Beat perception in polyrhythms: Units of time come in pairs

Cecilie Møller, Jan Stupacher, Alexandre Celma-Miralles & Peter Vuust

Center for Music in the Brain, Department of Clinical Medicine, Aarhus University & The Royal Academy of Music Aarhus/Aalborg, Denmark

The capacity for beat perception in music requires that the listener extracts at least two levels of a rhythm’s metrical hierarchy, i.e. the regular beat and its subdivisions (London, 2002). In the special case of polyrhythms, two or more mutually exclusive metrical hierarchies co-exist, yet the listener hears only one salient beat. The number of subdivisions within a polyrhythm cycle is defined by the least common denominator of the constituent isochronous pulse trains, and the beat level depends on the grouping of those subdivisions. For instance, the simplest 2:3 polyrhythm contains six grid points at the subdivision level, and the metrical structures underlying the slow (2) and fast (3) pulse trains contain ternary and binary subdivisions, respectively.
Here, we used polyrhythms to investigate the extent to which subdivision grouping is related to beat perception. In two online finger-tapping experiments, participants tapped in time with the perceived beat of (i) 2:3 and 3:4 polyrhythms in a wide range of tempi (n = 100), and (ii) polyrhythms with increasing levels of complexity, i.e., 2:3, 2:5, 3:4, 3:5, 4:5, 5:6 (n = 120). Using the Rayleigh test for circular statistics, participants’ consistent tapping responses were assigned to one of several possible beat categories, including slow and fast pulse trains and their half- and double-time equivalents. We hypothesized that participants would prefer to tap in time with a beat containing simpler subdivision grouping, i.e., they would prefer binary grouping over ternary grouping, and ternary grouping over irregular grouping of subdivisions.

Consistent with this main hypothesis, results of both experiments reflected tapping preferences for pulse trains containing simpler subdivision grouping. In the first experiment, response distributions were centered between 90 and 142 BPM, corresponding to the human preferred motor tempo (Parncutt, 1994). Notably, these response distributions were only observed within pulse trains containing binary subdivisions, i.e., the fast and slow pulse trains in the 2:3 and the 3:4 polyrhythms, respectively. The vast majority of participants consistently avoided ternary subdivisions. Their strategy was to metrically restructure the polyrhythm when tapping rates were too fast or too slow. Here, binary subdivision groupings were maintained by grouping cycles together and/or engaging in half- or double time tapping. Similar metrical restructuring was evident in the second experiment using more complex polyrhythms. Here, the preference for simpler subdivision groupings faded, however, as the polyrhythms required grouping of more than four subdivisions, suggesting that subdivision grouping predicts beat perception only below this limit. Closer inspection of the temporal aspects of the stimuli revealed that tapping preference transition points were tightly linked to the tempo of the subdivisions, rather than to the tempo of the pulse trains.

In conclusion, beat perception in polyrhythms is constrained not by the tempo of the beat itself, but by the tempo of the subdivisions underlying it. We have a propensity towards beats containing binary subdivisions. These findings add important and yet neglected nuance to the understanding of temporal aspects of beat perception.


References:
London, J. (2002). Cognitive Constraints on Metric Systems: Some Observations and Hypotheses. Music Perception, 19(4), 529–550. https://doi.org/10.1525/mp.2002.19.4.529

Parncutt, R. (1994). A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms. Music Perception, 11(4), 409–464. https://doi.org/10.2307/40285633