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Fixed Media
2021
Piano
- Program Notes
- Geometry (Homage to Schillinger) [not on the commercial CD] will not sound minimalist, but in at least one sense it is my most minimalist work: every moment is based on short repeating phrases going out of phase with each other (except for a section just past the midpoint, in which the loops are rather long). The device I was inspired by and sought to exploit was that each repeating phrase contains notes in several octaves, and the simultaneous ostinatos overlap greatly in range, so that the ear can't keep the simultaneous repeating figures separate, and the coincidences create a counterpoint of "accidental" melodies in each register. One can tease out the two repeating phrases at the opening, each employing two staves, one in septuplets and the other sextuplets: The simplest statement of the technique comes at m. 166ff, as shown below. The repeating figures are reduced to four notes each with only three pitches. Part A in the diagram shows the very simple repetition process. Part B shows the three independent and unpredictable melodies actually heard, whose process may still exert some subliminal influence. Something like an audio analogue of Op Art, it was minimalist to write, not so minimalist to perceive. I have only skimmed Joseph Schillinger, but one of his structural principles, the "interference of periodicities," is central to early minimalism and has long fascinated me. "The basis of beauty is mathematical," was his motto, and I tried it out here - again. Never before has a piece required so much revision, not because I didn't know what I wanted, but because the proportions and tempos of repeating figures often didn't produce the effect I wanted the first or second or third time, and I had to completely compose each section before I could tell whether it worked or not.
- Publisher
- Smiht Grabholz Music
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