Response to Fernando Benadon

[1] What a pleasure it is to have one's work read with such care by as astute and thoughtful an observer as Fernando Benadon. In his commentary on my essay "The Power of Anacrusis," Benadon has offered some provocative criticisms of my analysis of Herbie Hancock's "Chameleon" (Benadon 2007). I would like to address these criticisms here.[2] Benadon first questions the process by which I derived idealized timings of beats and beat subdivisions in the synthesized bass solo at the outset of "Chameleon." At issue, specifically, is the timing of the syncopated bass note on the "uh" of beat one in each bar: how does one determine whether it arrives early or late? I took the actual and projected length of each measure and arrived at timing figures by a simple process of division (see my Table 1). Benadon proposes instead to derive such timings from more "local" criteria "to underscore the importance of ecological validity in the testing of timing-related hypotheses" [par. 6]. His figures corroborate my own, but on what he believes to be more solid ecological footing.[3] I agree on the importance of ecological validity in deriving idealized timing figures for each beat and its subdivisions. I question, however, whether Benadon's proposed metrics have more ecological validity than my use of the measure (or projected measure) for this purpose. An ecological approach to perception should model a subject's perceptual engagement with his or her environment. It should take account of the structural attributes of the environment (with a special focus on invariant features), the perceptual and cognitive faculties of the subject, and his or her historical and cultural situatednessi?½all of which help the subject to understand what it is that is going on in a particular situation.(1) If we are to derive ecologically valid idealized timing figures for "Chameleon," then, we must find the metric that best models the perceptual strategies of the listener in engaging with the structural features of the rhythmic pattern at hand.[4] Finding the measure unsuitable "for assessing the microtemporal placement of values as small as the sixteenth note" [par. 4], Benadon proposes two alternative methods based on more local criteria (see his example 2 and Table 1). The first employs the formula y-(x/2) to derive the ideal timing for the "uh" of beat one. In strictly mathematical terms, this makes sense, but do listeners actually make judgments about the duration of y (and the timing of the "uh") on the basis of their experience of x? It is possible to judge y as half of x, of course, but only if one first experiences x as a salient duration that is available for comparison. This can happen only if x, upon its completion, realizes what Hasty calls "projective potential" (1997, 84-91).Thus in example 1a, if we perceive projective potential P, then x is available to serve as a measure for y, and it should be relatively easy to anticipate the timing of the A3 despite the implied hemiola, especially if the B3 arrives at just the right moment to confirm the realization of projected potential P'. However, there will be a projective potential P and a definite duration x available for comparison only if we experience this passage in 6/8, as shown in example 1b. In 4/4, by contrast, a projective potential P can come only at the cost of the quarter-note tactus, as shown in example 1c. In this case, for there to be an x, there must be a P, and if there is a P, there can be no projection Q-Q', and consequently no R for the duration of a quarter note.(2) Instead, if P-P' is realized, R will be unhearable, and the B3 on the "and" of beat two will sound more like a new beginning-like a new downbeat-than a syncopation anticipating a beat three. There would be nothing to indicate simple quadruple meter, and metric confusion would arise for the listener by the end of the bar.Example 1.[5] How, then, do listeners experience meter in this passage, and what durations are relevant for their feeling of timing? …