Wheels Within Wheels

Watch on YouTube (link skips long pre-concert interview)

Program notes

Commissioned by Walter Swap and the Arizona Friends of Chamber Music.

Wheels Within Wheels is a set of three movements played without pause. The first, "The Swerve," depicts the swirling maelstrom of subatomic activity, the burbling quantum vacuum. It borrows its title from the ancient philosopher Lucretius, who argued that atoms need to "swerve" from their predetermined paths in order to leave room for free will. The ten instruments mostly play as a unit, like a school of fish—a massed colorful force. The second movement, "Modernistic," borrows its title from a piece by the stride piano master James P. Johnson. It makes lighthearted use of various modern-music clichés including quarter tones ("out of tune" notes) and other unusual playing techniques. It is fragmentary and uncertain until it breaks out in a jovial dance, perhaps inspired by jazz. The last movement, "Runner's High," tries to capture the pain and joy of a fast five-minute run. It is rhythmic and unrelenting, a mix of pleasure and pain.

What I love about music is its unique combination of mathematical rigor and emotional expressiveness; it is a theorem expressed as drama. Often I start composing with some interesting theoretical structure—a set of chords or melodic pattern that has notable musical features. This becomes something like the sculptor's block of marble, raw material that I mold and shape to my own expressive and dramatic ends, negotiating between the tendencies of the substance and my own inclinations. It is a fairly inefficient process: sometimes the finished piece retains a good deal of the original structure; at others, only tiny glimpses and fragments survive. But it is my way of trying to honor the twin demands of rigor and passion.

The two most interesting structures in this work are, first, a long fractal chorale in which four-note chords move inside six-note scales which themselves move inside seven-note scales which themselves move inside an eleven-note chromatic collection, with each layer moving according to the same abstract pattern. (I was astonished to discover such a thing was even possible.) This is the "wheels within wheels" of the title. The chorale appears at the start and end of the piece, and makes a brief appearance at the end of the second movement. The second structure is a mathematical problem, the "lonely runner conjecture," which imagines runners jogging independently around a circle, in various directions and speeds. A musical depiction of this problem forms one of the main themes of the final movement.

My thanks to Walter Swap and the Arizona Friends of Chamber Music for making this music possible.

Instrumentation: Flute, Oboe, Clarinet, Horn, Bassoon, Violin, Viola, Cello, Bass, Piano

Performer: Carol Wincenc, flute, Nicholas Daniel, Oboe, Charles Neidich, Clarinet, William Purvis, Horn, Benjamin Kamins, bassoon, Axel Strauss, violin, Nokuthula Ngwenyama, viola, Clive Greensmith, cello, Philip Alejo, bass, Piers Lane, Piano, Steve Taylor, conductor