CPS sets]

Paul Erlich wrote:

> One potentially confusing thing is that the
> direction of A/E is parallel to that of B/D; hence sometimes these
> intervals may overlap on the lattice diagram.

Yes, this as an independent lattice he doesn't use. It is there more to make the next layer
down clearer. In practice, the centered Pentad lattice (with 6 points) with one of the arms
omitted is the best for exploring Pentadic space.

> So by only drawing some
> of the lines, Erv staves off potentially confusing overlapping lines
> by omitting lines for certain consonant intervals (fully half of them
> in the 5-factor case, and two-thirds of them in the 6-factor case --
> you will see the omitted lines as dotted lines in certain other
> figures in the D'Alessandro paper).
>
> Other than that, the orientations of the factors are simply chosen to
> produce pretty, symmetrical shapes in which at least some of the
> important intervallic and chordal relationships can be readily seen.

If you will notice that on the level with the Eikosany all visible lines will involve the
function of F either harmonically or subharmonically. When using such an object one can place
any factor in the middle which will give the figure a kind of interval "Mode". There are 144
permutations of which 72 are just a mirror. It is musically useful and significant in making
certain compositional decisions possible before hand. For instance I could say, I want the
feeling of sevens and place 7 at F. Thus all the ratios in the lattice will be a 7
relationship. It also allows a transformation of material by placing a pattern over different
permutation. It is Erv desire to make structures that are usable by musicians w/o years of
math. The simple transformations of the lattices gives any performer/composer a wealth of
resources

>

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