Kid Algebra: Radiohead's Euclidean and Maximally Even Rhythms

Abstract

The British rock group Radiohead has carved out a unique place in the post-millennial rock milieu by tempering their highly experimental idiolect with structures more commonly heard in Top Forty rock styles.1 In what I describe as a Goldilocks principle, much of their music after OK Computer (1997) inhabits a space between banal convention and sheer experimentation—a dichotomy which I have elsewhere dubbed the ‘Spears–Stockhausen Continuum.’2 In the timbral domain, the band often introduces sounds rather foreign to rock music such as the ondes Martenot and highly processed lead vocals within textures otherwise dominated by guitar, bass, and drums (e.g., ‘The National Anthem,’ 2000), and song forms that begin with paradigmatic verse–chorus structures often end with new material instead of a recapitulated chorus (e.g., ‘All I Need,’ 2007). In this article I will demonstrate a particular rhythmic manifestation of this Goldilocks principle known as Euclidean rhythms. Euclidean rhythms inhabit a space between two rhythmic extremes, namely binary metrical structures with regular beat divisions and irregular, unpredictable groupings at multiple levels of structure. After establishing a mathematical model for understanding these rhythms, I will identify and analyze several examples from Radiohead’s post-millennial catalog. Throughout the article, additional consideration will be devoted to further ramifications for the formalization of rhythm in this way, as well as how hearing rhythm in this way may be linked to interpreting the lyrical content of Radiohead’s music. After doing so, I will suggest a prescriptive model for hearing these rhythms, and will then conclude with some remarks on how Radiohead’s rhythmic practices may relate to larger concerns such as style and genre.