Are Wilson's three 22-tone CS scales periodicity blocks?

On 10/1/99, I wrote,

>The third page of http://www.anaphoria.com/trans22.html is >entitled
"22-tone constant scale structure" and gives three 22-tone >CS scales. The
first is none other than the classic 5-limit sruti >scale that I recently
derived from the Fokker periodicity block >formalism. I may be able to do
the same for the other two.

(1) To see the derivation for the first one, see
http://www.ixpres.com/interval/td/erlich/srutipblock.htm.

(2) The second one is the following pattern in the 5-limit lattice:

****
*****
*****
*****
***

This tiles the lattice as follows:

@@@@
@@@@@ 888
''''@@@@@ 88888
'''''@@@@@||||88888
****'''''@@@|||||88888
*****'''''....|||||888
*****'''.....|||||""""
*****0000.....|||"""""
***00000.....\\\\"""""
----00000...\\\\\"""""
-----00000////\\\\\"""
-----000/////\\\\\^^^^
-----++++/////\\\^^^^^
---+++++/////::::^^^^^
+++++///:::::^^^^^
+++++ :::::^^^
+++ :::::
:::

So its unison vectors are

(5 -3) = 243:250 = 49�
(1 -5) = 3072:3125 = 30�

The first of these gives me an idea -- Herman Miller's wacky progression
that doesn't drift in 15-tET wouldn't drift in 22-tET either!

(3) The third one is 3-d -- harder to visualize at 2AM -- hmmm...

Paul!
I don't understand these symbols under 2 and 3. Also it is quite possible
to reinvent these scales in quite a number of different ways. The major scale
is a great example of something that can be explained by a variety of
approaches. This is what makes the scale so important. Not only as a chain of
fifths as a host of theorist have expanded upon but also in it being three
triads. A method John Chamers has expanded upon in detail with musically
interesting results. Both these methods have gone beyond explaining there
scales but have prompted new scales. I would be more interested in periodic
blocks, only if it could produce something beyond a slight replacement of one
interval with another.
The whole nature of Wilson's concept of scale is it being cyclical. That
near size intervals can be interchanged or equivalent scale wise is already
assumed before one starts. The three listed are the more "Poetic" ones that
have attracted Erv's fancy at this time. The three scales, especially when
placed on a keyboard, shows the great variety of interval sizes that can
represent a single "keyboard step" (being synonymous with scale step). Each
is different and the music they produced would be different. he might think
of the whole scale as a periodicity block of the others to be chosen
depending on the artistic statement one wanted to make.

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
>
> On 10/1/99, I wrote,
>
> >The third page of http://www.anaphoria.com/trans22.html is >entitled
> "22-tone constant scale structure" and gives three 22-tone >CS scales. The
> first is none other than the classic 5-limit sruti >scale that I recently
> derived from the Fokker periodicity block >formalism. I may be able to do
> the same for the other two.
>
> (1) To see the derivation for the first one, see
> http://www.ixpres.com/interval/td/erlich/srutipblock.htm.
>
> (2) The second one is the following pattern in the 5-limit lattice:
>
> ****
> *****
> *****
> *****
> ***
>
> This tiles the lattice as follows:
>
> @@@@
> @@@@@ 888
> ''''@@@@@ 88888
> '''''@@@@@||||88888
> ****'''''@@@|||||88888
> *****'''''....|||||888
> *****'''.....|||||""""
> *****0000.....|||"""""
> ***00000.....\\\\"""""
> ----00000...\\\\\"""""
> -----00000////\\\\\"""
> -----000/////\\\\\^^^^
> -----++++/////\\\^^^^^
> ---+++++/////::::^^^^^
> +++++///:::::^^^^^
> +++++ :::::^^^
> +++ :::::
> :::
>
> So its unison vectors are
>
> (5 -3) = 243:250 = 49�
> (1 -5) = 3072:3125 = 30�
>
> The first of these gives me an idea -- Herman Miller's wacky progression
> that doesn't drift in 15-tET wouldn't drift in 22-tET either!
>
> (3) The third one is 3-d -- harder to visualize at 2AM -- hmmm...
>

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