpyth" off the top of my head. "Meantone" usually
means the temperament mapping the thirds to 5/4 and 6/5, "superpyth"
is the one mapping them to 9/7 and 7/6, and "dominant" is the one that
mixes the two. It's simple and sensible and neat, and a good example
of the sorts of naming structures that have cropped up organically as
an attempt to digest this stuff.

> Sounds like a good move to me, but again, it would be
> good to do it with an algorithm everyone can understand
> and comment on.

An algorithm would be nice, but there are certain trouble spots which
probably require more finesse, and this is one of them.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> > > Keenan Pepper.
> >
> > Is there a link? (I wasn't aware he proposed a naming scheme)
>
> Yes, it was in these two threads:
> /tuning/topicId_101888.html#101888
> /tuning-math/message/19938

Thanks.

> 36/35 for superpyth? 7-limit superpyth doesn't temper out 36/35;
> that's tempered out by armodue and dominant and such. Did you mean
> something else?

Jesus H, I had these backwards. I have 22 on the brain.
You're right, 2.3.7 superpyth it is.

> > Sounds like a good move to me, but again, it would be
> > good to do it with an algorithm everyone can understand
> > and comment on.
>
> An algorithm would be nice, but there are certain trouble
> spots which probably require more finesse, and this is
> one of them.

That's fine, but where's the algorithm which we're
finessing? Keenan's (above)?

-Carl

On Mon, Jun 4, 2012 at 6:34 PM, Carl Lumma <carl@...> wrote:
>
> > 36/35 for superpyth? 7-limit superpyth doesn't temper out 36/35;
> > that's tempered out by armodue and dominant and such. Did you mean
> > something else?
>
> Jesus H, I had these backwards. I have 22 on the brain.
> You're right, 2.3.7 superpyth it is.

Hurrah!

> > An algorithm would be nice, but there are certain trouble
> > spots which probably require more finesse, and this is
> > one of them.
>
> That's fine, but where's the algorithm which we're
> finessing? Keenan's (above)?

Any algorithm is going to require comparing the badness of
temperaments across subgroups, and we're not going to be able to do
that until we have a great way to compare temperaments across
subgroups, e.g. something like the "superbadness" measure I proposed
earlier. Then we'll be able to talk sensibly about lowest-badness
temperaments in a way that crosses across subgroups.

A starting point, but probably an inadequate one, would be to look at
the best rank-2 full-limit temperament which restricts to the subgroup
name as per Keenan's naming scheme. Unfortunately, without the above
tool in place, it's not clear which subgroup temperaments even need
naming at all, or which is the "best subgroup restriction" of some
full-limit temperament which the temperament should be an extension of
(or how to break ties if there's more than one contender).

Even more importantly, though, it still wouldn't be clear when to use
the systematic names given by an algorithm, vs when you should pick a
name for the family directly as a "seed" to use in future names. We
probably don't want any more names if we can avoid them, but there are
probably times when the "obvious name" for a temperament will conflict
with the results of the algorithm, and in that case the obvious name
should be grandfathered in. My criteria for when to grandfather a name
in would be one of more of the following

1) There's already another name which is in common use, and which
doesn't conflict with the temperament structure or the basics of RMP
in general
2) There's some reasonable consensus that another name would be better
3) The "correct" name to use is more or less obvious

There are probably only four or five names I'd propose as meeting this
criterion, most of which were already handled - obvious things like
"semaphore" and "superpyth." There might be one or two left I think
should be assigned official names that correspond to their existing
unofficial names. Other than that, the rest should be done
algorithmically, and I think the first step to solving that problem
the right way is to come up with the proper superbadness measure
first.

-Mike

I prefer "maqamic" for 2.3.11 243/242 because that name makes an obvious
connection to maqam music. "Mohajira" would be too esoteric for such a
basic temperament family and no one would immediately recognize the
rationale for the name.

In what source did Jacque Dudon call 2.3.11 243/242 "mohajira"?

On Mon, Jun 4, 2012 at 7:12 AM, Mike Battaglia <battaglia01@...>wrote:

> We've sorted out 2.3.7 49/48, which is now "semaphore." Two others
> which really badly need sorting out are 2.3.7 12&17 and 2.3.11 7&17,
> which are arguably even more important. We currently have naming
> confusion surrounding those just like we did with semaphore. I think
> we should do again what we did with semaphore and try to organize
> things in a nice clean way.
>
> These are things which should define their own familes just like
> meantone 2.3.5 81/80 does, or semaphore 2.3.7 49/48 does, and which
> ought to have extensions in extension groups of the subgroup just like
> any other good rank-2 temperament does.
>
> As you know, these temperaments already have a plethora of possible
> names due to Keenan's naming scheme. 2.3.7 12&17 is 2.3.7 superpyth,
> 2.3.7 dominant, and so on. Likewise, 2.3.5 meantone is also 2.3.5
> dominant, 2.3.5 meanenneadecal, etc. However, 2.3.5 meantone also has
> one main name, which is "meantone." Below I propose what the main name
> for each temperament should be to make everything as clear as
> possible.
>
>
> =2.3.7 12&17 64/63 - SUPERPYTH=
> Sometimes I think that this is the most conceptually important rank-2
> temperament after meantone, if not the most exotic. It's gone through
> a few different names. At one point I think "septipyth" was being
> floated around, and now it's called "archy" on the wiki. Almost
> everyone calls this "superpyth," and it is indeed 2.3.7 superpyth.
> Much like how we swapped "semiphore" with "semaphore," I think it
> would be nice to call this "superpyth" and leave the "archy" to the
> 2.3.5.7 64/63 rank-3 temperament. Then the 2.3.5.7 temperament is just
> an extension of superpyth, which it is, and then superpyth and
> suprapyth are two 11-limit extensions, etc.
>
> A wrinkle arises in this case that didn't with semaphore. In this
> case, Graham's temperament finder also calls this "superpyth":
> http://x31eq.com/cgi-bin/rt.cgi?ets=22_5&limit=5
>
> This name is not on the wiki, so I'm not sure if there's a conflict or
> if it's supposed to be that way. However, note that this superpyth is
> indeed 2.3.5 superpyth using Keenan's naming scheme, so it's not a
> false name. However, note that 2.3.5 superpyth is not in the 2.3.7
> superpyth family, so it might be wise to call this something else.
>
> One solution presents itself from that I note Erv Wilson and John
> Chalmers are both talking about it in Xenharmonikon 1 (!!), which
> means they might have precedence anyway. Maybe John Chalmers can weigh
> in on who first worked it out. This could be Chalmers or Wilson
> temperament. I dunno. Point is, 2.3.7 64/63 should definitely be
> superpyth too.
>
>
> =2.3.11 7&17 1029/1024 - MOHAJIRA=
> This temperament is so damn important it needs to have its own page
> and family and everything. This temperament is one of the most damn
> important things in the entire regular temperament paradigm. In fact,
> 2.3.5.7.11 mohajira should be a proper extension of THIS guy, and get
> off the page which has it as some weird secondary 11-limit extension
> of meantone.
>
> The two most popular unofficial names for this are "mohajira" and
> "maqamic," both higher-limit temperaments that this is a valid
> restriction of. This is important enough that it needs a single valid
> name. It's unfortunately going by the name of
> "mohajira/maqamic/beatles/hemififths/neutralthirds/oh to hell with it"
> temperament though, because nobody knows what to call it. I've
> proposed "mohajira" above because it's the oldest as per Graham's
> request, and it also makes sense.
>
> This one lends itself immediately to a great family structure that
> should be taken advantage of. For instance, it branches off right away
> to 2.3.5.11, adding 81/80, and 2.3.7.11, adding 64/63. This is
> obviously the "mohajira" branch of the family. The 2.3.5.11
> temperament as it stands is currently called "mohajira," but there's
> really no reason it shouldn't just be the 2.3.5.11 extension of
> "mohajira", especially since its best 2.3.5.7.11-limit extension is
> also called "mohajira"!
>
> The other main branch is the 2.3.7.11 extension adding 64/63. Since
> the other common name for this neutral thirds temperament is maqamic,
> and since 2.3.5.7.11 maqamic is an extension of this adding 36/35,
> then this might as well be maqamic.
>
> There are other extensions as well, like the 2.3.11.13 branch adding
> 144/143, and maybe other 2.3.7.11 branches. They should all be in this
> family!
>
>
> Any objections? I think that this would be pretty huge to clear up.
>
> -Mike
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

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

> Any objections? I think that this would be pretty huge to clear up.

I mobject. Naming subgroup families is great, but you are proposing a massive and brutal renaming.

On Mon, Jun 4, 2012 at 8:39 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Any objections? I think that this would be pretty huge to clear up.
>
> I mobject. Naming subgroup families is great, but you are proposing a
> massive and brutal renaming.

The massive and brutal renaming would require me to spend about 30
minutes changing pages on the wiki.

Your objection seems to be "this would require us to change things,"
but I think that objection only works if everyone's happy with the way
things are. As it currently stands, I think the consensus is that the
way we're currently naming subgroup temperaments isn't working.

And at any rate it looks, for now, like the only thing which would
have to change is "archy" -> "superpyth," since it looks like the
2.3.11 243/242 discussion is going to go on. Surely you don't object
that this temperament should still be "archy"?

-Mike

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

> As for why people call it superpyth - if you play around with
> superpyth in 22-EDO or 27-EDO, the mapping for 5, or 5/3, or 7/5, or
> any simple ratio involving 5 doesn't appear in the diatonic scale at
> all, so it's quite natural to think of it as a 2.3.7 temperament "with
> some other mapping for 5 that doesn't turn up much."

Superpyth is a good temperament in the full 7-limit and has been called by that name for years. Find another name!

On Mon, Jun 4, 2012 at 8:46 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > As for why people call it superpyth - if you play around with
> > superpyth in 22-EDO or 27-EDO, the mapping for 5, or 5/3, or 7/5, or
> > any simple ratio involving 5 doesn't appear in the diatonic scale at
> > all, so it's quite natural to think of it as a 2.3.7 temperament "with
> > some other mapping for 5 that doesn't turn up much."
>
> Superpyth is a good temperament in the full 7-limit and has been called by
> that name for years. Find another name!

If you say that 2.3.7 64/63 is superpyth, then 2.3.5.7 superpyth still
is a good temperament in the full 7-limit. It's just an extension of
it.

-Mike

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

> And at any rate it looks, for now, like the only thing which would
> have to change is "archy" -> "superpyth," since it looks like the
> 2.3.11 243/242 discussion is going to go on. Surely you don't object
> that this temperament should still be "archy"?

I don't care what you call it, so long as you don't steal a name such as superpyth which has long been used to mean something else.

On Mon, Jun 4, 2012 at 8:51 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > And at any rate it looks, for now, like the only thing which would
> > have to change is "archy" -> "superpyth," since it looks like the
> > 2.3.11 243/242 discussion is going to go on. Surely you don't object
> > that this temperament should still be "archy"?
>
> I don't care what you call it, so long as you don't steal a name such as
> superpyth which has long been used to mean something else.

Objecting that 2.3.7 superpyth and 2.3.5.7 superpyth shouldn't both be
superpyth is like objecting that 2.3.5 meantone and 2.3.5.7 meantone
shouldn't both be meantone.

-Mike

On Mon, Jun 4, 2012 at 8:39 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Any objections? I think that this would be pretty huge to clear up.
>
> I mobject. Naming subgroup families is great, but you are proposing a
> massive and brutal renaming.

Plus, I totally object to this statement. How is there any massiveness
or brutality in anything I said? So far I haven't required any names
to be changed at all, save for one 5-limit temperament which had a
conflict with the wiki. The whole point of this is to design in
grandfathered names which require almost nothing to change.

-Mike

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

> I don't care what you call it, so long as you don't steal a name such as superpyth which has long been used to mean something else.
>

Aside from the historical argument, you need to consider what a vast and complicated can of worms you open up in terms of all of the possibilities for JI groups. P-limits give us a systematic way to categorize these groups as subgroups, for which you've provided no alternative. I simply happily go ahead and treat each group separately, but you are wanting to do something else, without any tools to do it with I can see. Also, of course, you need to consider that if you look at something like 2.3.7-64/63; you are in the exact same position as 2.3.5-81/80, except now the new prime which forces itself on you is not higher limit (7), but lower limit (5). Why not be systematic about it to start out with if that is going to happen?

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

> Objecting that 2.3.7 superpyth and 2.3.5.7 superpyth shouldn't both be
> superpyth is like objecting that 2.3.5 meantone and 2.3.5.7 meantone
> shouldn't both be meantone.

Not hardly. I don't object to 2.3.7-superpyth as analogous to 5-limit or 7-limit meantone though.

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

> Plus, I totally object to this statement. How is there any massiveness
> or brutality in anything I said?

Oh, please. You want to kick superpyth to the curb and that's clearly just for starters.

On Mon, Jun 4, 2012 at 9:09 PM, genewardsmith <genewardsmith@...>
wrote:
>
> > Plus, I totally object to this statement. How is there any massiveness
> > or brutality in anything I said?
>
> Oh, please. You want to kick superpyth to the curb and that's clearly just
> for starters.

I don't get why you keep saying I want to "kick it to the curb." I'm
saying that there should still be a 2.3.5.7 superpyth. I'm not sure
what you think I'm saying.

There's no problem with this structure
2.3.5 81/80 - meantone
2.3.5.7 81/80 126/125 - meantone

So there shouldn't be any problem with this structure
2.3.7 64/63 - superpyth
2.3.5.7 64/63 245/243 - superpyth

But you have a problem with one and not the other. What is the
problem? How is this kicking it to the curb?

-Mike

On Mon, Jun 4, 2012 at 9:05 PM, genewardsmith <genewardsmith@...>
wrote:
>
> Aside from the historical argument, you need to consider what a vast and
> complicated can of worms you open up in terms of all of the possibilities
> for JI groups. P-limits give us a systematic way to categorize these groups
> as subgroups, for which you've provided no alternative.

I'll respond to all this on tuning-math.

-Mike

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

> > That's fine, but where's the algorithm which we're
> > finessing? Keenan's (above)?
>
> Any algorithm is going to require comparing the badness of
> temperaments across subgroups, and we're not going to be able
> to do that until we have a great way to compare temperaments
> across subgroups, e.g. something like the "superbadness"
> measure I proposed earlier.

I implied earlier that the badness of a temperament should
be entirely determined by its kernel. That's clearly true
for codimension 1 temperaments, but it may not be true for
larger kernels. Tenney weighting will keep distances constant
but the change of basis can change angles... -Carl

On Tue, Jun 5, 2012 at 2:36 AM, Carl Lumma <carl@...> wrote:
>
> I implied earlier that the badness of a temperament should
> be entirely determined by its kernel. That's clearly true
> for codimension 1 temperaments, but it may not be true for
> larger kernels. Tenney weighting will keep distances constant
> but the change of basis can change angles... -Carl

This would rate 2.3.5 JI and 53.137.269/263 JI equally, since they
both have trivial kernels. But the former is Good and the latter is
clearly Bad.

-Mike

On Tue, Jun 5, 2012 at 2:47 AM, Mike Battaglia <battaglia01@...> wrote:
> This would rate 2.3.5 JI and 53.137.269/263 JI equally, since they
> both have trivial kernels. But the former is Good and the latter is
> clearly Bad.

I also note that this means that subgroup complexity * temperament
complexity * temperament error is not a good idea for badness, as it
means the best rank-2 temperaments are going to end up being rank-2 JI
subgroups; 223.911 JI will beat out 2.3.5 81/80 under that scheme.
Subgroup complexity * temperament complexity * (1+temperament error)
might do the trick, but now I'm getting ahead of myself.

-Mike

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

> > I implied earlier that the badness of a temperament should
> > be entirely determined by its kernel. That's clearly true
> > for codimension 1 temperaments, but it may not be true for
> > larger kernels. Tenney weighting will keep distances constant
> > but the change of basis can change angles... -Carl
>
> This would rate 2.3.5 JI and 53.137.269/263 JI equally, since
> they both have trivial kernels. But the former is Good and the
> latter is clearly Bad.

Not the kind of counterexample I had in mind... Is 2.3.5.7 81/80
worse than 2.3.5 81/80? Maybe, but it's not the same as asking
whether 2.3.5.7 81/80 64/63 is worse than 2.9.5.7 81/80 64/63...

-Carl

On Jun 5, 2012, at 4:00 AM, Carl Lumma <carl@...> wrote:

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

> > I implied earlier that the badness of a temperament should
> > be entirely determined by its kernel. That's clearly true
> > for codimension 1 temperaments, but it may not be true for
> > larger kernels. Tenney weighting will keep distances constant
> > but the change of basis can change angles... -Carl
>
> This would rate 2.3.5 JI and 53.137.269/263 JI equally, since
> they both have trivial kernels. But the former is Good and the
> latter is clearly Bad.

Not the kind of counterexample I had in mind... Is 2.3.5.7 81/80
worse than 2.3.5 81/80?

Yeah, now that's the question. More generally, is 2.3.5.7 JI worse than
2.3.5 JI?

- If they're the same, then 2.3.5.11 has to be worse than 2.3.5.

- If 2.3.5 is better, then the best subgroup is {1/1}.

- If 2.3.5.7 is better, then we can expect 2.3.5.x to approach the goodness
of 2.3.5 for increasing prime x.

The latter sounds like the most sensible way to go. But, that also sounds
like we're going to get an infinite series of arbitrarily stupid meantones
on subgroups like 2.3.5.8291, with 81/80 and one other weird comma
vanishing, the damage from which we only care about by an extremely small
amount, all of which arbitrarily approach 2.3.5 meantone...

-Mike

Dong Bin Choi <dtothefourthchoi@...> wrote:

> In what source did Jacque Dudon call 2.3.11 243/242
> "mohajira"?

/tuning/topicId_95224.html#95270

This is the definitive message, and includes "any triple of
a Miracle generator is a Mohajira":

/tuning/topicId_28844.html#88491

I put 2.3.11 (and 2.3.13, as it happens) Mohajira in
my database after that message. Later on, "the triple
of a Secor":

/tuning/topicId_89197.html#89289

Graham

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Jun 5, 2012, at 4:00 AM, Carl Lumma <carl@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > > I implied earlier that the badness of a temperament should
> > > be entirely determined by its kernel. That's clearly true
> > > for codimension 1 temperaments, but it may not be true for
> > > larger kernels. Tenney weighting will keep distances constant
> > > but the change of basis can change angles... -Carl
> >
> > This would rate 2.3.5 JI and 53.137.269/263 JI equally, since
> > they both have trivial kernels. But the former is Good and the
> > latter is clearly Bad.
>
> Not the kind of counterexample I had in mind... Is 2.3.5.7 81/80
> worse than 2.3.5 81/80?
>
> Yeah, now that's the question.

No, I meant that's still not the question I had in mind.
This question is easy -- either the choice of a subgroup
is a statement of interest, in which case you don't use
any subgroup penalty, or it isn't, in which case something
like Paul's suggestion (also made by me when I was working
with Igs in January) should do.

It seems harder to compare kernels in different subgroups
(my last sentence, clipped above).

> - If 2.3.5.7 is better, then we can expect 2.3.5.x to approach
> the goodness of 2.3.5 for increasing prime x.

Better? You mean worse?

> But, that also sounds
> like we're going to get an infinite series of arbitrarily
> stupid meantones on subgroups like 2.3.5.8291,

I guess you didn't mean worse...

-Carl

On Jun 5, 2012, at 1:19 PM, Carl Lumma <carl@...> wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > This would rate 2.3.5 JI and 53.137.269/263 JI equally, since
> > they both have trivial kernels. But the former is Good and the
> > latter is clearly Bad.
>
> Not the kind of counterexample I had in mind... Is 2.3.5.7 81/80
> worse than 2.3.5 81/80?
>
> Yeah, now that's the question.

No, I meant that's still not the question I had in mind.
This question is easy -- either the choice of a subgroup
is a statement of interest, in which case you don't use
any subgroup penalty, or it isn't, in which case something
like Paul's suggestion (also made by me when I was working
with Igs in January) should do.

It seems harder to compare kernels in different subgroups
(my last sentence, clipped above).

I'm just trying to work it out consistently so that JI is a temperament
like anything else, just one with trivial kernel. So if some function says
that 2.3.5 1/1 is better than 2.81.5 1/1, it should also say thay 2.3.5
81/80 is better than 2.81.5 81/80, no?

> - If 2.3.5.7 is better, then we can expect 2.3.5.x to approach
> the goodness of 2.3.5 for increasing prime x.

Better? You mean worse?

> But, that also sounds
> like we're going to get an infinite series of arbitrarily
> stupid meantones on subgroups like 2.3.5.8291,

I guess you didn't mean worse...

There are 3 options I gave, which are that 2.3.5.7 is worse, the same, or
better than 2.3.5. If it's worse, you can expect the best subgroup to be
the one generated by 1/1, which is no good. If 2.3.5.anything is better
than 2.3.5, but arbitrarily approaches 2.3.5 as anything -> Inf, you get
the behavior anove. I actually think that might be the right way to go, and
that it'll be more of a pragmatic problem for temperament finder apps than
a problem with the actual theory...

-Mike

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

> There are 3 options I gave, which are that 2.3.5.7 is worse, the
> same, or better than 2.3.5. If it's worse, you can expect the best
> subgroup to be the one generated by 1/1, which is no good.

What's wrong with Paul's suggestion?

-Carl

> > > Keenan Pepper.
> >
> > Is there a link? (I wasn't aware he proposed a naming scheme)
>
> Yes, it was in these two threads:
>
> /tuning/topicId_101888.html#101888
> /tuning-math/message/19938

Not sure I follow all the consequences of the naming
proposal. I love the insanity idea though. Has anyone
gone through Graham's database to see if any insane
temperaments have been named? -Carl

On Jun 5, 2012, at 3:35 PM, Carl Lumma <carl@...> wrote:

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

> There are 3 options I gave, which are that 2.3.5.7 is worse, the
> same, or better than 2.3.5. If it's worse, you can expect the best
> subgroup to be the one generated by 1/1, which is no good.

What's wrong with Paul's suggestion?

-Carl

How do you compare 2.3.5 to 2.3.5.7 then? You have to compare the area of a
square to the volume of a cube and so on.

-Mike

On Jun 5, 2012, at 3:43 PM, Carl Lumma <carl@...> wrote:

> > > Keenan Pepper.
> >
> > Is there a link? (I wasn't aware he proposed a naming scheme)
>
> Yes, it was in these two threads:
>
> /tuning/topicId_101888.html#101888
> /tuning-math/message/19938

Not sure I follow all the consequences of the naming
proposal. I love the insanity idea though. Has anyone
gone through Graham's database to see if any insane
temperaments have been named? -Carl

It was just a rigorous way to formalize the intuitive concept of "2.3.7
superpyth" or something. For instance, 2.3.11 mohajira is valid, but 2.3.5
mohajira isn't, because it's contorted. The insanity thing is just another
wrinkle to watch for. I suggested the name "proper subgroup restriction"
for those temperaments which meet the requirements.

-Mike