[silence] An aspect on the square root method

[kraiggrady@anaphoria.com]

 I sent this to another list which is more concerned with tuning but i (relunctantly) descded to also send it here, but i thought that some might be interested in the maybe some of the properties that the square root method actually generates beyond the mere two dimensional way that it is presented. We all know that JC moved on from this, but like so many things , it doesn't mean things were not left behind that would not lead in other directions



f we apply Cages idea with only 4 elements which i don't think he ever used so few, yet it enables us to see some aspect of this set that we might not realized 
we end up with the following set which i hope those who are not familiar with it will see the pattern anyway
AxA AxB AxC AxD
BxA BxB BxC BxD
CxA CxB CxC CxD
DxA DxB DxC DxD

This is the the same set that one finds at at the beginning of Wilson's letter Chalmers on the Combination Product set.
seen here.
http://anaphoria.com/CPstoC-pt.1.PDF

I mention this only because it shows other application of Cages idea here in a different context.
 For one, in referance to the article we can see that one could have the inversion of the square root as a set of meters or the combination of the two. 
or even maybe more potentially interesting is the use of the hexany ( the 2 out of 4 set) in terms of meter. from there it is easy to extend these ideas into what geometry one wishes. 

It is interesting to me that the hexany would already be contained in the square root method.

The classic Cage example is with 7 elements so he would have been working with a septad of septads. Knowing his associating with Bucky Fuller, it would be interesting to see if that is the possible source of influence, but it appears this all came about before those contacts
i might send this to the silence list also.


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