Ommateum, for Woodwind Quintet






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I start with a group of 5 notes. Why not?!

Call this group of notes 5-28 (“five twenty eight”). Just for me?

(This is the name Allen Forte gives this group. He cataloged all the possible different groups of notes, so he gets to name the groups...)

I transpose 5-28 five times. I make sure a C is in each transposition:

Now I listen to the four note chords formed by removing the C from each group.

I arrange the notes in any octave, and the 5 groups in whatever order serves my purpose.

In the following case, one aspect of the result is a rising chromatic top line:

So the four note chords are different from each other. But they would be merely the same chord in five different transpositions if a C were added to each group. So each of the four note groups is a “subset” of the 5-28 set.

If my procedure had merely been to compose with the subsets of 5-28, I could have picked any of the subsets and each subset could have been in any of up to 12 transpositions. But by doing things the way I did, I have constrained myself.

So what? So in constraining myself in just this way, I have composed myself! More literally, I have composed more by constraining more, by choosing just these transpositions. Finding the right amount of constraint is a big issue in composing. An unconstrained infant is free to play any bunch of notes at any time, which should never be confused with artistic freedom, since it is highly unlikely that a sophisticated pattern will result. And with only a little training, a composer might cling to just a few transpositions of two or three chord types, as in pop music.