Topic: 19-limit Pluto temperament

1 scales

Thread (5 messages)

From: genewardsmith (2010-12-20)
Subject: 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.

From: Chris Vaisvil (2010-12-20)
Subject: Re: [tuning-math] 19-limit Pluto temperament

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.
>
>  
>

From: genewardsmith (2010-12-20)
Subject: Re: 19-limit Pluto temperament

--- 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:

http://launch.groups.yahoo.com/group/tuning/message/95078

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

From: Mike Battaglia (2010-12-21)
Subject: Re: [tuning-math] 19-limit Pluto temperament

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

From: genewardsmith (2010-12-21)
Subject: Re: 19-limit Pluto temperament

--- 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.