Body sway reflects leadership in joint music performance

Abstract

The cultural and technological achievements of the human species depend on complex social interactions. Nonverbal interpersonal coordination, or joint action, is a crucial element of social interaction, but the dynamics of nonverbal information flow among people are not well understood. We used joint music making in string quartets, a complex, naturalistic nonverbal behavior, as a model system. Using motion capture, we recorded body sway simultaneously in four musicians, which reflected real-time interpersonal information sharing. We used Granger causality to analyze predictive relationships among the motion time series of the players to determine the magnitude and direction of information flow among the players. We experimentally manipulated which musician was the leader (followers were not informed who was leading) and whether they could see each other, to investigate how these variables affect information flow. We found that assigned leaders exerted significantly greater influence on others and were less influenced by others compared with followers. This effect was present, whether or not they could see each other, but was enhanced with visual information, indicating that visual as well as auditory information is used in musical coordination. Importantly, performers' ratings of the "goodness" of their performances were positively correlated with the overall degree of body sway coupling, indicating that communication through body sway reflects perceived performance success. These results confirm that information sharing in a nonverbal joint action task occurs through both auditory and visual cues and that the dynamics of information flow are affected by changing group relationships.

Keywords: Granger causality; body sway; joint action; leadership; music performance.

Fig. 1.

Illustrations of the experimental design and Granger causality analyses. (A) Top-down view of the locations of performers on stage. (B) Example excerpt of recorded anterior–posterior body sway motion time series in four performers from the middle of a trial. The Granger causality (GC) of the body sway of violin 1 directionally coupling to (or predicting) violin 2, for example, was calculated by taking the log-likelihood ratio of the degree to which the prior body sway time series of violin 1 (predictor 1, shaded in light blue) contributes to predicting the current status of violin 2 (red dot), over and above the degree to which it is predicted by its own prior time series (predictor 2, shaded in light yellow), while conditional on the prior time series of the other performers (predictors 3 and 4, shaded in gray). This calculation was repeated along the entire time axis to estimate GC. The length of the predictor window (shaded areas) was determined by the model order. The algorithm is conceptually expressed by the equation shown (see ref. for mathematical details). (C) Categorization of the 12 directional relationship pairs between the four performers into three Paired-Roles. We calculated the GCs of directional body sway couplings (using the formula outlined in B) for all 12 directional pairs of performers (shown as arrows) in each quartet as shown on the left. For Single-Leader-Role trials, the 12 GCs were then categorized according to whether the Paired-Role was leader-to-follower (LF), follower-to-leader (FL), or follower-to-follower (FF). For example, if violin 2 was assigned as the single leader while the others were followers in a trial, the arrows (blue) coming out from violin 2 were categorized as LF, the arrows (red) pointing at violin 2 as FL, and the other arrows (green) as FF. For Ambiguous-Role trials, all 12 GCs were categorized as either all leaders (L-all) or all followers (F-all) (not shown in the figure). We treated the 12 unique directional pairs in a quartet on each trial as 12 unique samples for repeated-measures statistical analyses.

Fig. 2.

GC of interpersonal body sway couplings. Comparisons are marked as *P < 0.05, **P < 0.01, ***P < 0.001. Error bars represent SE. (A and B) GCs of Single-Leader-Role trials are presented in (A) for quartet 1 and (B) for quartet 2. Both experiments showed a significant interaction between Paired-Role and Vision. Specifically, the LF (leader-to-follower) coupling was higher than both FL (follower-to-leader) and FF (follower-to-follower) couplings when performers could see each other, but this effect was attenuated when performers could not see each other. Also, the GC of LF coupling was higher when performers could see each other than when they could not. These results show that GC reflects leader–follower relationships, and seeing or not seeing others specifically mediates the FL coupling. (C and D) GC scores at the beginnings and ends of Ambiguous-Role trials are presented in (C) for quartet 1 and (D) for quartet 2. In quartet 1 (Baroque music), there was a significant three-way interaction (Time × Role × Vision). Specifically, GC increased from the first 30 s to the last 30 s of pieces performed when all performers were assigned as followers and they could see each other. The same analyses on quartet 2 (Classical music) did not show any significant effects.

Fig. 3.

Correlations between subjective ratings and group body sway couplings. (A, C, and E) Scatter plots of the results of quartet 1. (B, D, and F) Scatter plots of the results of quartet 2. On each trial, each performer subjectively rated the levels of goodness of performance (A and B), temporal synchronization (C and D), and ease of coordination (E and F), with five-point Likert scales, and we calculated the mean rating across the performers for each of these three aspects for each trial. To represent the group causal density (44) of body sway, we calculated the mean of the 12 GCs reflecting the pairwise influences for each trial, which reflects the overall causal interactivity sustained in a quartet. The Spearman rank correlation tests on all trials (n = 24) showed that the group body sway coupling was positively correlated with goodness of performance level in both experiments and also positively correlated with temporal synchronization level in quartet 1 but not in quartet 2.

Fig. S1.

The baseline-GC of each performer without regard to leadership role is presented in (A) for playing Baroque music in quartet 1 and (B) for playing Classical music in quartet 2. The greater difference across instruments for quartet 2 compared with quartet 1 likely reflects the different musical styles of the pieces played by the two quartets, with the quartet playing Baroque music having intrinsically more equal parts across instruments compared with the quartet playing Classical music, in which one of the violins tends to have the melody at a particular point in time. Thus, this difference likely indicates that the musical structure of the pieces plays a role in social leadership interactions in addition to effects of assigned leadership role. Significant comparisons are marked as *P < 0.05, **P < 0.01. Error bars represent SE.

Fig. S2.

Mean body sway temporal asynchrony of leader preceding follower, as identified by the maximum unsigned cross-correlation coefficient. The y axis reflects the maximum cross-correlation, with scores above 0 indicating that the leader preceded the follower and scores below 0 indicating that the follower preceded the leader in time. Error bars represent SE. The t tests revealed that in no condition in any quartet was the mean asynchrony significantly different from 0, nor was the asynchrony significantly different between Seeing and Nonseeing conditions in either quartet. These results suggested that the cross-correlational analysis was not powerful enough to reveal leading–following relationships, as was revealed by our Granger causality analysis.