A Platonic Model of Funky Rhythms

[0.1] Ragtime and big-band jazz, rhythm and blues, rock and funk, salsa and electronic dance music are characteristically duple at multiple levels of the metric hierarchy. These and other African-diasporic and popular repertories commonly stretch a series of three-unit, or "dotted," spans across a pure-duple frame, inducing pulse conflicts at one or more metric levels. The terms associated with this class of rhythms include tresillo (Cuba), bossa nova (Brazil), secondary rag (American ragtime), and second-line rhythm (New Orleans). When these durational patterns repeat cyclically over extended spans of time, as ostinati, they are among the core conveyors of a song's identity, feel, or groove. They also arise more transiently, often at moments that listeners identify as hooks (Traut 2005).[0.2] The phenomenon of layering dotted rhythms over a duple frame is found in a number of African repertories, both north and south of the Sahara (Toussaint 2013). It seems to be a generally accepted hypothesis that this rhythmic practice was channeled by the slave trade from Africa to the Caribbean, from which it washed symmetrically into adjacent mainland regions on both sides of the equator, eddied into urban musics on both continents, and ultimately emptied into what we now recognize as the vast ocean of global musical culture, where its status sits somewhere on the continuum from prominent to ubiquitous.[0.3] Musicians and popular-music scholars have characteristically classified rhythms of this genus as syncopations or polymeters (Copland 1927, Sargeant 1938). The two terms suggest two distinct models of the dotted spans: syncopation relates a meter to a rhythm, while polymeter suggests a relationship between two distinct meters. The approach here occupies a middle ground, treating dotted spans primarily as rhythmic patterns with properties, such as cyclicity and quasi-isochrony, that are shared by meter. The patterns thus have the potential to blossom into meters if developed in certain ways, although in the repertories studied here those potentials are rarely fulfilled. (We will study one exception, presented here as Audio 2). Iyer 1998 (87-88) writes of similar properties in some musics of West Africa: "When two meters appear to the listener, it is because there are periodic groupings of short, serially organized rhythmic fragments or phrases, and their periodicity seems to imply a different meter from the primary one. . . . Most commonly it is some variety of triple meter that seems to appear over some variety of duple meter."[0.4] Recent music-theoretic work has identified a cluster of related properties that rhythms of this genus share, including non-isochronous meter and maximal evenness (London 2004), maximal individuation and maximal evenness (Rahn 1996, Butler 2006), rhythmic oddity and Euclidean algorithms (Toussaint 2013, Osborn 2014). This paper treats these rhythms as three-generated, and theorizes them as a species of prime generation, which was introduced in this context by Jeff Pressing in 1983. (As this term may feel uncomfortably scientistic for some readers, I shall sometimes substitute more vernacular terms, such as extended tresillo, tresillo family, and funky rhythms.) This paper argues that a generative model both honors aspects of the way that these rhythms might be experienced by musicians, listeners, and dancers "in real time," and brings out some compelling abstract relationships between African-American rhythmic systems and the tonal systems at the foundation of European musical practice and theory.[1.1] In Duke Ellington's "It Don't Mean a Thing (if It Ain't Got That Swing)," composed in 1931, the bass projects a half-note pulse, and also participates in a quarter-note pulse with the hocketing chords, forming a fast duple meter. Duple proportions also characterize relations among pairs of slower pulses: there are two half-note beats to a bar, and four bars to a phrase; call-and-response phrase-pairs articulate eight-bar segments; and segments group by fours to constitute thirty-two bar "song form" (AABA) quatrains. …