Quantifying Tightness - Looseness of Interactions with Dynamical Systems Methods A Comment on “Musical engagement as a duet of tight synchrony and loose interpretability” by T. C. Rabinowitch

In her paper, Rabinowitch [1] develops a theoretical framework to explain the power that music seems to have to harness the prosocial benefits of interpersonal synchrony while minimizing its negative effects (e.g., conformity and ingroup bias). She argues that this power comes from the simultaneous coexistence of elements that make musical interactions tight – a common rhythmic structure, for example – with elements that make musical interactions loose – such as its room for ambiguity and subjective interpretation. A similar analysis of coordination as the result of the tension between structure and individuality has been put forward to explain the self-organization of coordinated action in the theory of coordination dynamics [2,3]. Rooted in dynamical systems, the theory coordination dynamics provides an alternative and complementary framing to the conceptualization of tightness and looseness in Rabinowitch’s paper, which has its roots in social psychology.

In the theory of coordination dynamics, the “tightness” or “looseness” of a system of interacting elements (e.g., individuals performing music together, or groups of neurons) is conceptualized as the result of the dynamic interplay between two complementary tendencies of such elements: the tendency to express their own individual properties (e.g., a musician exploring new melodic or rhythmic opportunities as they improvise), and the tendency to respond to shared functional constraints and to each other, creating and maintaining collective patterns of coordination, also known as synergies (e.g., musicians adopting a common rhythm to perform a pleasant tune; 2,4,5). Intelligent systems at all scales and across many contexts (e.g., 6,7), from neurons in the brain (e.g., 5) to humans coordinating during musical interactions (e.g., 8), tend to be drawn to a sweet spot between these two states – strong collective structure and increased individuality – known as self-organized criticality [4,9]. This state affords the greatest degree of adaptability and structure for a system, making it easy to move in and out of synergies or collective patterns of coordination as the constraints and goals of behavior change [4]. When measured, the balance between these two complementary tendencies tends to show up in time series data as the presence of long-range correlations and recurrent patterns of behavior across time scales [7,10].

The conceptual tenets of coordination dynamics as applied to music-making and musical interactions have been productively explored in a recent paper by Schiavio, Maes, and Van der Schyff [11]. Beyond its conceptual applications, the theory of coordination dynamics also goes hand in hand with a variety of methods to quantify the structure of coordinated action from time series that capture repeated measures of a given aspect of a system’s behavior [11,12]. Previous studies of musical interactions and music-making have used, for example, methods like Recurrence Quantification Analyses (RQA, e.g., 8), Detrended Fluctuation Analysis (DFA, e.g., 13), Allan Factor analysis [10], and spectral analysis (e.g., 14,15); and have analyzed a variety of time series such as the amplitude of waveforms (e.g., 8,15), the amplitude or velocity of the movements of the hands or neck as individuals play music (e.g., 16,17), and even the duration of the intervals between the beats produced (e.g., 6,13). In general, these methods work best with longer time series (e.g., 3 - 5 minutes) so robust estimates can be obtained; can be applied to either separate recordings of each musician or to one joint recording of their interaction; and are fairly robust to noise. All these characteristics make these approaches useful for experimental and naturalistic datasets alike and enable comparisons across contexts traditionally classified as “musical” or “non-musical,” as well as along the continuum between these poles [6]

Dynamical systems methods can be a useful addition to test Rabinowitch’s hypotheses about the relationship between the tightness-looseness of interpersonal coordination and measures of tolerant group membership. These approaches offer Rabinowitch’s framework new analytic tools to not only manipulate the tightness-looseness experimentally, but also to directly measure the degree of structure across given musical and non-musical interactions to determine where these interactions fall on the tightness-looseness continuum. This could be particularly useful to extend Rabinowitch’s proposal to contexts in which it might be beneficial to measure natural changes in the tightness and looseness of social interactions as a result of the use of music, such as during early development when musical components are naturally embedded within social interactions (e.g., a caregiver flexibly transitioning between infant-directed song and speech to modulate their children’s social attention) and when music is used therapeutically in neurodiverse populations [18]. Doing so could shed light on another potential mechanism by which music facilitates and improves outcomes, including and extending beyond prosociality for many populations.