19-limit Pluto temperament

I'm looking at possible tunings for my next composition project, and thought I'd share this possibility.

Pluto
Commas: 190/189, 325/324, 969/968, 361/360, 364/363, 595/594

Map: [<1 5 15 15 2 -8 -12 14|, <0 -7 -26 -25 3 24 33 -20|]

The generator is a sharpned 7/5; 59/121 is about perfect. The 41 note MOS gives plenty of scope, and of course 80 much more.

Hi Gene,

Can this come in a 17 note format?

Thanks,

Chris

On Mon, Dec 20, 2010 at 8:02 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
> I'm looking at possible tunings for my next composition project, and
> thought I'd share this possibility.
>
> Pluto
> Commas: 190/189, 325/324, 969/968, 361/360, 364/363, 595/594
>
> Map: [<1 5 15 15 2 -8 -12 14|, <0 -7 -26 -25 3 24 33 -20|]
>
> The generator is a sharpned 7/5; 59/121 is about perfect. The 41 note MOS
> gives plenty of scope, and of course 80 much more.
>
>
>

--- In tuning-math@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Gene,
>
> Can this come in a 17 note format?

It can, but the result is a bit--let's call it exotic. Pluto is too complex a temperament to fit comfortably into a span of 17 notes, and the difference between the large step and the small one is pretty extreme. On the other hand, it *is* a MOS--there are a lot of Pluto MOSes. The did the scale below on Scala, so you probably could also. I multiplied 1200.0 cents times 59/121 to get results in cents, and stuck that value in when using the pull-down menu for "new linear temperament".

! pluto17.scl
!

17
!
29.75207
59.50413
89.25620
119.00826
495.86777
525.61983
555.37190
585.12397
614.87603
644.62810
674.38017
704.13223
1080.99174
1110.74380
1140.49587
1170.24793
2/1

I think the scales I recently posted here:

/tuning/topicId_95078.html#95078

would make more sense to try from a performer's viewpoint.

On Mon, Dec 20, 2010 at 3:02 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> I'm looking at possible tunings for my next composition project, and thought I'd share this possibility.
>
> Pluto
> Commas: 190/189, 325/324, 969/968, 361/360, 364/363, 595/594
>
> Map: [<1 5 15 15 2 -8 -12 14|, <0 -7 -26 -25 3 24 33 -20|]
>
> The generator is a sharpned 7/5; 59/121 is about perfect. The 41 note MOS gives plenty of scope, and of course 80 much more.

This seems really interesting. Have you explored any subgroup
temperaments that go up to the 19-limit? I've been re-exploring 12-tet
as a 3.5.7.17.19 subgroup temperament recently (as well as diminished
temperaments in general).

-Mike

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

> This seems really interesting. Have you explored any subgroup
> temperaments that go up to the 19-limit?

I mostly stop at the 13-limit, though I've used 17 to tune just versions of the diminished seventh chord.

I've been re-exploring 12-tet
> as a 3.5.7.17.19 subgroup temperament recently (as well as diminished
> temperaments in general).

There are a lot of subgroups out there. Because the complexity of intervals varies in a linear temperament, you can get a lot of incomplete higher limit chords which favor one subgroup over another, even if the span of the scale you are using includes everything up to some odd limit you want to stop at. Hence, different temperaments have different flavors, even leaving aside melodic and tuning considerations. The Rodan piece I turned in for UnTwelve has lots of 3 and 7, because that's how Rodan works, for example.