Tactus in Performance: Constraints and Possibilities

Example 1. Haydn, String Quartet op. 33, no. 3, IV, measures 1-8[1] Example 1 reproduces the opening measures of a movement for string quartet by Haydn. If the reader were to auralize this excerpt in the neighborhood of the indicated tempo, I can make a few predictions about that reader's temporal orientation within the music. First, the reader will have become a listener, which is to say that the process of imagining the music activates similar brain activity as would processing actual acoustic events that correspond to the score (Hubbard 2010). Second, the listener is very likely to be organizing the excerpt's pitches and rhythms in relation to some consistent pulse that is represented in the notation, felt as a counting beat or tactus (Jones and Boltz 1989).(1) In this excerpt, the most comfortable pulses with respect to tempo are the quarter- and half-note pulses at the tempo indicated, 144 and 72 BPM, respectively. Researchers have explored the constraints that tempo places on pulse perception (Parncutt 1994; Drake and Bertrand 2001); in the context of fully musical material, however, recent research has shown that tempo alone does not dictate a specific tactus within the fairly large window of 30-300 BPM (McKinney and Moelants 2006; Martens 2011). These later studies posit several factors that can direct a listener's attention to one or another pulse within that window: the presence of subdividing pulses, genre-specific cues such as a backbeat pattern, years of musical training, and the specific instrument on which that training focused are just a few. If tactus-seeking listeners are busy attending to this noisy and opinionated crowd-tempo, rhythmic features, metric structure, and individual preferences based on prior experience-can the performer be heard above the din?[2] The purpose of the exploratory research presented here is to investigate precisely this question: Can performers influence or direct listeners' attention toward a specific tactus? The notion that tactus is communicated during performance is implicit in its very definition, and is encoded in our pedagogy and theories of beats and meter,(2) yet we have few detailed principles for performers. Will performers succeed simply based on a conscious decision, adeptly executed? Are often-neglected visual components of a viewed-and-heard performance important, even crucial, for this type of communication? In what follows, I will present results from two empirical studies and a computer model that speak to these issues, and I will set up each of these approaches immediately below in order to weave together their results later on.Experiment 1[3] Seven excerpts of common practice music were arranged for an undergraduate string quartet at Texas Tech University School of Music, the titles, composers, and scores of which are given in Appendix A. The pieces themselves, and a performance tempo for each excerpt, were chosen to allow for two pulses in the music to be plausible tactus choices. I will refer to the two tactus options generically as the "slower" and "faster" tactus throughout this article; across the seven excerpts, the slower tactus ranged from 42-76 BPM, the faster from 102-52 BPM. For example, the faster and slower tactus options in Example 1 were the two pulses already mentioned, at 144 and 72 BPM. Of the seven excerpts used in the study, four were in simple duple or quadruple meters and three were in simple triple meters; in the triple meter excerpts the triple ratio existed between the two tactus options.[4] The quartet met for two rehearsals prior to a recording session in which they performed all of the excerpts. During the rehearsals I dictated a performance tempo for each piece and coached the quartet to express either the slower or faster tactus in each excerpt as their main beat, without discussing the other option at all. I had chosen a mixture of the slower and faster tactus options across the seven excerpts, and within each meter type. …