Derek Polischuk, piano
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Étude on a Twelve-Tone Row

A highly-serialized twelve-tone composition, Étude on a Twelve-Tone Row was composed in the Spring of 1999. The piece's introductory section is comprised of many statements of the row and its variations. These statements were organized using a process that is so mathematically complex, explaining it in this brief program is futile.
However, the majority of the piece is constructed more simply and traditionally. Observe the matrix below, taken from my many volumes of sketches for this piece. Important row variations have been clearly marked with black boxes.



The prime form of the row is stated very strongly several times during the piece. However, between these statements are sections of material derived from other variations on this row. These developmental sections begin with a statement of the second full hexachord of P-11. After these six pitches, I calculated for the placement of two three-note clusters from P-8 and RI-1. Finally, these sections conclude with a cluster of pitches from P-2, before returning to the prime form of the row.
Creating a new matrix out of this hexachord and cluster combination reveals the following:

This material is used primarily between statements of the complete twelve-tone row in its prime form.


Performance Practice for Étude on a Twelve-Tone Row