Composing this piece with sonic and conceptual goals in mind, I was surprised to find I had produced something simple enough for novice piano students—or alternatively, a trio of treble instruments.

As the hands can remain stationary, the piece makes only the most modest physical demands.

That said, it poses other kinds of challenges.

The performer must read from three staves, each carrying a simple but reasonably independent voice.

The meter changes constantly, shaped by the additive logic of the underlying rhythm.

And while a beginner might ignore the dynamics and still produce an acceptable result, a finished interpretation depends on the ability to play piano and forte simultaneously, in order to bring out just one or two voices when required.

Whatever makes music simple also makes it transparent—and transparency always demands control. Put differently, the same minimalism that lightens the physical load calls on the performer to maintain connection and seek out rhythmic and tonal nuance that will sustain interest.

In one respect, however, the piece is unapologetically pedagogical.

It communicates a mathematical argument in support of an elementary but non-trivial proposition.

In more detail: the highest voice moves in durations of 1, 7, and 8 eighth notes; the lowest in durations of 1 and 5. Each voice constitutes a kind of translation of the other. Remarkably, any 1–7–8 rhythm can be transformed—without much change in length—into a corresponding 1–5 rhythm, via a completely reversible process. This is only possible for very special sets of durations. And by the way, those 1’s—the eighth notes—don’t just tag along. Their role is more complicated, and necessarily so.

As often happens in mathematics, revealing a hidden connection between two structures requires inventing a third that can serve as intermediary. The middle voice plays that role, moving only in durations of 2 and 3 eighth notes.

Analyze the piece for its patterns, and the translation principles hinted at here will become clear.

One may simply take this as an opportunity to learn some mathematics while learning music. Better still, one might strive to hear both at once—and so enjoy a kind of dual experience. That possibility of duality might even inform the interpretation.

Direct message me if you would like to see the score.

Proof Piece for piano or three treble instruments

Composer, mathematician, visual artist. 
Seeks collaboration with performers and choreographers.

Please don't spam this account!

Proof Piece for piano or three treble instruments

David Victor Feldman