I used the matrix derived from the tone row 0,5,8,1,4,9,2,7,10,3,6,11 (my favorite) to reharmonize Mary Had a Little Lamb.
I didn't follow all of Herr Schoenberg's rules about 12-tone music making it, rather I treated the matrix as 2-dimentional scale, so you won't see all 12 notes in it. I guess you could say I followed the spirit of his method, rather than the letter. I treated notes that are closer together on the matrix as more sympathetic harmonically.
Here's the piano roll of the end result:
And a midi:
mary lamb reharm.mid