Suoerduperkleismic

At present we have:

2.3.5.7 superkleismic, tempering out 875/864 and 1029/1024

2.3.5.7.11 superkleismic, tempering out 100/99, 245/242 and 385/384

orgone, a 2.7.11 tempering out 65536/65219

magicaltet, a 2.5/3.7.11 tempering out 100/99 and 385/384

There's even oregon, a 2.9.15.7.11 tempering out 55/54, 64/63 and 100/99

Since everyone but me seems to think this new "system" is easy to apply, perhaps the collective wisdom of this group can explain which should be called what, and why.

The fact that you think that 2.7.11 orgone and 2.3.5.7 superkleismic have
anything to do with one another at all means that you're mentally grouping
temperaments together by something other than what commas they're tempering
out.

Are you grouping them together because they have the same optimal generator
size, or because they have the same mapping for 7

-Mike

On Jul 14, 2012, at 1:51 PM, genewardsmith <genewardsmith@...>
wrote:

At present we have:

2.3.5.7 superkleismic, tempering out 875/864 and 1029/1024

2.3.5.7.11 superkleismic, tempering out 100/99, 245/242 and 385/384

orgone, a 2.7.11 tempering out 65536/65219

magicaltet, a 2.5/3.7.11 tempering out 100/99 and 385/384

There's even oregon, a 2.9.15.7.11 tempering out 55/54, 64/63 and 100/99

Since everyone but me seems to think this new "system" is easy to apply,
perhaps the collective wisdom of this group can explain which should be
called what, and why.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> The fact that you think that 2.7.11 orgone and 2.3.5.7 superkleismic have
> anything to do with one another at all means that you're mentally grouping
> temperaments together by something other than what commas they're tempering
> out.
>
> Are you grouping them together because they have the same optimal generator
> size, or because they have the same mapping for 7

They have generators of fungible size and they are both contained in 2.3.5.7.11 superkleismic.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> They have generators of fungible size and they are both contained in 2.3.5.7.11 superkleismic.

Right, exactly. They're both the unique restrictions of 2.3.5.7.11 superkleismic to their respective subgroups. So we should be able to say that one is 2.3.5.7 superkleismic and the other is 2.7.11 superkleismic. "Common names" or "trivial names" like "orgone" are perfectly acceptable too.

Keenan

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> At present we have:
>
> 2.3.5.7 superkleismic, tempering out 875/864 and 1029/1024
>
> 2.3.5.7.11 superkleismic, tempering out 100/99, 245/242 and 385/384
>
> orgone, a 2.7.11 tempering out 65536/65219
>
> magicaltet, a 2.5/3.7.11 tempering out 100/99 and 385/384
>
> There's even oregon, a 2.9.15.7.11 tempering out 55/54, 64/63 and 100/99
>
> Since everyone but me seems to think this new "system" is easy to apply, perhaps the collective wisdom of this group can explain which should be called what, and why.

There's a 13-limit temperament called "superkleismic" (tempering out 100/99, 105/104, 144/143, and 245/242), so any restriction of this temperament to a subgroup of the 13-limit can be named as "x.x.x.x... superkleismic". If there were a 17-limit temperament named "superkleismic" then we could do any subgroup of the 17-limit. If there were a 2.3.5.7.11.13.19 temperament named "superkleismic" then we could do any subgroup of 2.3.5.7.11.13.19. (I'm just saying this to emphasize that p-limit subgroups are given no special treatment whatsoever.)

In particular,

2.3.5.7 superkleismic is the restriction of 13-limit superkleismic to the 2.3.5.7 subgroup, so it should be called "2.3.5.7 superkleismic" or "7-limit superkleismic". ("7-limit" is an exact synonym for "2.3.5.7".)

2.3.5.7.11 superkleismic is the restriction of 13-limit superkleismic to 2.3.5.7.11, so it's "2.3.5.7.11 superkleismic" or "11-limit superkleismic".

Orgone is the restriction of 13-limit superkleismic to the 2.7.11 subgroup, so it can be called "2.7.11 superkleismic". It also has the recognized trivial name "orgone", which is OK. You're free to call it either "2.7.11 superkleismic" (a systematic name), or "orgone" (a trivial name).

Magicaltet is the restriction of 13-limit superkleismic to the 2.5/3.7.11 subgroup, so it can be called "2.5/3.7.11 superkleismic". I've never heard anyone call it "magicaltet" except Gene, but that's OK, it still has the trivial name "magicaltet".

Oregon is *NOT* the restriction of 13-limit superkleismic to the 2.9.15.7.11 subgroup. The mapping of 9 screws it up. Therefore the name "2.9.15.7.11 superkleismic" does not refer to oregon, but to this distinct temperament: http://x31eq.com/cgi-bin/rt.cgi?ets=15_41&limit=2.9.15.7.11 . So oregon will continue to be simply "oregon".

Now, one issue I'm sure you'll bring up with this is that although the systematic names are unambiguous, they are not unique. That is, although "2.7.11 superkleismic" refers unambiguously to orgone (not to any other temperament), it's not unique because "2.7.11 keemun" also refers to orgone.

The same issue exists in IUPAC nomenclature for organic chemistry, where you can construct systematic names for the same molecule starting from different places, obtaining for example "methylbenzene" and "phenylmethane". IUPAC solves this by an extremely complicated system of precedence rules that tells you which one of the possible names is the "preferred" name. ( http://en.wikipedia.org/wiki/Preferred_IUPAC_name#Basic_principles )

I think Mike may be working on something like this, that would tell you which one of "2.7.11 superkleismic" and "2.7.11 keemun" is preferred, but it doesn't currently exist.

Keenan

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

> There's a 13-limit temperament called "superkleismic" (tempering out 100/99, 105/104, 144/143, and 245/242), so any restriction of this temperament to a subgroup of the 13-limit can be named as "x.x.x.x... superkleismic".

Thanks, this is the first time I see glimmerings of light. Two questions:

(1) Do you do higher rank systems in the same way?
(2) In rank 2, do the generators need to correspond?

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > There's a 13-limit temperament called "superkleismic" (tempering out 100/99, 105/104, 144/143, and 245/242), so any restriction of this temperament to a subgroup of the 13-limit can be named as "x.x.x.x... superkleismic".
>
> Thanks, this is the first time I see glimmerings of light. Two questions:
>
> (1) Do you do higher rank systems in the same way?

Yes, the relationship of "being a restriction to a subgroup" is well-defined for any two temperaments of the same rank. So we can name a rank-3 temperament as the restriction to a subgroup of another rank-3 temperament.

> (2) In rank 2, do the generators need to correspond?

Depends what you mean by "correspond". The coset of JI intervals mapped to the generator in the subgroup temperament is simply the intersection of the coset for the full temperament with the subgroup. In 11-limit superkleismic the generator is both 6/5 and 77/64. In orgone it's not 6/5 anymore because 6/5 isn't in 2.7.11, but it still must be 77/64. That's implied by orgone being the restriction to 2.7.11 of superkleismic.

Keenan

Steve,
Perhaps you still are interested in a final arrangement of the Progression of cells. I have it and also have the perfect fifth and fourth cells.

Attached you have the new progression (3 pages). In case that you find and error, very probably it is a manual error and it can be corrected.
I will thank you if you send me some new about it

Mario

July 16
<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Monday, July 16, 2012 1:30 PM
Subject: [tuning] Re: Suoerduperkleismic

> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>>
>> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>>
>> > There's a 13-limit temperament called "superkleismic" (tempering out >> > 100/99, 105/104, 144/143, and 245/242), so any restriction of this >> > temperament to a subgroup of the 13-limit can be named as "x.x.x.x... >> > superkleismic".
>>
>> Thanks, this is the first time I see glimmerings of light. Two questions:
>>
>> (1) Do you do higher rank systems in the same way?
>
> Yes, the relationship of "being a restriction to a subgroup" is > well-defined for any two temperaments of the same rank. So we can name a > rank-3 temperament as the restriction to a subgroup of another rank-3 > temperament.
>
>> (2) In rank 2, do the generators need to correspond?
>
> Depends what you mean by "correspond". The coset of JI intervals mapped to > the generator in the subgroup temperament is simply the intersection of > the coset for the full temperament with the subgroup. In 11-limit > superkleismic the generator is both 6/5 and 77/64. In orgone it's not 6/5 > anymore because 6/5 isn't in 2.7.11, but it still must be 77/64. That's > implied by orgone being the restriction to 2.7.11 of superkleismic.
>
> Keenan
>
>
>
>
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--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Steve,
> Perhaps you still are interested in a final arrangement of the Progression
> of cells. I have it and also have the perfect fifth and fourth cells.
>
> Attached you have the new progression (3 pages). In case that you find and
> error, very probably it is a manual error and it can be corrected.
> I will thank you if you send me some new about it

Who's Steve? You are replying to a conversation between me (Keenan Pepper) and Gene Ward Smith.

Keenan

On Sun, Jul 15, 2012 at 2:08 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> > There's a 13-limit temperament called "superkleismic" (tempering out
> > 100/99, 105/104, 144/143, and 245/242), so any restriction of this
> > temperament to a subgroup of the 13-limit can be named as "x.x.x.x...
> > superkleismic".
>
> Thanks, this is the first time I see glimmerings of light. Two questions:
>
> (1) Do you do higher rank systems in the same way?

Yes, Keenan explained it well. Just multiply the mapping matrix by the
"V-map" for the corresponding subgroup and it gives you the unique
subgroup restriction for your temperament no matter what the rank.

> (2) In rank 2, do the generators need to correspond?

Yes, in the sense that 2.3.5 meantone is not a valid restriction for
2.3.5.7.11 mohajira. It would be sensible to say that 2.3.5 contorted
meantone constitutes a valid restriction of mohajira to the 2.3.5
subgroup, but we're not concerned with contorted temperaments.

-Mike