Lehmer’s Machine (2018)
As a trombonist with the Yale Jazz Ensemble, I had the privilege and pleasure to learn from some of the greatest modern talents in jazz performance, arrangement, and composition. This composition was written for that ensemble, for the benefit of my talented mentors. It’s dually inspired by my reading of Dmitri Tymoczko’s excellent book A Geometry of Music and my first forays into John Coltrane’s infamous ‘Coltrane Circle,’ a sketch of geometric relations across tonal centers in 12-tone equal temperament. I wanted to embed this work inside a rigid systematic architecture, and then to test the bounds of that architecture by means of angularity, drive, and groove. At the time, I had just learned about number theorist Derrick Lehmer and his Lehmer Sieve—an early computer made of bike parts, designed to factor large numbers. I was struck by the juxtaposition between the gritty, mechanical engineering of the thing and the world of infinities, abstractions, unknowables into which it humbly forayed. Tymoczko—Coltrane—Lehmer—all searching for self-contained systems in a roiling sea of infinite possibility. I wanted to write something that felt like that process—of searching, stumbling, failing, succeeding, starting up, shutting down, arriving, greasy-handed, at some demur first solution that will yield uncountably many after it.
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