Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Re: Stellation continued

Paul! o.k. what does e.f stand for?

Paul Erlich wrote:

> Carl, take a close look at http://www.anaphoria.com/dal25.html. It
> shows the 1.3.5.7.9.11 Euler-Fokker genus (which Wilson calls
> the "Grand Slam") in four different lattice orientations. The Figures
> 37 and 36 should be familiar from our previous discussions -- the
> symmetrical figure at the center of each is of course the Eikosany,
> using the centered pentagon lattice, with different lines made
> visible in each case. The Stellated Eikosany would be as symmetrical
> as the Eikosany itself, while the E.F. genus, as you can see, is
> elongated in one direction. Figure 35 is how Fokker would probably
> lattice the thing -- using four directions for the four primes 3, 5,
> 7, and 11. The factor of 9 accounts for the basic hypercube structure
> being repeated two extra times along the 3 axis. Figure 34 is a
> Wilson variation that can be better understood by looking at
> http://www.anaphoria.com/dal23.html.
>
>

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

>>>Yeah, it was a shot in the dark, but... the 4-factor stellated 1:2
>>>CPS
>
>>Huh?

>I just meant the stellated hexany. I phrased it that way because Chalmers
>said his formula might only apply to m/n=1/2 CPSs.

>>> is a stellated E.F. genus,
>
>>Can you show me?

>The 4-factor E.F. genus is an octahedron with two of its faces stellated.

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

>>>>as I've noted, the E.F. genus is symmetrical in the square lattice,
>>>>while the CPSs and their stellations are symmetrical in the
>>>>triangular lattice.
>>
>>>And?
>
>>By symmetrical I mean "maximally symmetrical". Other than a single
>>point, a structure can't be maximally symmetrical in both lattices.

>Yes- could you explain how that fits into the discussion?

Just showimg that the _fully_ stellated CPS has to be distinct from the E.F.
genus.

>>I think the idea is that you always reach a point where you are up
>>against other copies of the CPS you started with in all directions,
>>so with stellation you've essentially included all the resources you
>>could possibly use to move from one CPS to another.

>The plain E.F. genus should do that

No, it only exploits a few of these resources.

>But my second question is a
>little more arcane; is there any structure, containing incomplete
>chords, such that every time you complete all the chords you create
>new structure with some incomplete chords? Or do all structures
>become fully stellated after x iterations?

I'm betting it's the latter.

>>while the E.F. genus, as you can see, is elongated in one direction.
>>Figure 35 is how Fokker would probably lattice the thing -- using four
>>directions for the four primes 3, 5, 7, and 11. The factor of 9
>>accounts for the basic hypercube structure being repeated two extra
>>times along the 3 axis.

>More about being symmetrical in one lattice and not another? Again,
>I'm missing the tie-in.

I can't think of any new ways to explain this right now. I guess you should
try to read the relevant posts again and do some thinking on your own.

>>Figure 34 is a Wilson variation that can be better understood by looking
>>at http://www.anaphoria.com/dal23.html.

>Yes- I believe those are true 6-D projections, but I find the 5-fold stuff
>of the "Treetoad" and "Pascal's Triangle of CPSs" easier to use.

Carl, they're all 6-D projections.

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Re: [tuning] Re: Stellation continued

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>