TUNING digest 1431: Wilson's nines

Very often Erv Wilson will put his nines on a separate axis from threes. =
A
look at his Xenharmonikon cover art will provide several examples. (All
back issues of XH are available from Frog Peak Music). =


One of the most interesting mappings done by Wilson is his mapping onto a=

Penrose tiling, treating it as a two dimensional representation of a 5
dimensional space. When nines or fifteens are treated as independent axes=

from threes and fives, interesting 'wormholes' in the lattice start to
appear, where alternative representations of the same pitch class occur i=
n
surprisingly different contexts. =


Although I have not followed up on this work for some years, I was gettin=
g
interesting results in using the Penrose tilings as a control mechanism
over random walks over the lattice.

While treating nine as two steps on the three axis will certainly be the
more efficient means of avoiding redundancies, there can be musically
compelling grounds for preserving such redundancies or ambiguities.