While many of Conlon Nancarrow’s Studies for Player Piano have been arranged for live human performance, the Studies that are based on irrational tempo ratios pose extreme rhythmic challenges that would seem impossible to overcome without mechanical assistance. Nonetheless, Paul Usher’s arrangement of Study 33, Canon 2:√2, has been successfully performed and recorded by the Arditti Quartet. The purpose of this paper is to explore some of the compositional, mathematical, and performance issues involved in the approximation of irrational rhythms, concentrating on Usher’s arrangement of Study 33 in order to more fully understand and appreciate this remarkable feat.

Performing the Irrational Paul Usher’s Arrangement of Nancarrow’s Study No. 33, Canon 2:√2, Music Theory Online, 20.1, 2014.