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