UCLA

This piece is an experiment on pitch equivalence from a theoretical, rather than perceptual, standpoint; in particular, I dispense with the notion of octave-equivalence, the notion that two pitches that are an octave apart are to be considered equal in many different senses of that word. This constraint, on the one hand, proved to be a severe challenge as it disallowed adjusting musical material for range (hence transposing in octaves) for a given instrument; on the other, the restriction opened new compositional vistas by forcing the composer to think in ways that otherwise would not have occurred to him.

The three movements utilize different modular distances. The first movement employs double-octave equivalence (so pitches are repeated at every other octave), the second a major-14th equivalence (so the distance is a semitone closer than a double octave), and the third a minor-16th equivalence (so the distance is a semitone farther than a double octave). In each movement the modularity is exposed rather explicity and deliberately, for example, by means of homorhythmic gestures doubled at the appropriate intervals. Since pitch itself is central to the structure and compositional integrity of the piece, certain instrumental techniques that obscure pitch content – such as glissandos – are kept to a minimum, as frequent use of such techniques would obliterate and defeat the purpose of this piece.