Yahoo Tuning Groups Ultimate Backup tuning Subgroup temperament naming

Before we just arbitrarily pick a name like "mohajira" or "neutraltet"
or whatever, I want to say this about the way we've been naming
subgroup temperaments in general:

The paradigm that was around when I joined the list was this: there
were 5-limit temperaments, and then they "extend" into 7-limit
temperaments, and they "extend" further into 11-limit temperaments and
so on. There was a nice sort of tree-like naming structure that
resulted from this, which organized everything beautifully.

Then subgroups came into it and ruined everything! We're still half
into that older paradigm, and half into a new one. We're treating
subgroups as these weird temperaments on the side which don't really
have a nice, consistent naming structure. We're typically giving them
a ton of cute respellings of full-limit temperament names too, and
since there are a million subgroup temperaments there are a million
names for essentially different versions of the same thing.

I'll be bold and say that there's a pretty strong consensus that
something about the naming system for subgroup temperaments is
suboptimal as it stands. The thing we're doing now is analogous to
Paul's having different names for "negripent" and "negrisept" and
such, which also didn't catch on. Coming up with different respelled
names for subgroup versions of the same thing is basically just -pent
and -sept extensions all over again.

But we also don't want to pollute the hell out of the naming
structure. WTF do we do? Fortunately, I think there's a simple
solution to the whole problem which will make everyone happy:

Instead of considering things like 2.3.5.7 temperaments to be
"fundamental" and 2.3.7 temperaments to be "weird subgroup versions"
of those, we should consider in certain cases that a 2.3.7 temperament
can be fundamental, and that a 2.3.5.7 temperament can be an
"extension" to it. In other words, we should just treat it the same
way we treat 5-limit and 7-limit temperaments: 2.3.7 temperaments are
simple temperaments which have 2.3.5.7-limit "extensions". The only
difference is, instead of these being "higher-limit" extensions,
they're more like "fuller-limit" extensions or something.

A 2.3.11 subgroup temperament ought to be able to have 2.3.7.11-limit
extensions, 2.3.5.11 extensions, 2.3.5.7.11 extensions, and so on. And
then, once you give something like a 2.3.11 subgroup temperament a
name, there's nothing wrong with higher-limit or fuller-limit
extensions sharing that name, just like there's nothing wrong with the
2.3.5, 2.3.5.7, and 2.3.5.7.11 temperaments all being meantone.

Using this approach, I think that we can come up with a much stronger
and sensible approach to naming subgroup temperaments - and one which
will break a minimum number of existing names. It does mean that
certain temperaments which were assigned systematic names (like
"neutraltet") or respelling of names (like "skwares") may make more
sense to be considered "fundamental" temperaments with
correspondingly-named full-limit extensions.

People these days don't seem to care as much about this idea that
there's a logical progression from the 5-limit into the 7-limit into
the 11-limit and so on. But I note that people ARE interested in a
progression from triadic harmony, to tetradic harmony, to pentadic
harmony and so on. Since MOS is so popular, this means that what's of
interest is in codimension-1, rank-2 temperaments on good subgroups,
which extend to codimension-2 rank-2 temperaments on a larger good
subgroup, which extend to codimension-3 rank-2 temperaments, and so
on. This is what's taking the place of 2.3.5 -> 2.3.5.7 -> 2.3.5.7.11
-> etc.

I'd like everyone's thoughts on this! I think it's sensible, and in
many ways the complement of Keenan's subgroup temperament naming idea.
I think it would be wise to see if we can reach some sort of useful
agreement on this point first, before we just pick a name for a
temperament as fundamentally important as 2.3.11 243/242 without
thinking of the implications of it.

It does lead to the question "how do we sort subgroups by
'goodness'?", but that's a topic for another post :)

-Mike

🔗Graham Breed <gbreed@...>

Mike Battaglia <battaglia01@...> wrote:

> I'd like everyone's thoughts on this! I think it's
> sensible, and in many ways the complement of Keenan's
> subgroup temperament naming idea. I think it would be
> wise to see if we can reach some sort of useful agreement
> on this point first, before we just pick a name for a
> temperament as fundamentally important as 2.3.11 243/242
> without thinking of the implications of it.

I should think it's a sensible idea. What else would we
do? I was working with neutral third scales -- 2.3.11
243/242 -- over 10 years ago. Of course they can be
extended into the 5-limit in a meantone-like way or into
the 7-limit different ways. You know 2.3.11 is the core
because these are the simplest primes, and define the
period and generator.

I thought we settled on the name two years ago ---
Mohajira, with Jacques Dudon specifying the mappings of
primes beyond 11. Apparently I was wrong, and now we need to
argue about it again.

Graham

🔗Mike Battaglia <battaglia01@...>

On Sat, May 19, 2012 at 4:02 PM, Graham Breed <gbreed@...> wrote:
>
> I thought we settled on the name two years ago ---
> Mohajira, with Jacques Dudon specifying the mappings of
> primes beyond 11. Apparently I was wrong, and now we need to
> argue about it again.

At this point I don't give a damn about mohajira vs maqamic or
whatever. I'm talking about the larger issue of how we should approach
subgroups in general. If anything, everything I'm saying should
support your argument that we should call it "mohajira" instead of
"neutraltet."

The last thing I want is for this thread to degenerate into an
argument over which names get precedence. There will undoubtedly be a
few of those. We worked it out nicely for semaphore and we can work it
out nicely with those too. I just want us to agree on an approach as a
first pass.

Arguments on these things can get petty sometimes. I'm trying to move
on past these sorts of things and come up with at least a high-level
solution to the problem in general, because everyone on XA is like
"what the frig are these people talking about? squares, skwares,
skwarez, mohaha, mohoho, mumumumu?" and that just can't continue.

-Mike

🔗Mike Battaglia <battaglia01@...>

Still curious to see if Gene might approve of this idea, which will
surely revolutionize our naming system and thus possibly our field,
and then potentially all the world forever.

-Mike

On Sat, May 19, 2012 at 3:41 PM, Mike Battaglia <battaglia01@...> wrote:
> Before we just arbitrarily pick a name like "mohajira" or "neutraltet"
> or whatever, I want to say this about the way we've been naming
> subgroup temperaments in general:
>
> The paradigm that was around when I joined the list was this: there
> were 5-limit temperaments, and then they "extend" into 7-limit
> temperaments, and they "extend" further into 11-limit temperaments and
> so on. There was a nice sort of tree-like naming structure that
> resulted from this, which organized everything beautifully.
>
> Then subgroups came into it and ruined everything! We're still half
> into that older paradigm, and half into a new one. We're treating
> subgroups as these weird temperaments on the side which don't really
> have a nice, consistent naming structure. We're typically giving them
> a ton of cute respellings of full-limit temperament names too, and
> since there are a million subgroup temperaments there are a million
> names for essentially different versions of the same thing.
>
> I'll be bold and say that there's a pretty strong consensus that
> something about the naming system for subgroup temperaments is
> suboptimal as it stands. The thing we're doing now is analogous to
> Paul's having different names for "negripent" and "negrisept" and
> such, which also didn't catch on. Coming up with different respelled
> names for subgroup versions of the same thing is basically just -pent
> and -sept extensions all over again.
>
> But we also don't want to pollute the hell out of the naming
> structure. WTF do we do? Fortunately, I think there's a simple
> solution to the whole problem which will make everyone happy:
>
> Instead of considering things like 2.3.5.7 temperaments to be
> "fundamental" and 2.3.7 temperaments to be "weird subgroup versions"
> of those, we should consider in certain cases that a 2.3.7 temperament
> can be fundamental, and that a 2.3.5.7 temperament can be an
> "extension" to it. In other words, we should just treat it the same
> way we treat 5-limit and 7-limit temperaments: 2.3.7 temperaments are
> simple temperaments which have 2.3.5.7-limit "extensions". The only
> difference is, instead of these being "higher-limit" extensions,
> they're more like "fuller-limit" extensions or something.
>
> A 2.3.11 subgroup temperament ought to be able to have 2.3.7.11-limit
> extensions, 2.3.5.11 extensions, 2.3.5.7.11 extensions, and so on. And
> then, once you give something like a 2.3.11 subgroup temperament a
> name, there's nothing wrong with higher-limit or fuller-limit
> extensions sharing that name, just like there's nothing wrong with the
> 2.3.5, 2.3.5.7, and 2.3.5.7.11 temperaments all being meantone.
>
> Using this approach, I think that we can come up with a much stronger
> and sensible approach to naming subgroup temperaments - and one which
> will break a minimum number of existing names. It does mean that
> certain temperaments which were assigned systematic names (like
> "neutraltet") or respelling of names (like "skwares") may make more
> sense to be considered "fundamental" temperaments with
> correspondingly-named full-limit extensions.
>
> People these days don't seem to care as much about this idea that
> there's a logical progression from the 5-limit into the 7-limit into
> the 11-limit and so on. But I note that people ARE interested in a
> progression from triadic harmony, to tetradic harmony, to pentadic
> harmony and so on. Since MOS is so popular, this means that what's of
> interest is in codimension-1, rank-2 temperaments on good subgroups,
> which extend to codimension-2 rank-2 temperaments on a larger good
> subgroup, which extend to codimension-3 rank-2 temperaments, and so
> on. This is what's taking the place of 2.3.5 -> 2.3.5.7 -> 2.3.5.7.11
> -> etc.
>
> I'd like everyone's thoughts on this! I think it's sensible, and in
> many ways the complement of Keenan's subgroup temperament naming idea.
> I think it would be wise to see if we can reach some sort of useful
> agreement on this point first, before we just pick a name for a
> temperament as fundamentally important as 2.3.11 243/242 without
> thinking of the implications of it.
>
> It does lead to the question "how do we sort subgroups by
> 'goodness'?", but that's a topic for another post :)
>
> -Mike

🔗Carl Lumma <carl@...>

Thanks (Mike) for bringing this up. Back in December
I suggested something called kernelnaming might solve
these problems. Graham sent me a dump of his database,
but I haven't looked at it until now.

He sent Hermite and LLL bases for 849 temperaments.
I cherry picked 844 for this experiment. They're all
rank 2 or 3 and map primes no greater than 19.

There are 490 unique commas in the Hermite bases.
The five most popular are

(-1 -7 4 1) 75
(4 -4 1) 59
(-2 -4 2 0 0 1) 52
(-12 1 3 0 1) 43
(-5 -3 3 1) 42

There are 335 unique commas in the LLL bases. The five
most popular are

(-3 2 -1 2 -1) 96
(-5 2 2 -1) 95
(2 3 1 -2 -1) 77
(4 0 -2 -1 1) 77
(-7 -1 1 1 1) 70

In total there are 730 unique commas, the most popular being

(-7 -1 1 1 1) 105
(-1 -7 4 1) 101
(-5 2 2 -1) 96
(-3 2 -1 2 -1) 96
(2 3 1 -2 -1) 77

These stats seem biased in favor of extended-JI commas.
Using comma sequences instead of reduced lattice bases might
fix this, but I don't have a routine for producing comma
sequences. (Another possible cause is that they're the
reduced bases in the temperament's particular subgroup, but
I've translated the commas to full prime limits in order to
compare them.)

But my December proposal can easily handle this many commas
/tuning/topicId_102018.html#102083
so in a forthcoming post, I'll plow ahead and show some
names produced by this system.

Until then, nobody mess with 385/384, 4375/4374, or 225/224.

-Carl

🔗Carl Lumma <carl@...>

Second post (of three). I wrote:

> In total there are 730 unique commas,

This includes a lot of 'dupes' like (-4 1 1) & (4 -1 -1).
These get the same under my proposal
/tuning/topicId_102018.html#102083

But unfortunately, some commas that really are different
are getting the same names here too. I haven't bothered
to implement collision avoidance. Given time constraints
I'll post what I have:
http://lumma.org/music/theory/KernelNaming.xls

Some famous personalities include

Hermite:

armodue ZidZed (2 3 5 7)

meantone Peb (2 3 5)
meantone VilPeb (2 3 5 7)
meantone WorVilPeb (2 3 5 7 11)

ennealimmal Det (2 3 5)
ennealimmal BijDet (2 3 5 7)
ennealimmal FovBijDet (2 3 5 7 11)
ennealimmic BijDet (2 3 5 7 11)
ennealimnic FopBijDet (2 3 5 7 11)
ennealimmic DunBijDet (2 3 5 7 11 13)
ennealimmic DutFopBijDet (2 3 5 7 11 13)

semihemiwuerschmidt GonHijLem (2 3 5 7 11)

Ok, apparently I should reverse the order of the commas
Graham sent, so all the meantones would start with Peb
(syntonic comma). But I'll keep going anyway

LLL:

armodue VibZed (2 3 5 7)

meantone Peb (2 3 5)
meantone LidPeb (2 3 5 7)
meantone NobPebKod (2 3 5 7 11)

ennealimmal Det (2 3 5)
ennealimmal BijBih (2 3 5 7)
ennealimmal BijBihFoj (2 3 5 7 11)
ennealimmic BijBih (2 3 5 7 11)
ennealimnic GofFofJoj (2 3 5 7 11)
ennealimmic DujDuhBul (2 3 5 7 11 13)
ennealimmic FofGufGofFuf (2 3 5 7 11 13)

semihemiwuerschmidt BohHohHok (2 3 5 7 11)

Next post: some observations,

-Carl

🔗Carl Lumma <carl@...>

Last post, continued from
/tuning/topicId_104603.html#104670?var=0

So, Hermite bases may be better for this than LLL bases.
Here are some Hermite basis names for meantone:

> meantone Peb (2 3 5)
> meantone PebVil (2 3 5 7)
> meantone PebVilWor (2 3 5 7 11)

These names may not look easy to pronounce, but each
syllable is phonetically distinct and has a phonetically
distinct spelling. The 844 temperaments in Graham's
database use up to 5 syllables. Most are only 3 syllables.

These names tell us something about the temperaments too.
We can see the three meantones above are related. We can
tell than Peb is a 5-limit comma (since "e" always means 5).
We can tell it's a fairly large comma (since P is toward
the end of the alphabet) and that it's a very simple one
(since B is near the beginning).

Compare to armodue: ZedZid (2 3 5 7)

The Zs tell us these commas are very large.

Even though there are no ETs in this database, we can
name <12 19 28| with 81/80 (Peb) & 128/125 (Ted)

"5-lim PebTed"

We know it's an ET because it's 5-limit with two commas.
To make it a Fokker block, we lengthen the vowels

"5-lim PeebTeed"

(A long vowel means a comma is untempered)

The syllables could probably be made to flow better.
Some roots like "syn" and "aug" might even be
grandfathered in. . .

-Carl

🔗Carl Lumma <carl@...>

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

> It does lead to the question "how do we sort subgroups by
> 'goodness'?", but that's a topic for another post :)
> -Mike

Sorry, I attached my replies to a weird spot in this thread.

I generally agree that prime limits should be privileged
subgroups and that names should show "family" relationships.
This came up around Christmas.

The answer I came up with is to use commas. Gene pointed
out long ago that they show family relationships. And
when it comes to subgroups, a good commas is a good comma
is a good comma.

I also agree rank 2 is the most important case. From my
previous posts, it looks like it doesn't take more than
5 commas to ID every temperament in Graham's Finder.
If each comma is mapped to a syllable, the names should
be manageable

I think the trick is to back off the systematic angle a
bit from what I did. Allow syllables to be different
lengths -- camel case can distinguish them. Grandfather
in existing syllables like "mean" or whatever.

Where there's a good name that's of historical or popular
importance, like porcupine, valentine, etc, even the
whole word could be kept, and extended with comma syllables.
I do think the limmic/limnic/etc stuff has gone off the
rails and should be backed out.

-Carl

🔗Carl Lumma <carl@...>

Mainly I think the names coming out of my spreadsheet
are too consonanty.

I did a quick scan of the trivial names and didn't see
too many things I couldn't live without

commas:
limm
schis

other prefixes:
aug
dim
dom
mean or syn

people/places:
blackwood (black)
hanson (han)
mavila (mav)
negri (neg)
valentine (val)

popular:
beep (beep)
father (fath)
magic (mag)
marvel (marv)
miracle (mir)
porcupine (porc)

My next try at this may just be to download a list of
1000 good-sounding syllables from somewhere, alpha sort
them, sort the commas by badness, and map straight over.
Then for the commas most associated with the above
temperaments, replace with the syllable in parens.

I still need to convince Gene to make a canonical
comma-sequence generating procedure.

-Carl

I wrote:
> Where there's a good name that's of historical or popular
> importance, like porcupine, valentine, etc, even the
> whole word could be kept, and extended with comma syllables.
> I do think the limmic/limnic/etc stuff has gone off the
> rails and should be backed out.
>
> -Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jun 3, 2012 at 7:53 PM, Carl Lumma <carl@...> wrote:
> >
> > I still need to convince Gene to make a canonical
> > comma-sequence generating procedure.
>
> What do you mean by this? Finding a canonical basis for the
> null space of the transformation that's better than LLL and
> Hermite form?

The Hermite sequence always works, so if we agree on that
then we're done. But the original definition uses builds
the sequence iteratively with TM reduction

http://lumma.org/tuning/gws/commaseq.htm

and only uses Hermite sequences when that fails. If
someone wants to design a failover in order to get slightly
neater sequences, I'm all for it. We just need to
standardize.

-Carl

PS- I was also wondering if Herman had any advice on the
syllables.

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Jun 3, 2012 at 8:03 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > I generally agree that prime limits should be privileged
> > subgroups
>
> Should read, "should NOT be privileged". -C.

Hurrah. So then, keeping in mind with that, then one common objection
is that sometimes people don't want temperaments to share names, like
2.3.5.7 squares, 2.3.7.11 "skwares" and 2.3.5.7.11 squares.

But given the above, which I hope all sounds reasonable, this problem
now solves itself: they can share the same name if they're both a
higher-limit extension of a temperament on a smaller subgroup, which
is what we're already doing - 2.3.5.7 meantone and 2.3.5.7.11 meantone
all share the name "meantone" with 2.3.5 meantone, which they're
extensions of. So the same principle should apply whenever two
temperaments share a common extension of something simpler.

In the case of squares above, we have the obvious choice - the 2.3.7
14&17 temperament eliminating 19683/19208, which makes four 9/7's
equal to one 8/3. This is about as square as it gets, and it's a
killer temperament on a great subgroup. If you say that this is the
fundamental "squares" temperament, then the 2.3.5.7 and 2.3.5.7.11
squares temperaments are just extensions of it. And then the 2.3.7.11
"skwares" temperament is also an extension of it, so there's no reason
that couldn't also just be squares.

This is no different than how 2.3.5.7.11 meantone et al are extensions
of 2.3.5 meantone, with which they share the name.

Any objections from people whose names may or may not sound similar to
Jeen Schmidt?

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

Mike Battaglia <battaglia01@...> wrote:

> > > I generally agree that prime limits should be privileged
> > > subgroups
> >
> > Should read, "should NOT be privileged". -C.
>
> Hurrah. So then, keeping in mind with that, then one common
> objection is that sometimes people don't want temperaments to
> share names, like 2.3.5.7 squares, 2.3.7.11 "skwares" and
> 2.3.5.7.11 squares.
> But given the above, which I hope all sounds reasonable, this
> problem now solves itself: they can share the same name if
> they're both a higher-limit extension of a temperament on a
> smaller subgroup, which is what we're already doing -
> 2.3.5.7 meantone and 2.3.5.7.11 meantone all share the name
> "meantone" with 2.3.5 meantone, which they're extensions of.

Depends what we mean by extension. I think people are using
"2.3.5 meantone" and "2.3.5.7 meantone" to refer to different
rank 2 temperaments. In my scheme, if you make the subgroup
part of the name bigger but keep the righthand part of the
name the same, you change the rank. For instance

2.3.5 Peb is rank 2 while
2.3.5.7 Peb is rank 3.

The point is that Peb (81/80) is a good comma regardless of
the JI subgroup it lives in. That means anything Peb is
going to be good. But it may not be the case that I still
have a good rank 2 temperament after I added whatever I
added to keep it rank 2 when I made the subgroup bigger.

So people have turned to various ideas like carrying a name
forward only to the thing with the nearest-size generator.
There's something to be said for that but it seems to me
that comma sequences make more sense.

But maybe I misunderstood what you were saying... -Carl

🔗Mike Battaglia <battaglia01@...>

On Sun, Jun 3, 2012 at 11:19 PM, Carl Lumma <carl@...> wrote:
>
> Depends what we mean by extension. I think people are using
> "2.3.5 meantone" and "2.3.5.7 meantone" to refer to different
> rank 2 temperaments. In my scheme, if you make the subgroup
> part of the name bigger but keep the righthand part of the
> name the same, you change the rank. For instance
>
> 2.3.5 Peb is rank 2 while
> 2.3.5.7 Peb is rank 3.

Yeah, you're talking about extensions that preserve codimension and
alter rank; I was talking about extensions that preserve rank and
alter codimension. They're good for different purposes, I suppose.

> The point is that Peb (81/80) is a good comma regardless of
> the JI subgroup it lives in. That means anything Peb is
> going to be good. But it may not be the case that I still
> have a good rank 2 temperament after I added whatever I
> added to keep it rank 2 when I made the subgroup bigger.

Right, intonationally speaking.

> So people have turned to various ideas like carrying a name
> forward only to the thing with the nearest-size generator.
> There's something to be said for that but it seems to me
> that comma sequences make more sense.
>
> But maybe I misunderstood what you were saying... -Carl

I was suggesting carrying then name forward to the thing which is the
lowest-badness same-rank temperament on some group extension of the
original group. e.g., if meantone is <7 11 16| ^ <12 19 28|, then the
7-limit extension to meantone will correspond <7 11 16 x| ^ <12 19 28
y| for the choice of x and y which minimizes badness.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Jun 4, 2012 at 2:38 AM, Carl Lumma <carl@...> wrote:
>
> That's basically what's happening now. It does have some
> things going for it. What on Graham's list are you objecting
> to? Just the clever alternate spellings of some of the
> extensions (eg limmic/limnic)? What would you call those
> temperaments that aren't the lowest-badness extensions...
> invent brand new names? -Carl

No, Graham's list is fine. And I don't care about higher-limit
extensions having different names.

My problem is with all the different names for subgroup temperaments
which are variants of the same thing. For instance, there's "skwares"
for one subgroup restriction of squares, I think there was a "skwarez"
for another, etc. There's a "mohoho" and a "mohaha" for different
types of mohajira. 2.3.7 64/63 isn't officially "superpyth," but
"archy" I think, because superpyth is defined as a full 7-limit
temperament.

We finally solved this problem for 2.3.7 49/48 by calling that
"semaphore," of which 2.3.5.7 49/48 and 81/80 Godzilla is a full-limit
extension. Prior to that, the unofficial name for that temperament was
"semaphore/godzilla/hemifourths/youknowhwatimean temperament." Now
everyone can just talk about "semaphore" and be correct no matter
what, because all these other temperaments (godzilla, superpelog,
whatever) are indeed extensions of semaphore.

While we're at it, we should just do that for everything as much as
possible. The old view was that there were 5-limit temperaments, which
then evolve into nice 7-limit extensions, and then 11-limit extensions
to that, and so on. The new emerging view I propose, now that
subgroups are in vogue, is that rank-2 codimension-1 temperaments on
good subgroups are what's fundamental, which then evolve into rank-2
codimension-2 temperaments on good extension subgroups, etc.

This approach is intuitive, basically what we're already doing with
full limits but applied to subgroups, and what the folks on XA seem to
have intuitively started doing in response to the naming confusion.
You make sure that the best rank-2 codimension-1 temperaments on the
best subgroups have clear-cut, unambiguous names, and make that match
the "unofficial" name that's sprung up around the subgroup as much as
possible. Then the rest works itself out with very little conflict.

I'll make a post about some proposed names now.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Mon, Jun 4, 2012 at 3:38 AM, Mike Battaglia <battaglia01@...> wrote:
> On Mon, Jun 4, 2012 at 2:38 AM, Carl Lumma <carl@...> wrote:
>>
>> That's basically what's happening now. It does have some
>> things going for it. What on Graham's list are you objecting
>> to? Just the clever alternate spellings of some of the
>> extensions (eg limmic/limnic)? What would you call those
>> temperaments that aren't the lowest-badness extensions...
>> invent brand new names? -Carl
>
> No, Graham's list is fine. And I don't care about higher-limit
> extensions having different names.

I should continue this more.

I think that there should be a better organization of temperaments
into families, each built around a good codimension-1, rank-2
temperament, which then have extensions. I think we should undo some
of these subgroup names like "archy" and "mohaha" and probably my own
"biome" and just organize them more sensibly into such families and
then all of this confusion will go away.

The real saving grace would be to develop something like Graham's
temperament finder on steroids, which would let you compare
temperaments between subgroups with some sort of "superbadness"
measure. Then you could do a search for the lowest superbadness
temperaments and all the best families would just pop right out. That
would make it obvious what's important and what isn't. I'd expect
that, in addition to the usual 5-limit families, things like 2.3.7
49/48, 2.3.7 64/63, 2.3.11 243/242 would pop out right away as
fundamentally important temperaments.

2.3.7 64/63 would probably be ranked higher than 2.3.5 32805/32768,
for instance. Most people call this "superpyth," but as far as the
wiki's concerned, it's a weird minor subgroup temperament called
"archy" which is like 2.3.5.7 superpyth's deranged cousin. Well, this
should BE superpyth, and 2.3.5.7 superpyth should be an extension of
it! And so should dominant, etc. There should be a page on the wiki
saying "superpyth family," and this should be the main guy in it.

What about 2.3.11 243/242, which is maybe more important than any of
them? That one right now has no name at all - people don't even know
what to call neutral third scales. They know the fifth is 3/2 and the
generator is about 11/9 and don't care about the rest of the
extensions - what do they call it? Currently they call it
"mohajira/maqamic/beatles/neutralthirds/youknowwhatimean temperament."
This thing needs to just be called "mohajira," define the "mohajira
family," and then 2.3.5.7.11 mohajira, 2.3.5.7.11 maqamic, etc should
be extensions of 2.3.11 mohajira temperament. And yet I think the wiki
is calling this "neutraltet" temperament now, and mohajira is a
secondary 11-limit extension on the meantone page.

I think you'll end up with like 30 "core temperaments" defining
obvious families. Every single one will have its own unique musical
structure from both a harmonic and melodic standpoint, and people
won't mind remembering the names. Then there can still be names for
the extensions of these families, but you'll never have to know them -
just knowing about "machine temperament" in general would be enough to
make music and communicate, even if you don't know or care about the
name of the specific 13-limit extension which is present in machine in
17-EDO. After all, you don't need to know what "meanenneadecal" is to
just talk about meantone in 19-EDO, right? That'd be for theorists to
worry about and not composers. It sets things up like a Huffman code
or something.

In hindsight, I think this is how we should have handled subgroups to
begin with, since it's the same way 5-limit families were handled. I
think it would just be a good thing to handle it sensibly this way
going forward. This means some eggs might have to break, since there's
a hodgepodge of inconsistent naming conventions going on with
subgroups, but I think it'll mostly work out.

I also think it's a good idea to pay careful attention to the names
that composers are actually using for some of these things, if their
names are compatible with the basics of RMP at all, where no name
exists or where it's ambiguous, since I have a strong feeling like
this is about to jump mainstream in a big way, and the last remaining
hurdle is just to organize the names and such into like 20 or 30 core
new tuning systems for people to play with, the endless variations of
which they never have to think about. If that means that 2.3.5
superpyth should be something else so that 2.3.7 superpyth can really
be superpyth, so be it.

-Mike

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jun 4, 2012 at 2:38 AM, Carl Lumma <carl@...> wrote:
> >
> > That's basically what's happening now. It does have some
> > things going for it. What on Graham's list are you objecting
> > to? Just the clever alternate spellings of some of the
> > extensions (eg limmic/limnic)? What would you call those
> > temperaments that aren't the lowest-badness extensions...
> > invent brand new names? -Carl
>
> No, Graham's list is fine. And I don't care about higher-limit
> extensions having different names.
>
> My problem is with all the different names for subgroup
> temperaments which are variants of the same thing. For
> instance, there's "skwares" for one subgroup restriction of
> squares, I think there was a "skwarez"

Then Graham's list isn't fine!
(This is what I'm called the limmic/limnic problem)

> We finally solved this problem for 2.3.7 49/48 by calling that
> "semaphore," of which 2.3.5.7 49/48 and 81/80 Godzilla is a
> full-limit extension. Prior to that, the unofficial name for
> that temperament was "semaphore/godzilla/hemifourths
> /youknowhwatimean temperament." Now everyone can just talk
> about "semaphore" and be correct no matter what, because all
> these other temperaments (godzilla, superpelog, whatever) are
> indeed extensions of semaphore.

Sure. But how do you decide what an extension is?
Can you use it to transform Graham's list?

> The new emerging view I propose, now that subgroups are
> in vogue, is that rank-2 codimension-1 temperaments on good
> subgroups are what's fundamental, which then evolve into rank-2
> codimension-2 temperaments on good extension subgroups, etc.

Got it.

-Carl

🔗Carl Lumma <carl@...>

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

> The real saving grace would be to develop something like Graham's
> temperament finder on steroids, which would let you compare
> temperaments between subgroups with some sort of "superbadness"
> measure. Then you could do a search for the lowest superbadness
> temperaments and all the best families would just pop right out.

For codimension 1 you only need comma badness, which is
trivial.

> That
> would make it obvious what's important and what isn't. I'd expect
> that, in addition to the usual 5-limit families, things like 2.3.7
> 49/48, 2.3.7 64/63, 2.3.11 243/242 would pop out right away as
> fundamentally important temperaments.

Changing the subgroup does nothing. 64/63, the dom or
paj comma, is a good comma in any subgroup that contains
the necessary primes.

> I think you'll end up with like 30 "core temperaments" defining
> obvious families.

Well, if you want to end up with 30, you will. That line
is discretionary. Seems like a good number to me too.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Mon, Jun 4, 2012 at 3:50 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The real saving grace would be to develop something like Graham's
> > temperament finder on steroids, which would let you compare
> > temperaments between subgroups with some sort of "superbadness"
> > measure. Then you could do a search for the lowest superbadness
> > temperaments and all the best families would just pop right out.
>
> For codimension 1 you only need comma badness, which is
> trivial.
//snip
> Changing the subgroup does nothing. 64/63, the dom or
> paj comma, is a good comma in any subgroup that contains
> the necessary primes.

For instance, consider 2.3.5 81/80 and 2.9.5 81/80. The first is
meantone, and the second is unnamed but I've suggested "wholetone."
The commas have identical Tenney height and weighted L1 distance in
both subgroups. However, the first subgroup lets you play 4:5:6
chords, but the second only lets you get 4:5:9. So the first one is
better in that sense.

You could possibly weight the subgroups by the size of the unit cell
their generating intervals form in the 5-limit.

-Mike

🔗Carl Lumma <carl@...>

Mike Battaglia <battaglia01@...> wrote:

> > Changing the subgroup does nothing. 64/63, the dom or
> > paj comma, is a good comma in any subgroup that contains
> > the necessary primes.
>
> For instance, consider 2.3.5 81/80 and 2.9.5 81/80. The first
> is meantone, and the second is unnamed but I've suggested
> "wholetone." The commas have identical Tenney height and
> weighted L1 distance in both subgroups. However, the first
> subgroup lets you play 4:5:6 chords, but the second only lets
> you get 4:5:9. So the first one is better in that sense.

The weighted lattice distance is the same,

log2(81*80) = 4 + 4log2(3) + log2(5) = 4 + 2log2(9) + log2(5)

and the size is the same,

log2(81/80)

so their quotient, the comma badness, is the same.
More generally, somebody looking at the 2.9.5 subgroup
shouldn't be disappointed with 4:5:9 chords.

> You could possibly weight the subgroups by the size of the
> unit cell their generating intervals form in the 5-limit.

Lost me here.

-Carl

🔗Ryan Avella <domeofatonement@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Jun 4, 2012 at 4:29 PM, Carl Lumma <carl@...> wrote:
>
> The weighted lattice distance is the same,
>
> log2(81*80) = 4 + 4log2(3) + log2(5) = 4 + 2log2(9) + log2(5)
>
> and the size is the same,
>
> log2(81/80)
>
> so their quotient, the comma badness, is the same.
> More generally, somebody looking at the 2.9.5 subgroup
> shouldn't be disappointed with 4:5:9 chords.

Yes, their badness is the same. And the thing I called "superbadness"
would be something which factors in both their badness and the
complexity of the subgroup as a whole.

> > You could possibly weight the subgroups by the size of the
> > unit cell their generating intervals form in the 5-limit.
>
> Lost me here.

Just represent the subgroup intervals as full-limit intervals and take
the L2 norm of their multimonzo, which will have one coefficient
anyway.

-Mike