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Can Musicians Track Two Different Beats Simultaneously? Author(S): Ève Poudrier and Bruno H Can Musicians Track Two Different Beats Simultaneously? Author(s): Ève Poudrier and Bruno H. Repp Source: Music Perception: An Interdisciplinary Journal, Vol. 30, No. 4 (April 2013), pp. 369- 390 Published by: University of California Press Stable URL: http://www.jstor.org/stable/10.1525/mp.2013.30.4.369 . Accessed: 17/11/2015 19:06 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. University of California Press is collaborating with JSTOR to digitize, preserve and extend access to Music Perception: An Interdisciplinary Journal. http://www.jstor.org This content downloaded from 23.235.32.0 on Tue, 17 Nov 2015 19:06:20 PM All use subject to JSTOR Terms and Conditions Tracking Different Beats Simultaneously 369 CAN MUSICIANS TRACK TWO DIFFERENT BEATS SIMULTANEOUSLY? E` VE POUDRIER Swedish death metal group Meshuggah; see Pieslak, Yale University 2007), and 20th century Western art music. In the latter, composers whose stylistic orientations range from exper- BRUNO H. REPP imentalism (notably in the works of the American com- Haskins Laboratories, New Haven, Connecticut posers Charles Ives, Henry Cowell, and Conlon Nancarrow) and modernism (Elliott Carter and Gyo¨rgy THE SIMULTANEOUS PRESENCE OF DIFFERENT Ligeti, the latter having been influenced by the music of meters is not uncommon in Western art music and the the Aka Pygmies; see Taylor, 2003) to minimalism and music of various non-Western cultures. However, it is ‘‘New Complexity’’ (as represented by Steve Reich, John unclear how listeners and performers deal with this Adams, and Michael Gordon on the one hand, and Brian situation, and whether it is possible to cognitively estab- Ferneyhough and Michael Finnissy on the other) have lish and maintain different beats simultaneously with- combined the use of polyrhythms with other types of out integrating them into a single metric framework. rhythmic devices, such as syncopation, metric modula- The present study is an attempt to address this issue tion, irrational subdivisions of the beat, and tempo fluc- empirically. Two rhythms, distinguished by pitch regis- tuations. As represented by these repertoires, the ter and representing different meters (2/4 and 6/8), were simultaneous presence of distinct metric frameworks can presented simultaneously in various phase relation- function as an expressive tool that aims to generate a wide ships, and participants (who were classically trained range of musical experiences for composers, performers, musicians) had to judge whether a probe fell on the beat and listeners. For example, by superposing three different in one or both rhythms. In a selective attention condition, rhythms in Yo Shakespeare, Michael Gordon seeks to cre- they had to attend to one rhythm and to ignore the other, ate the effect of ‘‘three different dance rooms with three whereas in a divided attention condition, they had to different dance bands playing at the same time’’ (Baker, attend to both. In Experiment 1, participants performed 2002). Contrastingly, in the works of Elliott Carter, ‘‘giant significantly better in the divided attention condition than polyrhythms’’ (i.e., slow polyrhythms that span the entire predicted if they had been able to attend to only one duration of a work) provide a background for different rhythm at a time. In Experiments 2 and 3, however, which types of polymetric structures (Poudrier, 2009) and for used more complex combinations of rhythms, perfor- the interplay of contrasting musical characters whose mance did not differ significantly from chance. These dramatic interaction is made perceptible to the initiated results suggest that in Experiment 1 participants relied listener by the use of associated pitch materials, rhythmic on the composite beat pattern (i.e., a nonisochronous gestures, and tempi (Ravenscroft, 1993; Roeder, 2006; sequence corresponding to the serial ordering of the two Schiff, 1998). Little is known, however, about the psycho- underlying beats) rather than tracking the two beats inde- logical basis of such polymetric structures. pendently, while in Experiments 2 and 3, the level of com- plexity of the composite beat pattern may have prevented Theoretical Framework participants from tracking both beats simultaneously. At the outset, it is crucial to make a distinction between Received: December 2, 2011, accepted July 31, 2012. polyrhythm and polymeter.Arhythm can be defined as Key words: polyrhythm, polymeter, auditory streaming, any auditory sequence of event onsets. Musical attention, beat induction rhythms, however, often have underlying temporal regularities that can lead to their being perceived as metrical. Meter is commonly described as a nested hier- OLYRHYTHM AND POLYMETER ARE IMPOR- archy; that is, an underlying network of at least two tant compositional techniques in a wide range of periodic pulses (i.e., series of evenly spaced time-points) P musical practices, from West African drumming where non-adjacent time-points at a faster pulse level ensembles (Arom, 1991; Locke, 1982) to jazz (Folio, become adjacent time-points at a slower pulse level 1995; Pressing, 2002), rock-derived genres (e.g., the (e.g., Lerdahl & Jackendoff, 1983; Yeston, 1976). Metric Music Perception, VOLUME 30, ISSUE 4, PP. 369–390, ISSN 0730-7829, ELECTRONIC ISSN 1533-8312. © 2013 BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIA ALL RIGHTS RESERVED. PLEASE DIRECT ALL REQUESTS FOR PERMISSION TO PHOTOCOPY OR REPRODUCE ARTICLE CONTENT THROUGH THE UNIVERSITY OF CALIFORNIA PRESS’S RIGHTS AND PERMISSIONS WEBSITE, HTTP://WWW.UCPRESSJOURNALS.COM/REPRINTINFO.ASP.DOI:10.1525/MP.2013.30.4.369 This content downloaded from 23.235.32.0 on Tue, 17 Nov 2015 19:06:20 PM All use subject to JSTOR Terms and Conditions 370 E`ve Poudrier & Bruno H. Repp entrainment is the dynamic process by which internal their likely underlying metric frameworks. In this sche- or external periodic processes (such as oscillatory brain matic representation, each vertical line represents an activity, attention, expectations, or motor activity) are event onset in a musical surface and each dot corre- aligned with one or several of these periodic pulses sponds to a time-point within an underlying pulse level. (Jones, 1976, 2009; Large & Jones, 1999; London, In Figure 1a, which presents a simple in-phase 3:2 poly- 2004; Nozaradan, Peretz, Missal, & Mouraux, 2011). rhythm, the frequent recurrence of coinciding event A polyrhythm results from the superposition of two onsets is likely to give rise to the emergence of a unifying or more rhythms that are distinguishable from each tactus ("1") for the composite rhythm (CR) formed by other along some dimension (e.g., pitch, timbre, the two component pulse trains, especially if the tempo tempo). In practice, the term is most often used to refer is relatively fast. In a musical work, depending on the to the superposition of two or more pulse trains (i.e., prescribed tempo, this tactus level might correspond to isochronous series of event onsets) whose periods are the notated beat, a subdivision of the notated beat, or related by a frequency ratio other than N:1, where N is even a measure. Whether the meter of the composite an integer (such as 3:2). We will refer to this type of rhythm is perceived as duple (2:1) or triple (3:1) will structure as a simple polyrhythm. The superposed pulse depend on the tempo as well as on associated para- trains that make up a simple polyrhythm may be in- meters (melodic patterns, dynamic accents, harmonic phase, which means that they are characterized by the rhythm, etc.) that make one of the two pulse trains more cyclical return of coinciding onsets, or out-of-phase (no salient than the other; otherwise, the meter will remain coinciding onsets). Most experimental studies on ambiguous. Given that the competing layers are nested polyrhythm perception and production have used sim- within the tactus and thus effectively function as sub- ple in-phase polyrhythms (e.g., Handel, 1984; Pressing, divisions of the tactus, there is no firm basis for duple Summers, & Magill, 1996). By contrast, we define com- and triple meters to be construed simultaneously. In the plex polyrhythm as a structure that results from the complex (albeit still relatively simple) polyrhythm pre- superposition of two or more nonisochronous rhythms, sented as Figure 1b, the two rhythms (corresponding to some of whose underlying periodicities (or pulse levels) 2:1:1 and 3:1:1:1 duration series) can be described in are related by a ratio other than N:1. Complex poly- terms of two well-formed metric frameworks, each of rhythms, too, can be in-phase or out-of-phase. Polymeter, which exhibits a nested hierarchy of three pulse levels, then, refers to the simultaneous presence, at either 4:2:1 and 6:2:1 respectively. The slowest pulse level (‘‘1’’) a descriptive or psychological level, of two distinct corresponds to the onset of the repeating duration metric frameworks. Although all polyrhythms are series. (In a complex polyrhythm, the even slower pulse potentially polymetric, we contend that simple poly- corresponding to the points of coincidence of the ‘‘1’’ rhythms are rarely so perceived because simple pulse pulses is generally too slow to function as a unifying trains are generally insufficient to give rise to indepen- tactus.) As defined above, a polymetric framework dent metric hierarchies. Rather, the common way to implies two or more metric frameworks with at least perceive such polyrhythms is as a sequentially inte- one pair of competing pulses (i.e., pulses with periods grated rhythmic pattern (a ‘‘composite rhythm") that are not related by a N:1 ratio).
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