How to Perform Impossible Rhythms

Abstract

This paper investigates a fairly common but seldom-studied rhythmic notation in the nineteenth-century piano literature, in which duplets in one voice occur against triplets in another, and the second duplet shares its notehead with the third triplet—a logical impossibility, as the former note should theoretically fall halfway through the beat, the latter two-thirds of the way. Examples are given from the works of several composers, especially Brahms, who employed such notations throughout his career. Several alternative realizations are discussed and demonstrated in audio examples; the most appropriate performance strategy is seen to vary from one example to another. Impossibilities of type1⁄2=2⁄3, as described above, are the most common, but many other types occur. Connections between such rhythmic impossibilities and the controversy surrounding assimilation of dotted rhythms and triplets are considered; the two phenomena are related, but typically arise in different repertoires. A few other types of impossible notations are shown, concluding with an example from Scriabin’s Prelude in C Major, op. 11, no. 1, in which triplets and quintuplets occur in complex superposition. The notation implies several features of alignment that cannot all be realized at once; recorded examples illustrate that a variety of realizations are viable in performance.