Derivation and Polyphony
Daniel Starr · Perspectives of New Music · 1984
HIS STUDY ATTEMPTS to fill a certain gap in twelve-tone technique. I wanted to deal with the partially ordered aggregates resulting from combinatoriality. Combinatoriality assembles rows so as to preserve aggregates, but not orderedness, since it translates rows into columns of row-segments that are only partially ordered. I wanted to stipulate that the columnar aggregates also be totally ordered transforms of each other, like the rows. It turns out that such counterpoint can be constructed for arbitrary rows. By combining transforms of a row P, we make a sequence of transforms of some other row Q. We thus derive Qfrom P. We can also do the reverse, starting with a sequence ofQ-transforms, and polyphonize them into counterpoint of P-transforms.