I was recently at a session when one of the players pulled out square with a bunch of notes written out in letter form. He said it was a matrix and we proceeded to improvise based on the matrix. Now I guess I am very interested in the compositional uses of this said matrix. From what I gatehred it was based on Schenberg's twelve tone row. I brought it home and am having a time trying to analyze it. If anyone can offer any insight into the mysteries of this amazing tool for improvisation. I would appreciate the enlightenment.

I've done a little improvisation on a tone row, but it was just one row, and in somewhat a somewhat structured application of that row. I'd be interested in how it could be used when expanded out into a matrix. I've used matrices in jazz composition, and that's very interesesting, but I would have to leave the entire mathmatical process of making a matrix out of a row to someone else. The pianist who introduced me to the process was crazy enough to write a program in C+ that would do the trick for me, and dumb enough to give the program to me, thus allowing me to forget at this moment what that process is.

I have a theory degree so I should be able to answer this. However, I haven't looked at a matrix in about 5 years. I will consult my old books when I get home to confirm this. It's all a matter of transposition and intervals. You need to copy the first row down to make the first note of each of the next rows. I'll put in an easy example. A Bb B C Db D Eb E F Gb G Ab Bb B C Db D Eb E F Gb G Ab As you can see the first row across is the same as the first row down. In this easy example every interval is a half step. Therefore to fill out the matrix you need to move a half step up for each space across the matrix. continued...

Lets use the intervals in your example: E-F-G-Dflat-Gflat-Eflat-Aflat-D-B-C-A-Bflat E to F is a half step. The first interval in each row is a half step. F to G whole step so that is your next interval. G to Db, tritone. So the first four tones of the second line would be: F Gb Ab D F to Gb half step, Gb to Ab whole and Ab to D is a tritone. Now that I've thought this through I think I'm remembering correctly, however if anyone can correct me please do so. It's been fun to revisit this stuff. Let me know if you can take it from there or if you have more questions.