Re: eikosany/diamond intersection

Paul!
I finally have up the diagram that show the diamond overlapping the
eikosany. If you imagine the diamond placed 180 degrees to the other
side you will see that all the notes of the eikosany are generated! look
at http://www.anaphoria.com/dal17.html
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Kraig Grady wrote,

>Paul!
> I finally have up the diagram that show the diamond overlapping the
>eikosany. If you imagine the diamond placed 180 degrees to the other
>side you will see that all the notes of the eikosany are generated!
look
>at http://www.anaphoria.com/dal17.html

You're right. OK, let's understand this. This CPS is 3 factors at a time
out of 6. The first diamond is centered around the product of 3 of the
factors, and the other diamond around the product of the other 3. The
diamond contains all notes that differ by one factor from the center.
Taking 3 factors out of 6, you have two choices: (a) you can take all 3
from the center of one diamond; or (b) you can take 2 from one and 1
from the other, which would be a note belonging to whichever diamond you
were taking 2 factors from the center of.

In the case of the 4)8 CPS, two diamonds wouldn't be able to cover it,
since you could take 2 factors from the center of one diamond and 2 from
the center of the other, resulting in a note (36 notes, in fact) not in
either diamond. I think someone was asking about extending some result
about diamonds and n)2n CPSs into higher dimensions, but they may have
been asking something else . . . ?

"Paul H. Erlich" wrote:

> Kraig Grady wrote,
>
> >Paul!
> > I finally have up the diagram that show the diamond overlapping the
> >eikosany. If you imagine the diamond placed 180 degrees to the other
> >side you will see that all the notes of the eikosany are generated!
> look
> >at http://www.anaphoria.com/dal17.html
>
> You're right. OK, let's understand this. This CPS is 3 factors at a time
> out of 6. The first diamond is centered around the product of 3 of the
> factors, and the other diamond around the product of the other 3. The
> diamond contains all notes that differ by one factor from the center.
> Taking 3 factors out of 6, you have two choices: (a) you can take all 3
> from the center of one diamond; or (b) you can take 2 from one and 1
> from the other, which would be a note belonging to whichever diamond you
> were taking 2 factors from the center of.
>
> In the case of the 4)8 CPS, two diamonds wouldn't be able to cover it,
> since you could take 2 factors from the center of one diamond and 2 from
> the center of the other, resulting in a note (36 notes, in fact) not in
> either diamond. I think someone was asking about extending some result
> about diamonds and n)2n CPSs into higher dimensions, but they may have
> been asking something else . . . ?

My compliments in catching this one so quickly! I hadn't gone up to this
level yet and what you say is true. I'll look into this one some more. It
is an important feature of the eikosany that these diamonds could be placed
on any of the 10 opposite pair of products. With the 4)8 CPS we would have
35 pairs of Ogdoadic Diamonds. In the simpler Tetradic tone space, two
tetradic diamonds on opposite functions of a Hexany will have tones in
common. I still believe that this is the one of the most fruitful areas for
those working in electronics. It goes into areas where us acoustic girls
and boys are left behind.
Having worked with the eikosany for over 20 years let me say that its
structural features are easily perceived in a short period of time. At this
point a single tetrad has a certain "meaning" in the overall context as
strong as tonality but not centered. It like a globe where once you know
your way around any point works. In this case you have multidimensional
cycles that our mind is much more comfortable than you could think.
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com