which (2.3)7.9.11 temperament is this?

I've been working on an atmospheric thing for an art video, and the central sonority is 2 divvied up into a pair of 9/7's and an 11/9 (tempered). The temperament that works for me is to use as a generator 9/7 tempered downward by 1/3 of the unidecimal comma, period is 2. MOS's are at 8, 11 and 14 IIRC (I'm currently using 14). It works out very near to closing at 14-edo, but the difference to my ears is significant because 3 sounds like heavy meantone and not like a dog fifth as it does in 14, and the 7:9:11 chords sound better to me than in 14. Similar sound to orwell.

I wasn't able to find this temperament in the Xenwiki so if anyone knows offhand what it is, lemmee know. I imagine Gene knows it, as it seems to be essentially perfect at 917-edo, handy for reckoning future structures should I need them.

Is the undecimal comma 99/98?

You might find squares or skwares interesting.

-Mike

On Mar 30, 2012, at 1:29 PM, lobawad <lobawad@...> wrote:

I've been working on an atmospheric thing for an art video, and the central
sonority is 2 divvied up into a pair of 9/7's and an 11/9 (tempered). The
temperament that works for me is to use as a generator 9/7 tempered
downward by 1/3 of the unidecimal comma, period is 2. MOS's are at 8, 11
and 14 IIRC (I'm currently using 14). It works out very near to closing at
14-edo, but the difference to my ears is significant because 3 sounds like
heavy meantone and not like a dog fifth as it does in 14, and the 7:9:11
chords sound better to me than in 14. Similar sound to orwell.

I wasn't able to find this temperament in the Xenwiki so if anyone knows
offhand what it is, lemmee know. I imagine Gene knows it, as it seems to be
essentially perfect at 917-edo, handy for reckoning future structures
should I need them.

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

> I wasn't able to find this temperament in the Xenwiki so if anyone knows offhand what it is, lemmee know. I imagine Gene knows it, as it seems to be essentially perfect at 917-edo, handy for reckoning future structures should I need them.

My name for it, for what that is worth, is mothwellsmic. If you look at two 9/7s and an 11/9 in mothwellsmic, you can also call it a 9/7, a 14/11 and an 11/9, making it a tempered JI chord which you can call otonal or utonal, your choice. It's all the same, of course. Does this kind of chord deserve a special name?

Mike Battaglia <battaglia01@...> wrote:
> Is the undecimal comma 99/98?

99/98 is the relevant one as 9/7*9/7*11/9/2

> You might find squares or skwares interesting.

Or Hedgehog (12&14c).

Graham

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > I wasn't able to find this temperament in the Xenwiki so if anyone knows offhand what it is, lemmee know. I imagine Gene knows it, as it seems to be essentially perfect at 917-edo, handy for reckoning future structures should I need them.
>
> My name for it, for what that is worth, is mothwellsmic. If you look at two 9/7s and an 11/9 in mothwellsmic, you can also call it a 9/7, a 14/11 and an 11/9, making it a tempered JI chord which you can call otonal or utonal, your choice. It's all the same, of course. Does this kind of chord deserve a special name?
>

I call harmonic and subharmonic structures harmonic and subharmonic unless I mean them in a Partchian sense, with all that entails.

At any rate, as 99/98 is tempered out, it could be 14/11 as well. I don't know if this kind of chord deserves a tuning-list name. I mean, what harm did it ever do anyone? :-) Seriously though, maybe there should be a name for sonorities that split up 2 into three Just (or nearly Just) intervals to make an ambiguous sonority, if there isn't one already. This particular one conceals a leap of a (tempered) fourth if you move from voicing SLL to LLS, something I like.

The generator of hedgehog is too high, and squares is too low, but I'm pretty sure it would qualify as some kind of 11-limit variation of squares.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Is the undecimal comma 99/98?
>
> You might find squares or skwares interesting.
>
> -Mike
>
> On Mar 30, 2012, at 1:29 PM, lobawad <lobawad@...> wrote:
>
>
>
> I've been working on an atmospheric thing for an art video, and the central
> sonority is 2 divvied up into a pair of 9/7's and an 11/9 (tempered). The
> temperament that works for me is to use as a generator 9/7 tempered
> downward by 1/3 of the unidecimal comma, period is 2. MOS's are at 8, 11
> and 14 IIRC (I'm currently using 14). It works out very near to closing at
> 14-edo, but the difference to my ears is significant because 3 sounds like
> heavy meantone and not like a dog fifth as it does in 14, and the 7:9:11
> chords sound better to me than in 14. Similar sound to orwell.
>
> I wasn't able to find this temperament in the Xenwiki so if anyone knows
> offhand what it is, lemmee know. I imagine Gene knows it, as it seems to be
> essentially perfect at 917-edo, handy for reckoning future structures
> should I need them.
>

"lobawad" <lobawad@...> wrote:
> The generator of hedgehog is too high, and squares is too
> low, but I'm pretty sure it would qualify as some kind of
> 11-limit variation of squares.

In the 2.7.9.11-limit, Machine comes out best. But below
that is an 11&14 that's like Hedgehog but with pure
octaves. The generator is 434 cents.

http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_7_9_11

Add in 3 and I don't think you can avoid Skwares.

Graham

Hmmm.... I have been trying these, but the 1/3 unidecimal comma temperament I've been using sounds better to me as I am playing my clarinet over the chords- I can tune in better.

The ur-thing of it is as Gene pointed out, the 9/7, 14/11, 11/9 division of the octave, and the 1/3 unidecimal comma temperament seems to capture that feel.

I would prefer to use 14-edo and not mess with it, and I think if I were playing over 14-edo harmonium it wouldn't make a darn bit of difference, but over a synthesizer it is different, it's harder to tune into the equal division.

--- In tuning@...m, Graham Breed <gbreed@...> wrote:
>
> "lobawad" <lobawad@...> wrote:
> > The generator of hedgehog is too high, and squares is too
> > low, but I'm pretty sure it would qualify as some kind of
> > 11-limit variation of squares.
>
> In the 2.7.9.11-limit, Machine comes out best. But below
> that is an 11&14 that's like Hedgehog but with pure
> octaves. The generator is 434 cents.
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_7_9_11
>
> Add in 3 and I don't think you can avoid Skwares.
>
>
> Graham
>