2.3.7 superpyth

I still maintain that 2.3.7 64/63 should be superpyth temperament, and
2.3.5.7 64/63 + 245/243 should be an extension of it.

Last I mentioned this, someone told me I needed to invent an entire
theory of subgroup extensions and subgroup badness and so on before I
do this. This is obviously be a long term undertaking. However, this
proposed name is simple and should just happen now.

I propose calling 2.3.7 64/63 "superpyth," and then also calling
2.3.5.7 64/63 245/243 "superpyth," just like 2.3.5 81/80 is "meantone"
and 2.3.5.7 81/80 and 126/125 is also "meantone." This is why:
1) The name "superpyth" for this temperament is in common usage
2) It's already valid to call it "2.3.7 superpyth," so I'm simply
proposing that out of all the "2.3.7 _____________" things it could
be, superpyth simply gets precedence
3) It's better than giving the 2.3.7 64/63 temperament its own name
for no reason

Aside from the challenges that we face in coming up with a
-systematic- way to extend subgroup temperaments from one to the
other, what is the problem with this? I'm gonna say right now that
whatever systematic, algorithmic approach we come up with for handling
subgroup extensions, 2.3.7 64/63 should be "superpyth" no matter what,
and 2.3.5.7 superpyth should be an extension of it.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I still maintain that 2.3.7 64/63 should be superpyth temperament, and
> 2.3.5.7 64/63 + 245/243 should be an extension of it.
>
> Last I mentioned this, someone told me I needed to invent an entire
> theory of subgroup extensions and subgroup badness and so on before I
> do this. This is obviously be a long term undertaking. However, this
> proposed name is simple and should just happen now.
>
> I propose calling 2.3.7 64/63 "superpyth," and then also calling
> 2.3.5.7 64/63 245/243 "superpyth," just like 2.3.5 81/80 is "meantone"
> and 2.3.5.7 81/80 and 126/125 is also "meantone." This is why:
> 1) The name "superpyth" for this temperament is in common usage
> 2) It's already valid to call it "2.3.7 superpyth," so I'm simply
> proposing that out of all the "2.3.7 _____________" things it could
> be, superpyth simply gets precedence
> 3) It's better than giving the 2.3.7 64/63 temperament its own name
> for no reason
>
> Aside from the challenges that we face in coming up with a
> -systematic- way to extend subgroup temperaments from one to the
> other, what is the problem with this? I'm gonna say right now that
> whatever systematic, algorithmic approach we come up with for handling
> subgroup extensions, 2.3.7 64/63 should be "superpyth" no matter what,
> and 2.3.5.7 superpyth should be an extension of it.

I agree with this, and just want to add that technically we're merely choosing one of the possible systematic names to be the canonical one. These are all already technically correct synonyms for this temperament:

2.3.7 dominant
2.3.7 mother
2.3.7 quasisuper
2.3.7 schism
2.3.7 superpyth

All of these unambiguously refer to the 2.3.7 temperament where only 64/63 is tempered out (because their mapping matrices all map 2, 3, and 7 the same way). But some of them are stupid names for it, for example "2.3.7 mother" because mother is much less accurate.

It's important to have a canonical name to make information about the temperament easy to find and avoid confusion, and to me it seems like the only way to choose the canonical ones is on a case-by-case basis, based on etymology and existing usage. In this particular case the obvious choice is "superpyth", so we want to say that the full name for this temperament is "2.3.7 superpyth" and all the other names above are merely synonyms.

Keenan

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

> It's important to have a canonical name to make information about the temperament easy to find and avoid confusion, and to me it seems like the only way to choose the canonical ones is on a case-by-case basis, based on etymology and existing usage. In this particular case the obvious choice is "superpyth", so we want to say that the full name for this temperament is "2.3.7 superpyth" and all the other names above are merely synonyms.

I don't want to be forced into saying "2.3.5.7 superpyth" or "full 7-limit superpyth".

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > It's important to have a canonical name to make information about the temperament easy to find and avoid confusion, and to me it seems like the only way to choose the canonical ones is on a case-by-case basis, based on etymology and existing usage. In this particular case the obvious choice is "superpyth", so we want to say that the full name for this temperament is "2.3.7 superpyth" and all the other names above are merely synonyms.
>
> I don't want to be forced into saying "2.3.5.7 superpyth" or "full 7-limit superpyth".

But you *already* need to say that to avoid ambiguity, because "superpyth" is also the name of a 5-limit temperament, and an 11-limit temperament.

The time to raise this objection was way back when we first ditched "sensipent" and "sensisept" in favor of "sensi" for both.

Keenan

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

> > I don't want to be forced into saying "2.3.5.7 superpyth" or "full 7-limit superpyth".
>
> But you *already* need to say that to avoid ambiguity, because "superpyth" is also the name of a 5-limit temperament, and an 11-limit temperament.

No, all I need to say is "7-limit superpyth".

That's because "7-limit" is code for 2.3.5.7.

-Mike

On Jun 14, 2012, at 3:11 PM, genewardsmith <genewardsmith@...>
wrote:

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

> > I don't want to be forced into saying "2.3.5.7 superpyth" or "full
7-limit superpyth".
>
> But you *already* need to say that to avoid ambiguity, because
"superpyth" is also the name of a 5-limit temperament, and an 11-limit
temperament.

No, all I need to say is "7-limit superpyth".

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > > I don't want to be forced into saying "2.3.5.7 superpyth" or "full 7-limit superpyth".
> >
> > But you *already* need to say that to avoid ambiguity, because "superpyth" is also the name of a 5-limit temperament, and an 11-limit temperament.
>
> No, all I need to say is "7-limit superpyth".
>

I'm not sure if I fully understand what you guys are arguing about, but here is my two cents:

2.3.5.7 (the "7-limit") is an extension of 2.3.7, by definition. There is therefore no need to use the prefix "full," when we can just use the "7-limit" label.

Ryan

--- In tuning@yahoogroups.com, "Ryan Avella" <domeofatonement@...> wrote:
> 2.3.5.7 (the "7-limit") is an extension of 2.3.7, by definition. There is therefore no need to use the prefix "full," when we can just use the "7-limit" label.

Ditto.

"7-limit" has always been shorthand for the 2.3.5.7 subgroup. We're not trying to change that.

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "Ryan Avella" <domeofatonement@> wrote:
> > 2.3.5.7 (the "7-limit") is an extension of 2.3.7, by definition. There is therefore no need to use the prefix "full," when we can just use the "7-limit" label.
>
> Ditto.
>
> "7-limit" has always been shorthand for the 2.3.5.7 subgroup. We're not trying to change that.

The 2.3.7 subgroup always has been and still is a subgroup of the 7-limit but not of any smaller limit, so it's a 7-limit group in one obvious sense. If you say "7-limit superpyth", what, specifically, does that exclude?

On Sat, Jun 16, 2012 at 1:19 AM, genewardsmith <genewardsmith@...>
wrote:
>
> The 2.3.7 subgroup always has been and still is a subgroup of the 7-limit
> but not of any smaller limit, so it's a 7-limit group in one obvious sense.
> If you say "7-limit superpyth", what, specifically, does that exclude?

This is the whole reason why I don't like thinking of 2.3.7 as a
subgroup specifically of the 7-limit group. It all makes way more
sense if you consider 2.3.7 and "the 7-limit," which is code for
2.3.5.7, all to just be subgroups of Q+ under multiplication.

But this is really a terminology issue, isn't it? What do you want
7-limit to mean? The way you're using "7-limit superpyth" above, I
could throw out the same objection that you threw at me when I equated
kees height with odd-limit - if you really want to use 7-limit
superpyth in the way you're using it above, then it doesn't just
include 2.3.7 superpyth, but 2.3.5 superpyth too, and 2.5.7 superpyth,
and 2.3.7/5 superpyth.

On the other hand, you can just decide that "7-limit" means the
multiplicative group generated by primes 2, 3, 5, and 7, and is
basically just a nice way of writing 2.3.5.7; in this sense 2.3.7
isn't a subgroup of 2.3.5.7 any more than it's a subgroup of
2.3.5.7.11.

-Mike

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

> On the other hand, you can just decide that "7-limit" means the
> multiplicative group generated by primes 2, 3, 5, and 7, and is
> basically just a nice way of writing 2.3.5.7; in this sense 2.3.7
> isn't a subgroup of 2.3.5.7 any more than it's a subgroup of
> 2.3.5.7.11.

Mathematicans have this crazy idea that it is.

On Jun 17, 2012, at 6:36 PM, genewardsmith <genewardsmith@...>
wrote:

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

> On the other hand, you can just decide that "7-limit" means the
> multiplicative group generated by primes 2, 3, 5, and 7, and is
> basically just a nice way of writing 2.3.5.7; in this sense 2.3.7
> isn't a subgroup of 2.3.5.7 any more than it's a subgroup of
> 2.3.5.7.11.

Mathematicans have this crazy idea that it is.

Why? How so?

-Mike

On Sun, Jun 17, 2012 at 6:36 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > On the other hand, you can just decide that "7-limit" means the
> > multiplicative group generated by primes 2, 3, 5, and 7, and is
> > basically just a nice way of writing 2.3.5.7; in this sense 2.3.7
> > isn't a subgroup of 2.3.5.7 any more than it's a subgroup of
> > 2.3.5.7.11.
>
> Mathematicans have this crazy idea that it is.

If they're all just subgroups of Q+, then what difference is there
between being "a subgroup of a subgroup of Q+" and just being "a
subgroup of Q+"?

-Mike

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

> > On the other hand, you can just decide that "7-limit" means the
> > multiplicative group generated by primes 2, 3, 5, and 7, and is
> > basically just a nice way of writing 2.3.5.7; in this sense 2.3.7
> > isn't a subgroup of 2.3.5.7 any more than it's a subgroup of
> > 2.3.5.7.11.
>
> Mathematicans have this crazy idea that it is.
>
> Why? How so?

Both 2.3.5 and 2.3.7 are subgroups of both 2.3.5.7 and 2.3.5.7.11, by definition.

On Sun, Jun 17, 2012 at 11:27 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > On the other hand, you can just decide that "7-limit" means the
> > > multiplicative group generated by primes 2, 3, 5, and 7, and is
> > > basically just a nice way of writing 2.3.5.7; in this sense 2.3.7
> > > isn't a subgroup of 2.3.5.7 any more than it's a subgroup of
> > > 2.3.5.7.11.
> >
> > Mathematicans have this crazy idea that it is.
> >
> > Why? How so?
>
> Both 2.3.5 and 2.3.7 are subgroups of both 2.3.5.7 and 2.3.5.7.11, by
> definition.

So how does that make 2.3.7 more a subgroup of 2.3.5.7 than it is
2.3.5.7.11? It's just a subgroup of both, yes?

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > On the other hand, you can just decide that "7-limit" means the
> > multiplicative group generated by primes 2, 3, 5, and 7, and is
> > basically just a nice way of writing 2.3.5.7; in this sense 2.3.7
> > isn't a subgroup of 2.3.5.7 any more than it's a subgroup of
> > 2.3.5.7.11.
>
> Mathematicans have this crazy idea that it is.

Gene, note that Mike didn't say "2.3.7 isn't a subgroup of 2.3.5.7", he said "2.3.7 isn't a subgroup of 2.3.5.7 ANY MORE THAN it's a subgroup of 2.3.5.7.11". In other words, 2.3.7 IS a subgroup of 2.3.5.7, but it's also a subgroup of 2.3.5.7.11. There's no unique prime limit of which it's a subgroup, merely a smallest one.

This is all obvious, but Mike was just making a rhetorical point that while 2.3.7 is 7-limit, it's also 11-limit, 13-limit etc. It is a subgroup of all those prime limits.

I guess that you, Gene, are still arguing that using the name "superpyth" for a 2.3.7 temperament (with some modifier like "2.3.7" obviously being necessary to avoid ambiguity) is a bad idea. Why is it a bad idea?

Keenan

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

> So how does that make 2.3.7 more a subgroup of 2.3.5.7 than it is
> 2.3.5.7.11? It's just a subgroup of both, yes?

Of course.

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

> Gene, note that Mike didn't say "2.3.7 isn't a subgroup of 2.3.5.7", he said "2.3.7 isn't a subgroup of 2.3.5.7 ANY MORE THAN it's a subgroup of 2.3.5.7.11".

Which in my version of English, which is pretty standard, means "2.3.7 is no more a subgroup of 2.3.5.7 than it is a subgroup of 2.3.5.7.11". Don't blame me for this confusion, I'm innocent.

On Mon, Jun 18, 2012 at 4:42 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> > Gene, note that Mike didn't say "2.3.7 isn't a subgroup of 2.3.5.7", he
> > said "2.3.7 isn't a subgroup of 2.3.5.7 ANY MORE THAN it's a subgroup of
> > 2.3.5.7.11".
>
> Which in my version of English, which is pretty standard, means "2.3.7 is
> no more a subgroup of 2.3.5.7 than it is a subgroup of 2.3.5.7.11". Don't
> blame me for this confusion, I'm innocent.

OK. So now that we're all on the same page, I still don't get what
distinction you're drawing between "2.3.5.7 superpyth" and "7-limit
superpyth."

-Mike

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

> OK. So now that we're all on the same page, I still don't get what
> distinction you're drawing between "2.3.5.7 superpyth" and "7-limit
> superpyth."

Someone could easily suppose that 2.3.7 superpyth also counts as 7-limit, as it fits the definition and does not fit the definition for any lower prime limit.

On Tue, Jun 19, 2012 at 1:09 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > OK. So now that we're all on the same page, I still don't get what
> > distinction you're drawing between "2.3.5.7 superpyth" and "7-limit
> > superpyth."
>
> Someone could easily suppose that 2.3.7 superpyth also counts as 7-limit,
> as it fits the definition and does not fit the definition for any lower
> prime limit.

This seems to be primarily a terminological or semantic point, rather
than a conceptual one. What bearing does this have on the notion that
2.3.5.7 64/63 245/243 is an extension of 2.3.7 64/63, and that they
can both share the name "superpyth" just like 2.3.5.7 81/80 126/125
and 2.3.5 81/80 do?

-Mike

> Someone could easily suppose that 2.3.7 superpyth also counts
> as 7-limit, as it fits the definition and does not fit the definition for
> any lower prime limit.

Speaking as a relative outsider, it seems to me that people on this
list and XA *tend* to use "7-limit" to mean "the full 7-limit", i.e.,
2.3.5.7, when talking about temperaments.

I say "tend" because it's probably not consistent.

One might say, "This scale has 7-limit intervals in it" when he means
that the largest prime used in any given interval is 7, but he clearly
doesn't mean that there is an interval that uses 2, 3, 5, and 7 in it.

However, when people talk about a 7-limit temperament, they frequently
seem to mean that it involves all primes up to 7.

Given all of that, it's not confusing to me to say that
* 2.3.7 superpyth is just "superpyth"
* equivalently: that an unqualified "superpyth" is, by definition,
limited to the 2.3.7 version
* to get 2.3.5 superpyth you need to say "5-limit superpyth" or "2.3.5
superpyth" (if such a thing exists)
* to get 2.3.5.7 superpyth you need to say "7-limit superpyth" or
"2.3.5.7 superpyth".

As long as people agree on the definitions, this works just fine for me.

In fact, it would be nice to see a definite name for some particular
temperament, and then see qualifications as extensions rather than as
different names.

For instance, Mohaha is a 2.3.5.11 temperament tempering out 81/80 and
121/120; Mohoho is a 2.3.5.11.13 temperament tempering out 81/80,
121/120, and 66/65. It seems that "Mohoho" could just be called
"2.3.5.11.13 Mohaha". (Maybe you could say "Mohaha+13" instead if you
like.) And it doesn't matter to me if you define Mohaha as "2.3.5.11
Mohoho", either, if that makes sense to someone for traditional or
theoretical reasons.

Some of the basic characteristics of both (e.g., 11/8 * 11/8 = 3/2 *
5/4, deriving from the common 121/120 comma) would be immediately
understood; also, I could remember the prime limits or subgroups for a
smaller number of temperaments, so I wouldn't have to run to the wiki
to see how different the subgroups / limits are.

There may be subtleties I'm missing, but this seems to make sense to me so far.

Regards,
Jake

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

> This seems to be primarily a terminological or semantic point, rather
> than a conceptual one.

I don't think there is a conceptual point at issue. I don't see anything wrong with 2.3.7 superpyth, but I think there's potential for confusion and clumsy locutions in the proposed reform.

On Tue, Jun 19, 2012 at 2:04 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > This seems to be primarily a terminological or semantic point, rather
> > than a conceptual one.
>
> I don't think there is a conceptual point at issue. I don't see anything
> wrong with 2.3.7 superpyth, but I think there's potential for confusion and
> clumsy locutions in the proposed reform.

What specifically do you think will be confusing?

Also, with respect to locutions, isn't it notable that people are
already calling it superpyth and not archy, suggesting that something
in the vein of what I'm proposing would at least be an improvement?

-Mike

Bump this. As you can see, there's a few people here who support this
kind of structure at least specifically for superpyth, so if you have
a serious objection that we may not be thinking of I'd at least like
to know what it is.

-Mike

On Tue, Jun 19, 2012 at 2:14 PM, Mike Battaglia <battaglia01@...>
wrote:
>
> On Tue, Jun 19, 2012 at 2:04 PM, genewardsmith
> <genewardsmith@...>
> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > > This seems to be primarily a terminological or semantic point, rather
> > > than a conceptual one.
> >
> > I don't think there is a conceptual point at issue. I don't see anything
> > wrong with 2.3.7 superpyth, but I think there's potential for confusion
> > and
> > clumsy locutions in the proposed reform.
>
> What specifically do you think will be confusing?
>
> Also, with respect to locutions, isn't it notable that people are
> already calling it superpyth and not archy, suggesting that something
> in the vein of what I'm proposing would at least be an improvement?
>
> -Mike