In a musical ensemble such as a string quartet, the musicians interact and influence each other's actions in several aspects of the performance simultaneously in order to achieve a common aesthetic goal. In this article, we present and evaluate a computational approach for measuring the degree to which these interactions exist in a given performance. We recorded a number of string quartet exercises under two experimental conditions (solo and ensemble), acquiring both audio and bowing motion data. Numerical features in the form of time series were extracted from the data as performance descriptors representative of four distinct dimensions of the performance: Intonation, Dynamics, Timbre, and Tempo. Four different interdependence estimation methods (two linear and two nonlinear) were applied to the extracted features in order to assess the overall level of interdependence between the four musicians. The obtained results suggest that it is possible to correctly discriminate between the two experimental conditions by quantifying interdependence between the musicians in each of the studied performance dimensions; the nonlinear methods appear to perform best for most of the numerical features tested. Moreover, by using the solo recordings as a reference to which the ensemble recordings are contrasted, it is feasible to compare the amount of interdependence that is established between the musicians in a given performance dimension across all exercises, and relate the results to the underlying goal of the exercise. We discuss our findings in the context of ensemble performance research, the current limitations of our approach, and the ways in which it can be expanded and consolidated.

This work was partially supported by the EU FP7 FET-Open SIEMPRE Project no. FP7-ICT-2009-C-250026, the Catalan Research Funding Agency AGAUR, Beatriu de Pinos Grant 2010 BP-A 00209, and FP7 Marie Curie Grant no. PIOF-GA-2012-331270. We would like to thank Erika Donald and Marcelo Wanderley, as well as Carolina Brum Medeiros, Vincent Freour, and Marcello Giordano for the support in organizing the experiment, and the CIRMMT and BRAMS labs at Montreal, Quebec, Canada for hosting them. Finally, we would like to thank the reviewers for their thoughtful comments as well as for pointing out errors/omissions in the manuscript.