Leonhard Euler’s Unfinished Theory of Rhythm

Abstract

The music-theoretical formulations of the early modern mathematician Leonhard Euler (1707-83) are customarily remembered—and often dismissed—for their unconventional rankings of the consonances. A closer examination of Euler’s writings, however, reveals that he intended his theory of consonance to assess and explain the interaction of rhythms as well as the interaction of pitches. At several points in his 1739 Tentamen novae theoriae musicae (Attempt at a New Theory of Music), Euler suggests that everything he has written about consonance should also apply to duration. Curiously, the transference of Euler’s consonance principles to the temporal elements of music renders a theory that has interesting and provocative connections to several contemporary theories of rhythm and meter, such as those of Harald Krebs, Richard Cohn, Daphne Leong, and Scott Murphy. This article sketches the theory of rhythm that Euler suggested but never finished. The analytical applications of this model are surprising and extend beyond the music of the eighteenth century. Elaborating Euler’s unfinished theory sheds light not only on his work as a music theorist but also—and perhaps more provocatively—on twenty-first-century music theory.