tempered versions of Ken Wauchope's scales

Some years ago Ken Wauchope posted to the list what he called a
symmetrical scale in just intonation:

http://www.aic.nrl.navy.mil/~wauchope/audio/tuning/symscale.html

It is a superpostion of two 10:12:15:18 chords rooted a 7:5 apart.

It seems that Gene's "star" scale is a tempered version of this.
Comments?

You can do the same thing with a pair of 8:10:12:15 chords. If
you temper the result in 22-tet, you get a subset of Paul Erlich's
Symmetrical Decatonic.

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
> Some years ago Ken Wauchope posted to the list what he called a
> symmetrical scale in just intonation:
>
> http://www.aic.nrl.navy.mil/~wauchope/audio/tuning/symscale.html
>
> It is a superpostion of two 10:12:15:18 chords rooted a 7:5 apart.
>
> It seems that Gene's "star" scale is a tempered version of this.
> Comments?

Star is also a 126/125 tempering of two chains of three minor thirds a fifth apart, giving a parallogram Fokker block in the 5-limit, which is a convenient thing to know if you are writing music in it:

1--27/25--6/5--5/4--36/25--3/2--5/3--9/5

In-Reply-To: <4.3.2.20020519173652.02471620@lumma.org>
Carl Lumma wrote:

> It is a superpostion of two 10:12:15:18 chords rooted a 7:5 apart.
>
> It seems that Gene's "star" scale is a tempered version of this.
> Comments?

That's Ken Wauchope's minor from your list.

1/1 21/20 7/6 5/4 7/5 3/2 5/3 7/4 2/1

I couldn't work out a temperament for it. What's this star scale?

> You can do the same thing with a pair of 8:10:12:15 chords. If
> you temper the result in 22-tet, you get a subset of Paul Erlich's
> Symmetrical Decatonic.

Ken Wauchope's major

1/1 21/20 5/4 21/16 7/5 3/2 7/4 15/8 2/1

does that. And the tempered equivalent is also a subset of the
pentachordal decatonic.

Graham

>That's Ken Wauchope's minor from your list.
>
>1/1 21/20 7/6 5/4 7/5 3/2 5/3 7/4 2/1

Right -- I pulled it this time around in favor of star.

>I couldn't work out a temperament for it. What's this star scale?

Gene just posted it, or see the Scala files in gd.zip.

>> You can do the same thing with a pair of 8:10:12:15 chords. If
>> you temper the result in 22-tet, you get a subset of Paul Erlich's
>> Symmetrical Decatonic.
>
>Ken Wauchope's major
>
>1/1 21/20 5/4 21/16 7/5 3/2 7/4 15/8 2/1
>
>does that. And the tempered equivalent is also a subset of the
>pentachordal decatonic.

I dropped it too, in favor of the decatonics. I should point out
that this one wasn't by Ken, but by me in the spirit of the other one.

-Carl

--- In tuning-math@yahoogroups.com, "genewardsmith"
<genewardsmith@j...> wrote:
> --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
> > Some years ago Ken Wauchope posted to the list what he called a
> > symmetrical scale in just intonation:
> >
> > http://www.aic.nrl.navy.mil/~wauchope/audio/tuning/symscale.html
> >
> > It is a superpostion of two 10:12:15:18 chords rooted a 7:5 apart.
> >
> > It seems that Gene's "star" scale is a tempered version of this.
> > Comments?
>
> Star is also a 126/125 tempering of two chains of three minor
thirds a fifth apart, giving a parallogram Fokker block in the 5-
limit, which is a convenient thing to know if you are writing music
in it:
>
> 1--27/25--6/5--5/4--36/25--3/2--5/3--9/5

As one might expect, this showed up (along with what Manuel has
listed as gwsmith_star2) when I surveyed 5-limit 8-note Fokker blocks.
I think it remains an interesting scale, either tempered or not.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning-math@yahoogroups.com, "genewardsmith"
> <genewardsmith@j...> wrote:
> > --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
> > > Some years ago Ken Wauchope posted to the list what he called a
> > > symmetrical scale in just intonation:
> > >
> > > http://www.aic.nrl.navy.mil/~wauchope/audio/tuning/symscale.html
> > >
> > > It is a superpostion of two 10:12:15:18 chords rooted a 7:5 apart.
> > >
> > > It seems that Gene's "star" scale is a tempered version of this.
> > > Comments?
> >
> > Star is also a 126/125 tempering of two chains of three minor
> thirds a fifth apart, giving a parallogram Fokker block in the 5-
> limit, which is a convenient thing to know if you are writing music
> in it:
> >
> > 1--27/25--6/5--5/4--36/25--3/2--5/3--9/5
>
> As one might expect, this showed up (along with what Manuel has
> listed as gwsmith_star2) when I surveyed 5-limit 8-note Fokker blocks.
> I think it remains an interesting scale, either tempered or not.

A detempered diminished scale.