RE: [tuning] re: stellation continued

I wrote,

>>Well, I guess you could call that "partially stellated", but of course
it's
>>not _the_ stellated hexany.

Carl Lumma wrote,

>Ah, huh. I said that the stellated hexany is a stellated E.F. genus.
>Not that the E.F. genus is a stellated hexany!

Well, this is really a definitional matter. Mr. Grady, Mr. Wolf, did Mr.
Wilson ever actually discuss the stellation of a single m)n CPS where n does
not equal m*2, let alone the stellation of a Grand Slam (aka an E.F. genus)?

>>No, it only exploits a few of these resources.

>Could you give an example?

Just find a couple of neighboring hexanies in the oct-tet lattice and see
for yourself how the E.F. genuses only include a few of the connecting
tetrads.

>>Carl, they're all 6-D projections.

>My own naive belief (based on what Wilson said to me,^1 and what little
>experience I have with these matters^2) is that the 5-fold projections
>are 2-D shadows of 6-D structures, with the 6-D structures rotated so
>they look the same as 5-D structures in 2-D. For example, you can rotate
>a 4-D cube so it looks like the shadow of 3-D cube in 2-D.

Right.

>^1 Wilson called the 6-factor stuff, with the 1 in the center of the
>pentagon, "cheating". If you look at the Pascal's triangle of CPSs,
>he uses the same projection for the x)5 CPSs as the x)6 ones.

But in the Wilson lattices I've seen, he doesn't put 1 in the center of the
pentagon, but at a vertex.

>^2 The centered-pentagon stuff shares the 5-fold symmetry of the
>triakontahedron mapping and the Penrose tilings, which can all be
>projected, I believe I've read, from polytopes of no higher dimension
>than five.

Unless you use the "shadow" trick you mentioned above!

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Paul!
Since Wilson's fascination with these structures is in its multidimensional, self
mirroring, enantiadromic properties, these partial stellation, although he knows are possible,
lack the interest for him to search them all out.
(enantiadromia=A term used By Carl Jung signifying something which transforms into its
opposite. Like one turning into the qualities of one enemy.

"Paul H. Erlich" wrote:

> Mr. Grady, Mr. Wolf, did Mr.
> Wilson ever actually discuss the stellation of a single m)n CPS where n does
> not equal m*2, let alone the stellation of a Grand Slam (aka an E.F. genus)?

Wilson will use any tone or factor in the middle of a lattice and considers this process
musically viable for transforming preexisting material in a composition. He has at times,
envisioned the various patterns that are discovered in such structures, being the basis of
improvisations that might have a multitude of possible realizations which might be decided
upon right before a performance.

>
>
> But in the Wilson lattices I've seen, he doesn't put 1 in the center of the
> pentagon, but at a vertex.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com