Abstract
Control of relative timing is critical in ensemble music performance. We hypothesize that players respond to and correct asynchronies in tone onsets that arise from fluctuations in their individual tempos. We propose a first-order linear phase correction model and demonstrate that optimal performance that minimizes asynchrony variance predicts a specific value for the correction gain. In two separate case studies, two internationally recognized string quartets repeatedly performed a short excerpt from the fourth movement of Haydn's quartet Op. 74 no. 1, with intentional, but unrehearsed, expressive variations in timing. Time series analysis of successive tone onset asynchronies was used to estimate correction gains for all pairs of players. On average, both quartets exhibited near-optimal gain. However, individual gains revealed contrasting patterns of adjustment between some pairs of players. In one quartet, the first violinist exhibited less adjustment to the others compared with their adjustment to her. In the second quartet, the levels of correction by the first violinist matched those exhibited by the others. These correction patterns may be seen as reflecting contrasting strategies of first-violin-led autocracy versus democracy. The time series approach we propose affords a sensitive method for investigating subtle contrasts in music ensemble synchronization.
Highlights
Coordination of movements to an external rhythmic auditory stimulus is a widespread biological phenomenon that occurs in non-human animals [1], as well as in humans from an early age [2], and possibly relates to vocal mimicry abilities [1,3]
In the case of the asynchronies, we discarded the first asynchrony and asynchronies for tones after tone 45
The mean intertone interval’ (ITI) between the 48 tone onsets averaged over the 15 repetitions was 191.5 ms (s.d. 25.0 ms) for quartet A and 191.8 ms (s.d. 16.7 ms) for quartet B
Summary
Coordination of movements to an external rhythmic auditory stimulus is a widespread biological phenomenon that occurs in non-human animals [1], as well as in humans from an early age [2], and possibly relates to vocal mimicry abilities [1,3]. Social groups frequently engage in activities which involve coordination of timing between group members. In many such activities, success depends on tightly synchronized timing. Engaging in coordinated timing activity has been shown to strengthen group cohesion [4]. For instance music performance, timing is an explicit goal of the activity [6]. In these examples, the question arises: how do participants in a group adjust their timing to each other? We propose a feedback correction model of timing in ensemble music performance. The model includes correction gain terms within each pair of players; we show that, on average, players approximate an optimum, defined as the minimal variance of asynchrony, albeit with notable exceptions that reflect on established musical practice
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