AW.: RE: clearing up TC

Carl Lumma:

A Schoenbergian 12-tone matrix, or array, or "row box" is the cross set of a
12-tone row and its inversion, thus each transposition of the original row is
found horizontally, each transposition of the inversion is found vertically
and the retrograde versions are found by reading each line in reverse.
(Partch's diamond is the cross set of a harmonic hexad and it's inversion.
Both the row and the diamond share the feature of a central unison -- the
diagonal in the row box and the middle row of unison 1/1's in Partch's
diamond. This feature is important to Carl Lumma's postings, to row use in
late Stravinsky, indexing in Babbitt, and -- I believe, please correct me if
I'm wrong -- to George Perle's "twelve-tone tonality".)

There is a mountain of twelve-tone theory, much redundant and most of little
interest. I find that if you want to wade through these waters, it is best
to start at the source, i.e.:

M. Babbitt: "Since Schoenberg", PNM 12 nos 1-2: 3-28 (see esp. page 26)

and for the topic of row verticals/diagonals:

M. Babbitt: "Remarks on the Recent Stravinsky", PNM 2, No. 2:35-55 (1964)