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.

Temporal coordination between members of a string quartet was investigated across repeated performances of an excerpt of Haydn’s string quartet in G Major, Op. 77 No. 1. Cross-correlations between interbeat intervals of performances at different lags showed a unidirectional dependence of Viola on Violin I, and of Violin I on Cello. Bidirectional dependence was observed for the relationships between Violin II and Cello and Violin II and Viola. Own-reported dependencies after the performances reflected these measured dependencies more closely than dependencies of players reported by the other players, which instead showed more typical leader–follower patterns in which Violin I leads. On the other hand, primary leadership from Violin I was observed in an analysis of the bow speed characteristics preceding the first tone onset. The anticipatory movement of Violin I set the tempo of the excerpt. Taken together the results show a more complex and differentiated pattern of dependencies than expected from a traditional role division of leadership suggesting several avenues for further research.

Timing variation in small group musical performance results from intentional, expressive, and unintentional, error components in individual player timing. These timing fluctuations produce variability in between-player note asynchrony and require timing adjustments to keep the ensemble together. The size of the adjustments relative to the asynchrony (correction gain) affects the amount and nature of asynchrony variability. We present new listening tests to estimate thresholds for perception of between-player asynchrony variability and to determine whether listeners use differences in the nature of the variability, as well as in its magnitude, to judge asynchrony. In two experiments, computer-simulated ensemble performances of a 48-note excerpt from Haydn Op. 74 No. 1 were generated. Between-player note asynchrony was systematically manipulated in terms of level of within-player timing variability (Experiment 1) and correction gain (Experiment 2). On each trial, participants listened to two samples, one (“target”) with more between-player asynchrony variability than the other (“test”), and reported which was “less together.” In both experiments, the test sample correction gain was fixed at the statistically optimal value of 0.25 and the within-player timing variability was minimal (zero except for random variability in the initial note). In Experiment 1 the target correction gain was fixed at 0.25 and the timing variability was adjusted over trials by a staircase algorithm designed to converge on the level of asynchrony variability giving 75% correct identification. In Experiment 2 the timing variability in the target was set at half that in Experiment 1 and the correction gain was varied to converge on 75% correct identification. Our results show that the between-player asynchrony variability giving 75% correct identification in Experiment 2 was significantly lower than in Experiment 1. This finding indicates that people are sensitive to both the degree of variance and the micro-structure of the time-series of the asynchronies caused by differences in correction gain when judging lack of togetherness in quartet performance.