Gridless Beats
Fernando Benadon · Perspectives of New Music · 2009
Gridless Beats ' Fernando Benadon Jazz music conflates two seeming opposites: the fixed foundation of a regular beat and the fluidity ofmicrorhythmic variation. By fuzzying subdivision values and slicing beats asymmetrically, jazz musicians enrich themonotony of steady beat patterns with an elastic treatment of time. Because such rhythmic sophistication derives from spontaneous inven tion and not from the directives ofmusic notation, a composer wishing to emulate jazz rubatos faces an interesting technical challenge. In this article I look at how certain microrhythmic properties of jazz can be simulated using standard music notation. My goal is to bridge aspects of jazz improvisation and contemporary composition by providing insights into the former and toolsets for the latter. Grids and Beats The beat (or tactus) is often theorized as one of several isochronous strands within a temporal hierarchy (Lerdahl and Jackendoff 1983, I 36 PerspectivesofNew Music Yeston 1976). The vertical julienning of horizontal time calls tomind a grid inwhich the smallest unit assembles rhythm and meter from the bottom up. One could think of both the grid and the beat as non sounding structural concepts, as inmusic where these are imagined by the performer and/or notated by the composer but not conveyed aurally to the listener.1 In this discussion, grids and beats are understood as perceptually salient and mutually interacting. The matrix in Example 1 shows four different types of grid/beat interaction. It is almost always the case thatwhenever a beat is present, so is its grid. "If beat, then grid" is the premise of quadrant I inter actions. "Stayin' Alive" falls in this quadrant, as does Schoenberg's Klavierstucke op. 33. Or, the grid can function as an audible frame onto which attack points are pinned without engendering a convincing sense of tactus, as in quadrant IPs beatless grid. Ligeti's "Desordre" and "L'escalier du diable" are good examples. Or, one could do away with the grid altogether, an action that dissolves the beat as well. Quadrant Ill's "no grid, no beat" is a frequent result of graphic scores, pointillism, chance, extreme slowness, Impressionistic timelessness, and rhythmic saturation. Godless beats fall into quadrant IV. A gridless beat is a beat contain ing onsets that are not aligned with its isochronous subdivisions. Hence gridless beats are in violation of Lerdahl and JackendofPs first Metrical Well-Formedness Rule, which states that onsets "must be associated with a beat [i.e., subdivision pulse] at the smallest metrical level present at that point in the piece" (1983, 72). To thiswe add the perceptual dimension contained in London's firstmetric Well-Formedness Con straint,which states that subdivision interonset intervals "must be at least ? 100 ms" (London 2004, 72).2 + II I G R_ ? III IV BEAT + EXAMPLE 1: FOUR TYPES OF GRID/BEAT INTERACTION Gridless Beats I 37 Gridlessness resembles microtonality's use of pitches not on the equal tempered lattice. Although it is not my wish to embrace pitch/rhythm isomorphisms, the idea that rhythmic dissonance can ensue given non categorizable temporal ratios parallels that of harmonic dissonance given non-equal-tempered harmonic ratios. John Adams touches on this analogy when discussing the role of the grid in his compositions (Adams et al. 1996, 96): In the creation of temporal relationships there seems to be a point beyond which musical time itselfbegins to sound dissonant. This is a funnyway of describing things, but I feel that there's a natural way of dividing time and then there's a dissonant way of dividing time. I don't know where the dissonance begins. Two against three obviously does not feel dissonant to me. . . . Three against five begins to push the envelope. Paul Berliner sums up this article's main gist by noting that "efforts to capture the complexity of jazz despite the limitations of notation often result in dense representations . . . that are difficult for performers to interpret" (1994, 158). The following pages illustrate how jazz musi cians bend the grid's vertical and horizontal coordinates to dissociate the beat-level from the other layers in the rhythmic hierarchy. I discuss five different forms of gridlessness: displacement, swing, acceleration, polyrhythm, and wavering. Even thought each of these categories also exists in gridded form...