Coordination dynamics of multi-agent interaction in a musical ensemble

Abstract

Humans interact with other humans at a variety of timescales and in a variety of social contexts. We exhibit patterns of coordination that may differ depending on whether we are genuinely interacting as part of a coordinated group of individuals vs merely co-existing within the same physical space. Moreover, the local coordination dynamics of an interacting pair of individuals in an otherwise non-interacting group may spread, propagating change in the global coordination dynamics and interaction of an entire crowd. Dynamical systems analyses, such as Recurrence Quantification Analysis (RQA), can shed light on some of the underlying coordination dynamics of multi-agent human interaction. We used RQA to examine the coordination dynamics of a performance of "Welcome to the Imagination World", composed for wind orchestra. This performance enacts a real-life simulation of the transition from uncoordinated, non-interacting individuals to a coordinated, interacting multi-agent group. Unlike previous studies of social interaction in musical performance which rely on different aspects of video and/or acoustic data recorded from each individual, this project analyzes group-level coordination patterns solely from the group-level acoustic data of an audio recording of the performance. Recurrence and stability measures extracted from the audio recording increased when musicians coordinated as an interacting group. Variability in these measures also increased, indicating that the interacting ensemble of musicians were able to explore a greater variety of behavior than when they performed as non-interacting individuals. As an orchestrated (non-emergent) example of coordination, we believe these analyses provide an indication of approximate expected distributions for recurrence patterns that may be measurable before and after truly emergent coordination.

Figure 1

Time series and recurrence plots for the first and last 30 s of each Coordination Category (Uncoordinated or Coordinated). Darker segments of the recurrence plots indicate the presence of more recurrent data points. Vertical and horizontal lines indicate periods of stability in the system, where one state was visited for a period of up to a few seconds at a time. Note: 9 s of audience applause during the Introduction Performance Event were not analyzed, and are subsequently excluded from all data visualizations.

Figure 2

Time series and recurrence Plots for representative 5-s samples drawn from each 30-s sample in Fig. 1, and labeled as the associated Performance Event the 5-s sample is drawn from. Uncoordinated Aleatoric and Transition plots more closely resemble white noise, with fewer recurrent points, shorter diagonals, and less apparent vertical structures. Increased presence of diagonal lines and vertical structures in Coordinated Introduction and Finale plots indicate increasingly coordinated interaction among the musicians. Note: 9 s of audience applause during the Introduction Performance Event were not analyzed, and are subsequently excluded from all data visualizations.

Figure 3

Raincloud plots show higher levels, and wider variance, in each RQA metric in Coordinated compared to Uncoordinated Categories. Boxplots show sample median and interquartile range. Note: 9 s of audience applause during the Introduction Performance Event were not analyzed, and are subsequently excluded from all data visualizations.

Figure 4

Serial plots visualizing the trajectories of recurrence behaviors over time. (A) Coordinated Performance Events (Introduction and Finale) show increased recurrent points overall (Recurrence Rate) compared with Uncoordinated Performance Events (Aleatoric and Transition). (B) Emerging presence of longer sequences of behavior as represented by higher levels of Determinism, and (C) higher levels of Entropy in Coordinated Performance Events, indicating more variability in sequence length. (D) Increased values of Laminarity in Coordinated Performance Events indicate enhanced stability in the system. The intermittency of these stable periods in the Coordinated Performance Events as shown in the recurrence plots (Figs. 1 and 2) can also be seen in the varying high and low values of Laminarity over time in the serial plots. Note: 9 s of audience applause during the Introduction Performance Event were not analyzed, and are subsequently excluded from all data visualizations.