"Orgone" temperament

http://xenharmonic.wikispaces.com/26edo

Orgone temperament? I originally thought it was Keemun, but apparently
it's not, because Keemun eliminates 49/48. Looks like it's porcupine,
just taken with every other generator. I've noticed this for a while
but was mistakenly calling it "Keemun." Andrew seems to have been the
first to map some of this out, so shall we call the respective
subgroup temperament "Orgone" temperament?

It's a killer scale, the 22-edo/11-edo version is one of my favorites
ever. The LsLsLsL mode sounds kind of like diminished[8] in 12-tet,
only better because it has a 4:7:11 right there. Yes, it is of
slightly limited tonal and harmonic use (maybe) but it's definitely a
useful scale to have around.

What would the subgroup be for this? I guess you could call it
2.5/3.7.9.11 and say that 250/243, 100/99, and 64/63 vanish?

-Mike

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

> Andrew seems to have been the
> first to map some of this out, so shall we call the respective
> subgroup temperament "Orgone" temperament?

I think so; the Xenwiki already basically says orgone is the 2.7.11 subgroup temperament tempering out the orgonisma, 65536/65219, so we may as well make it official.

> What would the subgroup be for this? I guess you could call it
> 2.5/3.7.9.11 and say that 250/243, 100/99, and 64/63 vanish?

Not the same thing so far as I can see.

On Thu, May 26, 2011 at 8:55 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Andrew seems to have been the
> > first to map some of this out, so shall we call the respective
> > subgroup temperament "Orgone" temperament?
>
> I think so; the Xenwiki already basically says orgone is the 2.7.11 subgroup temperament tempering out the orgonisma, 65536/65219, so we may as well make it official.
>
> > What would the subgroup be for this? I guess you could call it
> > 2.5/3.7.9.11 and say that 250/243, 100/99, and 64/63 vanish?
>
> Not the same thing so far as I can see.

It looks to me like the same thing. Mine equates 7/4 with 16/9 (64/63
vanishes) and three 6/5's with 16/9 (250/243 vanishes) and two 6/5's
with 16/11. How is that not what Andrew described?

-Mike

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

> It looks to me like the same thing. Mine equates 7/4 with 16/9 (64/63
> vanishes) and three 6/5's with 16/9 (250/243 vanishes) and two 6/5's
> with 16/11. How is that not what Andrew described?

What Andrew described was a highly accurate 2.7.11 temperament tempering out the orgonisma, 65536/65219. 3\11 is not a good generator for this; it should be somewhere in the 24\89 to 7\26 range. What you described was a low-accuracy temperament with a generator more like 3\11, tempering out 55/54, 64/63 and 100/99. I think I'll add an orgone pump to the examples.

On Fri, May 27, 2011 at 2:40 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > It looks to me like the same thing. Mine equates 7/4 with 16/9 (64/63
> > vanishes) and three 6/5's with 16/9 (250/243 vanishes) and two 6/5's
> > with 16/11. How is that not what Andrew described?
>
> What Andrew described was a highly accurate 2.7.11 temperament tempering out the orgonisma, 65536/65219. 3\11 is not a good generator for this; it should be somewhere in the 24\89 to 7\26 range. What you described was a low-accuracy temperament with a generator more like 3\11, tempering out 55/54, 64/63 and 100/99. I think I'll add an orgone pump to the examples.

Issues of accuracy aside, does the comma basis I wrote above actually
lead to a different set of mappings than the one you just laid out?
The basic idea I thought was that two 6/5's lead to 16/11, and three
lead to 7/4. I took the liberty of mapping the generator to 6/5 since
he referred to it as a "minor third" in his description, and figured I
should throw 9/8 in there because it's there.

-Mike

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

> What Andrew described was a highly accurate 2.7.11 temperament tempering out the orgonisma, 65536/65219. 3\11 is not a good generator for this; it should be somewhere in the 24\89 to 7\26 range.

If you want to extend this to the full 11-limit, you can add 441/440 and 1728/1715 to the orgonisma and get 26&89, by the way.

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

> Issues of accuracy aside, does the comma basis I wrote above actually
> lead to a different set of mappings than the one you just laid out?

It's not in the same subgroup, of course, but it does give the same mapping on 2.7.11. So do other things, such as the 26&89 temperament I just described.

> The basic idea I thought was that two 6/5's lead to 16/11, and three
> lead to 7/4. I took the liberty of mapping the generator to 6/5 since
> he referred to it as a "minor third" in his description, and figured I
> should throw 9/8 in there because it's there.

It's certainly a sort of minor third, but ideally about eight cents sharper than 6/5. How you tune and map things will depend on whether you want what Andrew characterized as the basic chords of the temperament, 1-11/8-7/4 and its inversion 1-14/11-7/4, in good tune or not. It seems to me getting your basic chords right is pretty basic and should be a priority.

On Fri, May 27, 2011 at 3:07 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Issues of accuracy aside, does the comma basis I wrote above actually
> > lead to a different set of mappings than the one you just laid out?
>
> It's not in the same subgroup, of course, but it does give the same mapping on 2.7.11. So do other things, such as the 26&89 temperament I just described.

Alright. Well, I like the mapping I mentioned. I guess it's time to
start another temperament family.

> It's certainly a sort of minor third, but ideally about eight cents sharper than 6/5. How you tune and map things will depend on whether you want what Andrew characterized as the basic chords of the temperament, 1-11/8-7/4 and its inversion 1-14/11-7/4, in good tune or not. It seems to me getting your basic chords right is pretty basic and should be a priority.

Both sound like useful mappings, but I would wager it's up to Andrew
if he wanted the generator to be 6/5 or not. He called it a "minor
third," so I'd wager that he does. Either way, I don't really care too
much about naming, let's call one "Orgone" and the other "Oregon" or
something like that.

-Mike

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

> Both sound like useful mappings, but I would wager it's up to Andrew
> if he wanted the generator to be 6/5 or not. He called it a "minor
> third," so I'd wager that he does. Either way, I don't really care too
> much about naming, let's call one "Orgone" and the other "Oregon" or
> something like that.

An orgonismic clan page would make sense, and if I knew whether the 2.7.11 subgroup one was Orgone or Oregon I could add it to the chromatic pairs page.

Mike wrote:

> Both sound like useful mappings, but I would wager it's up to Andrew
> if he wanted the generator to be 6/5 or not. He called it a "minor
> third," so I'd wager that he does. Either way, I don't really care too
> much about naming, let's call one "Orgone" and the other "Oregon" or
> something like that.

Then that's a different temperament. I agree with Gene completely.
What both Andrew and I seem to have talked about in the past was the good approximation of some non-3 intervals in 37-EDO. That's one thing that should be taken into account.
Another thing is, if Gene says that Andrew has talked about tempering out 65536/65219, I think that sums it all up pretty clearly that the 8:11:14 chord should be viewed the primary approximated chord. The fact that he calls the generator a "minor third" doesn't say absolutely nothing about it's proper size, while the 65536/65219 unison vector gives a pretty small tolerance.

Petr

I wrote:

> What both Andrew and I seem to have talked about in the past was the good
> approximation of some non-3 intervals in 37-EDO.

BTW: At the time I discovered 37-EDO myself back in 2006 or so, I also found the 2D temperament simply by taking the 8:11:14:16 chord and splitting it into smaller intervals by reducing the largest step by the smaller steps, until I found the pretty small one and tempered it out.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:

> Another thing is, if Gene says that Andrew has talked about tempering out
> 65536/65219, I think that sums it all up pretty clearly that the 8:11:14
> chord should be viewed the primary approximated chord.

I was the one who brought up 65536/65129, but that was based on the characterization of 1-11/8-7/4 as the basic chord and the characterization of the 3\11 generator as marginal. If you take any of the generators mentioned, even 3\11, but certainly 10\37 or 7\26, and confine them to the 2.7.11 subgroup, you get the orgonisma as the single comma. Starting from 3\11 and 2.7.11 you get the orgonisma and nothing else, from the orgonisma and 2.7.11, you get that 11 is marginal, 37 much better, and 26 better yet. I don't see anything in what Andrew said which goes beyond this or beyond the 2.7.11 subgroup.

If you do want to extend it, another possibility aside from the one I mentioned previously would be to focus on 37 and add 5 to the mix, so that we would be looking at the 10\37 generator in the 2.5.7.11 subgroup. This adds the comma 2420/2401 to the orgonisma, and would make 37\137 a good tuning. That, in turn, leads to a full 11-limit version tempering out 2430/2401, 4000/3993 and 6144/6125 in which 3 is however pretty complex.