I'm not sure if anyone can explain the purpose, per se, but I do know a
little bit about it. Pat has always been interested in forms and
symmetries, and he came up with this visual reprsentation of the
symmetries in music. He took an octave and divided it into all the
equally divisible units, for example, the tritone (C to F# to C) divides
the octave exacly in half, an augmented triad (C, E, G#) divides it inot
three equal parts, a diminished 7th chord (C, Eb, Gb, and B double flat,
aka A) divides the octave into four parts, etcetera. When you draw these
on separate staves and connect certain notes by lines you come up with
the 12 pointed star, which you can view as the background on Pat's
homepage at: http://www.cyboard.com/ent/PatMartino.html
Dividing the octave and making up patterns based on those divisions is
the same premise that Slonimsky uses in much of 'Thesaurus of Scales and
Melodic Patterns' BTW.
I know that Pat uses a lot of diminished and augmented chord structures
to take advantage of the symmetrical nature of the guitar, but it would
take me a long time to explain it all, if I indeed do understand it all!
If it's not too outside the list parameters I'll be glad to go into more
detail, or you can email me.
Clay