What should I call the following types of temperament extension?

I was going to make a follow-up post to my last one about temperament
extensions, but realized that I couldn't come up with a good name for
the different sorts of temperament extensions defined.

All of the temperament extensions I talked about had the following
features: if A and B are subgroup temperaments, and A extends to B,
then

1) dom(A) <= dom(B)
2) ker(A) <= ker(B)
3) rank(A) <= rank(B)

Building on top of that, there were three specific extensions which
have been talked about before, which have the following properties, as
well as one new one to complete the pattern:

1) Keenan's extension: rank(A) = rank(B), generators must stay the same
2) Gene's extension: rank(A) = rank(B), generators need not stay the same
3) Mike's extension: rank(A) <= rank(B), generators must stay the same
4) Other extension: rank(A) <= rank(B), generators need not stay the same

So you can see there are really just two degrees of freedom here:
a) if the rank has to stay the same, and
b) if the generators have to stay the same.

Any idea what I can do here to name things? Rank-Preserving
Non-Generator-Preserving Extension is a pretty irritating way to go
about it.

I was going to write my next post on this topic, but I didn't feel
like muddying up the math with this other side question about naming.
For the record, I'm going to focus on #1 and #2 in that post, mostly
#1, and put #3 and #4 off to the side for now.

Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Building on top of that, there were three specific extensions which
> have been talked about before, which have the following properties, as
> well as one new one to complete the pattern:
>
> 1) Keenan's extension: rank(A) = rank(B), generators must stay the same
> 2) Gene's extension: rank(A) = rank(B), generators need not stay the same
> 3) Mike's extension: rank(A) <= rank(B), generators must stay the same
> 4) Other extension: rank(A) <= rank(B), generators need not stay the same
>
> So you can see there are really just two degrees of freedom here:
> a) if the rank has to stay the same, and
> b) if the generators have to stay the same.
>
> Any idea what I can do here to name things? Rank-Preserving
> Non-Generator-Preserving Extension is a pretty irritating way to go
> about it.

How about this?

1) strict extension
2) rp (= rank-preserving) extension
3) gp (= generator-preserving) extension
4) (generalized) extension

(1) is obvious, since it's the most strict extension in your model.

If it is clear that we're talking about your model, (4) doesn't need a specific name, it's just an extension, without any additional restrictions.
If this is not clear, an adjective like "generalized" can be used to distinguish it from other definitions, like Gene's.

If (4) is the definition of "extension", then it's sufficient to characterize (2) and (3) only by the restrictions that apply (rp / gp), listing the restrictions that don't apply isn't necessary.

I don't know if this is good as a final solution, but it should be sufficient if you just want to write about your extension model. And maybe it's too early to think about final names anyway, since it's still possible that you'll change your mind about the classification.

Alternatively, you can use (1) as the definition of "extension", and list additional degrees of freedom to characterize the other types of extension, which might be more useful if you focus on (1) and (2):

1) (strict) extension
2) ngp (= non-generator-preserving) extension
3) nrp (= non-rank-preserving) extension
4) generalized extension

Is there a positive synonym for "non-preserving"?

Btw., what happened to the previous property #6: ker(A) < ker(B) ("Strict" kernel inclusion)? Did you merge #5 (generators can't be split) and #6 to "generator-preserving"?

Here's the post I'm refering to:
/tuning-math/message/21324

Best
- Geddy ;)

Gotta keep up here, falling behind on myself... response to Geddy

On Tue, Aug 20, 2013 at 10:04 AM, gedankenwelt94
<gedankenwelt94@yahoo.com> wrote:
>
> How about this?
>
> 1) strict extension
> 2) rp (= rank-preserving) extension
> 3) gp (= generator-preserving) extension
> 4) (generalized) extension

I was actually talking to Ryan Avella on IRC, and we decided on something like

1) strong extension
2) weak extension
3) strong expansion
4) weak expansion

I think the "strong" vs "weak" thing for preserving generators is
good, since that's how it's been used before.

With regards to rank-preservation, we also thought that calling
something which can increase the rank an "expansion" made sense and
sounded nice. The opposite of an extension is a "restriction," and the
opposite of an expansion is a "retraction." Every extension is also an
expansion.

That's just what we came up with though, not set in stone. I think
strong/weak extensions are nice, but maybe something's better than
"expansion."

> I don't know if this is good as a final solution, but it should be sufficient if you just want to write about your extension model. And maybe it's too early to think about final names anyway, since it's still possible that you'll change your mind about the classification.

Yes, I should definitely just call it whatever and move on, although
I've found that by the time you pick a name around here, even if it's
tentative, it ends up being The Name.

> Btw., what happened to the previous property #6: ker(A) < ker(B) ("Strict" kernel inclusion)? Did you merge #5 (generators can't be split) and #6 to "generator-preserving"?

I originally just listed that as one of the properties that can hold
for a type of extension. For instance, a "strong extension" must also
have "strict" kernel inclusion. The rest don't have to. In the case of
#2 and #4, 2.3.5 81/80 can extend 2.9.5 81/80, and in the case of #3,
2.3.5.7 81/80 can extend 2.3.5 81/80.

It was just something I threw in there; I don't mean to focus on it
too much. The other two properties are the important ones, and the
only really important one is the generator-preserving one, which is
going to be the focus of everything else from here on out. This was
just to clear away some of the clutter surrounding the word
"extension" and the various ways it's been used on here in the past.

Mike