Yahoo Tuning Groups Ultimate Backup tuning 20 out of 6 CPS

I am trying to make a chart over the 1-3-5-7-9-11 20-note CPS as a 2-dimensional field of interlocked hexagons,each hexagon being some kind of hexany(of four CPS factors plus one"offset"factor).But i keep running into problems with combinations,and it appears there would only be one way to make a complete map,that would somehow wrap over to itself at the ends.Anybody who can help solve this?

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MATS �LJARE
http://www.angelfire.com/mo/oljare
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🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "Mats Öljare" <oljare@h...> wrote:
> I am trying to make a chart over the 1-3-5-7-9-11 20-note CPS as a
> 2-dimensional field of interlocked hexagons,each hexagon being some
kind of
> hexany(of four CPS factors plus one"offset"factor).But i keep
running into
> problems with combinations,and it appears there would only be one
way to
> make a complete map,that would somehow wrap over to itself at the
> ends.Anybody who can help solve this?

Presumably you're talking about the 3)6 (1,3,5,7,9,11) CPS, which is
usually called the Eikosany? Erv Wilson's solutions for latticing
this "scale" involve setting a fixed configuration for each interval,
and then running from there. The trick is to find a configuration
that works. Erv is kind enough to usually map out the configuration
(of a complete hexad) on the same page as whatever lattice he's
drawing. For Eikosany examples, go to:

http://www.anaphoria.com/dal.PDF

page 16 (left side)
page 19 (left side)
page 24 (left side)
page 32 (left side)

I defer to Kraig Grady for deeper insights into Erv's work.

🔗Mats �ljare <oljare@hotmail.com>

>Presumably you're talking about the 3)6 (1,3,5,7,9,11) CPS, which is >usually called the Eikosany? Erv Wilson's solutions for latticing this >"scale" involve setting a fixed configuration for each interval, and then >running from there. The trick is to find a configuration that works. Erv is >kind enough to usually map out the configuration (of a complete hexad) on >the same page as whatever lattice he's drawing. For Eikosany examples, go >to:

Well,i�ve given up on it now.But i guess there must be one way to represent all the tonal connections in it without using more than 2 dimensions.

🔗carl@lumma.org

>>Presumably you're talking about the 3)6 (1,3,5,7,9,11) CPS, which
>>is usually called the Eikosany?

In which case the terminology is "3 out of 6", which is the "3)6"
in "3)6 [1,3,5,7,9,11]", above. The structure has 20 tones and many
hexanies, though its basic funtional units are usually taken to be
its 30 tetrads -- in this case, the tetradic subsets of the complete
11-limit hexads, 4)6 = 15 otonal and 15 utonal.

>Well,i´ve given up on it now. But i guess there must be one way to
>represent all the tonal connections in it without using more than
>2 dimensions.

There is, but it's quite busy, and hard on the eyes. But don't
give up, and definitely check out the D'Allesandro article in
the Wilson archives.

-Carl

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "Mats ?jare" <oljare@h...> wrote:
> >Presumably you're talking about the 3)6 (1,3,5,7,9,11) CPS, which is
> >usually called the Eikosany? Erv Wilson's solutions for latticing this
> >"scale" involve setting a fixed configuration for each interval, and then
> >running from there. The trick is to find a configuration that works. Erv is
> >kind enough to usually map out the configuration (of a complete hexad) on
> >the same page as whatever lattice he's drawing. For Eikosany examples, go
> >to:
>
> Well,i?e given up on it now.

Given up on what? Did the link not work for you?

But i guess there must be one way to represent
> all the tonal connections in it without using more than 2 dimensions.

Sure - most of Wilson's diagrams will do the trick if you put the dotted lines from the hexadic
"legends" back in.