Humans are social animals who engage in a variety of collective activities requiring coordinated joint action. Collective goals can be achieved through spontaneously distributed workloads among group members, such that the emerging collective dynamics confer benefits to performance not available to individuals—the ‘wisdom of crowds’ (Galton, 1907; Surowiecki, 2005).

Principles of collective dynamics explain the adaptive value of collective behavior in some species (Couzin, 2018). For example, collective dynamics can overcome the limitations of individuals’ knowledge and ability to communicate (Goldstone and Roberts, 2006) by integrating information quickly during group decision making (Ispolatov, 2015; Miller et al., 2013; Rosenthal et al., 2015). Large coherent swarming and flocking in groups can arise from short-range interactions among proximal individuals in non-human animals including primates (Farine et al., 2017), insects (Jacobs et al., 2007), fish, and birds (Miller et al., 2013; Parrish et al., 2002). As such dynamics have been demonstrated in numerous species, theoretical models have been developed to provide additional quantitative explanatory support. In contrast, in spatial tasks such as navigation, aggregate group behavior, formalized as a mean field, can serve to stabilize feedback to individuals by virtue of being a group average (Berdahl et al., 2018; Sumpter, 2006; Torney et al., 2009). Here, we test whether mean field behavior accounts for stability of temporal group dynamics in humans during a drumming task.

Collective dynamics are observable in animal as well as in human group behavior. Crowds of walking individuals achieve globally coherent states based on local inter-individual interactions (Rio et al., 2018; Warren, 2018). In audiences, individual-group interactions and social contagion govern the spontaneous onset and offset of applause (Mann et al., 2013). Collective dynamics can also play a constitutive role in sports by permitting advantages not available to individuals alone (Vilar et al., 2013). Evidence of collective dynamics is seen even in the minimal group, a dyad: spontaneous synchronization between two individuals emerges from constraints such as weak coupling (Oullier et al., 2008; Schmidt et al., 1990; Schmidt and O’Brien, 1997).

Synchronized group action is an essential element of music making, a defining social behavior of human interaction (Honing et al., 2015; Patel and Iversen, 2014; Salimpoor et al., 2011; Savage et al., 2015; Trainor, 2015), and the value of precise synchronization may vary from culture to culture and across musical contexts (Benadon et al., 2018; Davies et al., 2013; Lucas et al., 2011).The archaeological evidence of musical instruments goes back 30,000 years, and singing and drumming are thought to be even older (Conard et al., 2009). The evolutionary origins of musical rhythmic actions may relate to social motor behaviors in non-human species, such as the synchronization and desynchronization of vocalizations between individuals in group chorusing, arising from pressures to either collaborate or compete (Gamba et al., 2016; Greenfield et al., 2017; Ravignani et al., 2014; Ravignani et al., 2019). Fundamental aspects of music are present in humans from early stages in development: infants show early musical preferences, social-emotional responses to music, and rate-sensitive motoric responses to musical rhythm (Cirelli et al., 2014; Cirelli et al., 2018; Trainor and Marsh-Rollo, 2019; Zentner and Eerola, 2010). Although musical behavior is found in individuals alone, it occurs mainly in groups ranging from duets to hundreds of participants. Yet, the role of collective dynamics, especially in groups larger than dyads, has largely remained untested. Here, we consider a musical task in which timing consistency and synchrony are crucial. We investigate in what ways the group average performs better than the individuals, a temporal version of the wisdom of the crowd phenomenon.

To account for group interaction, one popular strategy is to first develop a theory for single-person tasks and then extrapolate into dyadic contexts. For example, the idea that the brain is a prediction machine that enables timely motor control in an uncertain environment can be extrapolated as two brains mutually predicting each other (Friston and Frith, 2015; Wolpert et al., 2003). This means that each individual instantiates two processes: the first for controlling one’s own rhythm and timing and the second for predicting the rhythm and timing of the partner in the dyad (Heggli et al., 2019; Heggli et al., 2021; Keller et al., 2014; van der Steen and Keller, 2013). It is not clear, however, if this can serve as an adequate foundation for behavior in larger groups. Every individual would have to predict every other individual and potentially factor-in higher-order predictions. Furthermore, at the perceptual level, group size changes the auditory information available to an individual. A listener is likely to hear an entire choir as one, or a small number of, coherent sounds rather than perceive every singer’s voice within that choir.

Group interaction can also be addressed in terms of theoretical models explicitly developed for synchronization in systems made of many dynamic units (Alderisio et al., 2016; Oullier et al., 2008; Schmidt et al., 1990; Schmidt and O’Brien, 1997). The individual units in such models usually do not contain processes dedicated separately to self-timing and other-predicting. Instead, each unit has only a self-timing and a phase-correction coupling term. The propagation of phase adjustment across all units is sufficient for the collective to enter a group-synchronized state, despite that each unit is only trying to cancel a phase difference. An important benefit of this approach is that it is inherently collective, converging on the same formalisms used for small or large groups of animals (Kelso, 2021; Zhang et al., 2019). Here, we consider such a system of coupled oscillators to account for empirical data on individual and group variability in a drumming task.

Group music making constitutes an ecologically valid and convenient paradigm for studying group action and collective experience in the laboratory (e.g. D’Ausilio et al., 2015). We used a timing task performed by groups of different sizes. Larger group dynamics are less studied because measuring highly precise timing while collecting group data is difficult for both logistical and methodological reasons (cf. Alderisio et al., 2016; Chang et al., 2017; Chang et al., 2019; Chauvigné et al., 2019; Shahal et al., 2020). Participants completed a group synchronization-continuation task (SCT; Figure 1A). It required them to drum in synchrony with an isochronous auditory stimulus and continue drumming at the same rate after the stimulus stopped, while we collected the onset times of each drum hit (Figure 1B). Stimulus tempo was varied across trials. We tested groups of two (dyads), four (quartets), and eight (octets) participants (Figure 1C). The task tested participants’ ability to synchronize to an external reference as well as to other participants, while also minimizing temporal variability and maintaining the initial stimulus rate. This ensemble drumming was also compared against the solo condition. Specifically, participants tested in duets or quartets completed both solo and ensemble conditions. The octet group did not complete the solo conditions for logistical reasons, but they instead completed a control condition in which the synchronization phase continued for the whole trial (i.e. there was no continuation phase) as well as trials using a more complex and musically realistic rhythm. Analyses of the more complex rhythm will be reported separately.

Figure 1

Download asset Open asset

Inspired by theoretical models from the animal literature (Sumpter, 2006), we assumed that individual interactions average to overall group behavior, a mean field, which provides stabilizing feedback to individual group members (Figure 2). A key prediction was that the relative influence of the stabilizing feedback would increase with increasing ensemble size. To this end, we measured separately the variability of individual drummers and the group. We constructed a theoretical group-aggregate onset time as the center of clusters of individual onset times. We expected that larger groups would exhibit lower variability as measured using the coefficient of variation of inter-onset intervals. We also tested this idea formally by adapting a Kuramoto model of group synchronization.

Figure 2 with 1 supplement see all

Download asset Open asset

The (Kuramoto, 1975) dynamic system of coupled phase oscillators, Equation 1, was conceptualized as a large population of oscillators with different natural frequencies capable of spontaneously locking to a common frequency.

Here, θ_i is the phase of oscillator i, ω_i is its preferred frequency, i.e., how fast around the unit circle it likes to go, K is coupling strength, and N is the number of oscillators.

The model gives a mathematical account of group synchronization as dependent on a mean field, referred to here as group aggregate. A central feature of the model is that the feedback is positive: the amplitude of the mean field grows as a function of inter-individual synchronization, and reciprocally, the individual oscillators are affected more by the mean field if its amplitude is larger, see Figure 2. This is shown by using the definition of the mean of phases, Equation 2, to express Equation 1 equivalently (Strogatz, 2000) in terms of the coupling between individual oscillators and the mean field, Equation 3. ${\displaystyle \mathrm{\Psi }}$ is the mean field phase, and r is the mean field coherence, also called order parameter (Kuramoto, 1975).

Such individual-collective positive feedback loops enable ant trails and other phenomena in swarming animals (Sumpter, 2006) as well as acoustic herding in chorusing animals (Ravignani et al., 2014). The system also serves as a model for neuronal collective synchronization (Breakspear et al., 2010; Frank et al., 2000; Noori et al., 2020). Theoretically, the principles embodied by this system should apply to group action in humans too (Zhang et al., 2019). It has found application in understanding inter-personal synchronization of dyads (Dotov et al., 2019; Heggli et al., 2019; Roman et al., 2019), individual rate preferences in the dyad (Bégel et al., 2022), and effects of coupling topology in larger groups (Alderisio et al., 2016). In the present context, the model predicts that ensembles will be more stable than individuals because of the feedback loop between the timing of individuals and the group aggregate of individuals.

The original Kuramoto model involves continuous dynamics and continuous coupling with constant gain and no delay. In a drumming task, participants are coupled by way of discrete acoustic onset times. Here, we propose a hybrid continuous-discrete system of oscillators with event-based feedback updated once per cycle, Equation 4. It utilizes a pulse function shaped like the acoustic envelope of a drum hit. To this end, Equation 5 specifies an asymmetric gamma distribution that rises sharply at time 0 and then decays slowly (Figure 2—figure supplement 1). In the model, an oscillator emits a pulse once per cycle when its phase angle crosses zero. Furthermore, we posit additive phase variability with a Gaussian distribution ${\displaystyle N\left(0,\sigma \right)}$.

Like the original system, this model involves intrinsic dynamics (ω_i) and interaction dynamics given by the whole coupling term. For comparison, we tested two additional models: the classic Kuramoto system with constant full coupling, Equation 1, as well as the hybrid continuous-discrete model, Equations 4; 5, with a sparse coupling matrix in a ring topology. Specifically, the individual units were only coupled to their two immediate neighbors, $j=i\pm 1$, with a periodic boundary condition, ${\theta }_{N+1}={\theta }_1$ and ${\theta }_0={\theta }_N$ .

In Performance, Dynamics and coordination in ensemble, SCT conditions, and Group dynamics, we present the analyses of the participants’ drumming behavior. In Variability in the mean-field model with discretely updated feedback, we present the results from our adapted hybrid model consisting of a continuous-discrete system of oscillators with pulse-based feedback updated once per cycle.

Performance

Variability

Does individual variability increase in ensemble compared to solo conditions?

To answer this question, we fitted a model including only individuals’ data in dyads and quartets (octets did not complete solo conditions). As Figure 3A shows, individuals’ variability increased when playing in an ensemble relative to playing solo (β=0.009, SE=0.001, t=6.65, and ω²=0.10).

Figure 3 with 2 supplements see all

Download asset Open asset

Figure 3—source data 1

https://cdn.elifesciences.org/articles/74816/elife-74816-fig3-data1-v2.xlsx

Download elife-74816-fig3-data1-v2.xlsx

In the context of true ensemble playing, how does variability of the individuals and group aggregate change across dyads, quartets, and octets?

To specifically test the main hypothesis, we fitted a model to continuation (SCT) trials from all three group sizes in the ensemble playing condition. We found that individual variability increased with group size (β=0.001, SE=0.0005, t=2.20, and ω²=0.09), group-aggregate variability was lower than individual variability (β=−0.010, SE=0.003, t=−3.29, and ω²=0.01), and the difference between individual and group-aggregate variability increased for larger group sizes (β=−0.0025, SE=0.0005, t=−5.19, and ω²=0.03), see Figure 3A. As a sanity check, we verified that the procedure for group-aggregate onset times did not lead to spuriously periodic data. We observed very high variability for the pseudo-group-aggregate in solo condition where individuals did not hear each other, see Figure 3—figure supplement 1A.

How does variability compare between continuation and synchronization?

The octet group completed trials in conditions of both SCT (i.e. after the offset of the reference metronome) and synchronization-only (with a constant reference metronome). Surprisingly, there were no differences between these conditions either in individual (t<1) or in group-aggregate variability (t<1).

Speeding up

Do individuals speed up more when playing solo than in dyad or quartet ensembles?

Speeding up was defined as the linear increase in tempo (i.e. decrease of IOIs) over the course of a trial. As expected, individuals sped up even when playing solo (β=0.018, SE=0.007, t=2.67, and ω²=0.10), and greater speeding up was observed in ensemble than in solo conditions (β=0.022, SE=0.007, t=3.29, and ω²=0.16). The effect of group size was not significant (t<1).

Do dyad, quartet, and octet ensembles speed up to different extents?

To test the effect of group size across the duets, quartets, and octets, a second model was fitted with group size as a continuous predictor, but only including trials in SCT ensemble playing. As suggested by Figure 4, there was a trend for speeding up to decrease as group size increased. The best linear model included an effect of tempo (β=−0.001, SE=0.00005, t=−1.98, and ω²=0.005) and an interaction between group size and tempo (β=−.00004, SE=0.000007, t=−6.20, and ω²=0.11), reflecting that at higher tempos larger ensembles sped up less than smaller ensembles, see Figure 4—figure supplement 1.

Figure 4 with 1 supplement see all

Download asset Open asset

Figure 4—source data 1

https://cdn.elifesciences.org/articles/74816/elife-74816-fig4-data1-v2.xlsx

Download elife-74816-fig4-data1-v2.xlsx

Dynamics and coordination in ensemble, SCT conditions

Individual and group-aggregate dynamics (autocorrelations)

Individuals

Figure 5A shows that individuals’ autocorrelations at lag 1 were negative across all group sizes and tempos. This is typical for the alternating long-short IOIs seen in synchronization tasks, reflecting alternating fast-slow synchronization errors when adapting to the previous interval. There was also a trend across all group sizes and tempo conditions for positive peaks at even lags (2, 4, 6, and 8) and negative peaks at odd lags (3, 5, and 7), see Figure 5—figure supplement 1. However, this general pattern became smoother with increasing group size. To test this statistically, in each trial, we took the average absolute difference between successive lags, thus measuring the average range of the autocorrelation function up to lag 8 and applied the same linear modeling approach as in Performance. The effect of group size was significant (β=−0.0054, SE=0.0023, t=−2.35, and ω²=0.13). There was also a decrease of range with increasing tempo (β=−0.00039, SE=0.0001, t=−4.92, and ω²=0.04). Additionally, we verified the signs, relative magnitudes, and the effects of group size and tempo on the autocorrelations by fitting separate linear models for each lag, see Supplementary file 1a.

Figure 5 with 1 supplement see all

Download asset Open asset

Figure 5—source data 1

https://cdn.elifesciences.org/articles/74816/elife-74816-fig5-data1-v2.xlsx

Download elife-74816-fig5-data1-v2.xlsx

Group-aggregate

Interestingly, group-aggregate IOIs revealed the same overall pattern of results even though by definition the group-aggregate timing was smoother and less variable (see Group-aggregate (mean field) measure for ensembles and pseudo-ensembles), see Figure 5B and Supplementary file 1b. There was a trend across all group sizes for relative positive peaks at even lags 2, 4, 6, and 8 and relative negative peaks at odd numbered lags 1, 3, 5, and 7. The similarity of the dynamics of individuals and the group aggregate is not trivial because it implies that even groups of up to eight participants spontaneously acquire the alternating long-short interval dynamics characteristic of when individual participants synchronize with a stimulus.

Inter-personal coordination (cross-correlations)

Cross-correlation applied to the pre-processed IOIs assessed inter-personal coordination between pairs of participants drumming together in the continuation phase of ensemble performances. On rare occasions, individuals produced diverging beat times by, for example, missing the drum or hitting it two times. The resulting outlier IOIs were removed, and the remaining were re-aligned relative to the other participants by temporal adjacency. The last pre-processing step consisted of whitening each time-series of IOIs (see From beat onset times to IOIs, outlier removal, and clustering–Pre-whitening).

We analyzed lags in the range 0–4 because cross-correlation coefficients tended to be symmetric between positive and negative lags, see Figure 6. As expected, cross-correlations at lag 0 were negative in duets (β=−0.039, SE=0.011, t=−3.60, and ω²=0.04), consistent with the pattern of results for autocorrelations, and inter-personal coordination dynamics were smoother in larger group sizes. Furthermore, lag 0 cross-correlations became less negative with increasing group size (β=0.012, SE=0.002, t=5.93, and ω²=0.13). Lag 1 cross-correlations were positive (β=0.14, SE=0.012, t=11.80, and ω²=0.32), but their magnitude decreased with group size (β=−0.016, SE=0.002, t=−7.14, and ω²=0.20). There were also effects of tempo, see Figure 6—figure supplement 1.

Figure 6 with 1 supplement see all

Download asset Open asset

Figure 6—source data 1

https://cdn.elifesciences.org/articles/74816/elife-74816-fig6-data1-v2.xlsx

Download elife-74816-fig6-data1-v2.xlsx

Group dynamics

Network analysis

We used network analysis in the continuation phase of trials of ensemble playing to describe group coordination at an even higher level of organization than interpersonal coordination. First, we obtained the directed graphs of functional connectivity among participant drummers. In each trial, the graph consisted of the real-valued directed links between pairs of drummers estimated by way of the transfer entropy (TE), see Figure 1C. Then, network properties of these graphs were computed, see Network analysis. There was a significant effect of group size on causal density (β=−0.0006, SE=0.0001, t=−5.88, and ω²=0.47), see Figure 7A. Causal density increased with tempo (β=0.008, SE=0.0019, t=4.01, and ω²=0.12). As Figure 7B shows, mean node strength increased with group size (β=0.0032, SE=0.00032, t=10.13, and ω²=0.73). Node strength was affected by tempo (β=0.016, SE=0.005, t=2.96, and ω²=0.07). For better model conditioning, tempos values were reduced and compressed by transforming them with a logistic function. Comparing between SCT trials and synchronization-only trials in the octet group found no difference for causal density (t<1) or mean node strength (t<1), suggesting group dynamics were similar regardless of whether a pacing stimulus was present or not.

Figure 7 with 2 supplements see all

Download asset Open asset

Figure 7—source data 1

https://cdn.elifesciences.org/articles/74816/elife-74816-fig7-data1-v2.xlsx

Download elife-74816-fig7-data1-v2.xlsx

Network properties and task performance

The relation between group dynamics and group performance was evaluated by regressing the network properties separately with respect to speeding up and IOI variability in ensemble playing. Speeding up decreased with increasing causal density (β=−0.005, SE=0.002, t=−2.22, and ω²=0.02) and was not associated with node strength (β=−0.01, SE=0.007, and t=−1.66), see Figure 7—figure supplement 1A–B. Variability was not associated with causal density (β=−.003, SE=0.0017, and t=−1.97) but decreased with increasing node strength (β=−0.007, SE=0.0019, t=−4.01, and ω²=0.09), see Figure 7—figure supplement 1C–D. Interestingly, we also observed that TE tended to be higher in trials that deviated less from the stimulus tempo, see Figure 7—figure supplement 2.

The present study examined how group performance in a synchronization timing task depends on group size and interactions among group members. Our overall hypothesis was that the mean field would influence individuals in a group, thereby stabilizing group performance. We expected that larger groups would exhibit more stable performance due to a more stable mean field. This hypothesis was motivated by the collective dynamics that allow animals with limited capacity for interacting with each other to achieve mutual goals by exploiting processes such as positive collective feedback and wisdom of crowds (Sumpter, 2006). As expected, we observed that temporal variability in group drumming decreased with group size. This occurred only at the level of the ensemble or mean field when the group was taken as a single entity. The effect was reversed for individual participants; their variability increased from solo to group playing conditions and with group size. We showed that this result agrees with a collective dynamics framework based on an adapted Kuramoto model. The model is consistent with the idea from theoretical biology that self-organizing systems can successfully coordinate with an external constraint by reducing their disorder at the macro-level at the expense of increasing their micro-level disorder (Kugler and Turvey, 1987; Prokopenko et al., 2014) and that medium-sized groups exhibit commonalities with principles of organization found both in two-unit and large collectives (Kelso, 2021; Zhang et al., 2019). Our theory is related to the Vicsek model, an influential account of collective animal behavior which explains the spontaneous coherent heading direction arising in collective animal movement, also in human crowds, in terms of local interactions of attraction and repulsion (Silverberg et al., 2013; Vicsek et al., 1995). The Vicsek model also relies on individual coupling with the average of a group, with the important difference that only a small radius of neighbors defines the interaction field, called a local order parameter (Chaté et al., 2008).

The continuous-discrete Kuramoto system introduced here included fluctuating intrinsic frequencies and event-based feedback. Consistent with the discrete nature of time asynchronies in a drumming task, the model used a pulse function instead of continuous coupling. The implications of this idea reach beyond the topic of the present study. The combination of continuous movement and discrete sensory sampling of the environment is a frequently observed scenario; in the present study, participants used the discrete auditory feedback of drum taps to inform their continuous movements leading up to future drum taps. Our task reduced the opportunity of visual coupling but did not eliminate it completely, leaving the possibility that group drumming involved both discrete and continuous feedback such as visual information about continuous arm, hand, and drumstick movements related to the timing of individual drumming sounds. Future studies should address whether visual feedback during group drumming is informative, as well as explore how that visual information is captured within the individual and collective dynamics of the system.

Interestingly, in the octet group, individual variability was similar in both the synchronization-only condition, where the metronome pacing stimulus was present, and in the self-paced continuation stage of the SCT trials, where no pacing stimulus was present. This result implies that, although tempo accuracy and drift were superior when the pacing stimulus was present, the stability of group timing in a group of eight participants may hit a ceiling, where performance becomes as stable as with a pacing stimulus.

Individuals’ tempos tended to increase in solo trials, and as expected, this effect was amplified (i.e. speeding up was greater) when trying to stay synchronized with other participants (Okano et al., 2017). Surprisingly, the amount of speeding up was not higher for larger groups of drummers, and it was even reduced for larger groups, at least at faster tempos. In contrast, accounts based on mutual prediction imply more speeding up for larger groups (Thomson et al., 2018; Wolf et al., 2019). This discrepancy highlights the importance of testing tempo drift with specific task constraints and avoiding hasty generalizations from smaller to larger groups. Indeed, tempo can also slowdown in some circumstances. This was observed, for example, in a group synchronization task when participants synchronized their oscillations using swung pendulums, a task involving continuous visual coupling rather than discrete acoustic event coupling (Bardy et al., 2020).

Having summarized task performance in terms of consistency and accuracy, we next considered drumming dynamics. Individuals’ autocorrelations exhibited negative coefficient peaks at odd lags and positive coefficient peaks at even lags. This is the typical error-correction process demonstrated when individuals synchronize their tapping with a stimulus or with each other in pairs (Konvalinka et al., 2010; Repp, 2005). With increasing group size, however, the magnitudes of the autocorrelation coefficient fluctuations with lag decreased; individuals’ alternating patterns became smoother. This suggests that as group size increases, drumming dynamics are dominated less by tap-by-tap error-correction and more by a group dynamic. Interestingly, the group-aggregate onsets exhibited the same autocorrelation pattern as individuals, even in octets. This implies that the collective mean field behavior spontaneously acquired some of the dynamic properties typically associated with individual performance.

Inter-personal coordination in duets exhibited the negative cross-correlation at lag 0 and positive cross-correlation at lag 1 expected from past studies (Repp, 2005). The results for speeding up, variability, and cross-correlations in the dyads were consistent with the literature on dyadic interaction with tapping tasks. Yet, as group size increased in the present study, the coefficient magnitudes for cross-correlations decreased. In fact, they all but disappeared for groups of eight, suggestive of a leader-less group coordination scenario (Heggli et al., 2019). In a small number of trials, we even observed positive lag 0 cross-correlations in groups of eight, a signature of anticipation emerging from dynamic interaction. This result is consistent with the idea that group members coordinated less with each other and more with the mean field. Along with a more slowly decaying autocorrelation function, this suggests the emergence of a larger-scale group dynamic in the octet. As we hypothesized, mutual prediction is not necessarily the only basis for coordination in larger groups. The present model would be more like a predictive account had we included a new variable and an additional equation in the model, ${\dot{\theta }}_{j,i}=f({\theta }_i,{\theta }_j,{\theta }_{j,i})$, corresponding to a separate internal oscillatory process ${\theta }_{j,i}$ that individual i dedicates to the prediction of an external signal j. Yet, there is no reason to assume that collective dynamics and mutual prediction are exclusive alternatives, only that collective dynamics are a mode of social interaction that emerges under certain constraints such as large groups of interacting agents.

Characterizing inter-personal interaction on the basis of bivariate measures is typical in the context of dyadic paradigms. Larger groups, however, create the possibility for higher-order interactions. Network analysis was applied to the connectivity graph of TEs among drummers. Larger groups had lower causal density but higher node strength. This is possible because individual nodes in larger groups project to a larger number of other individual nodes and suggests that in larger groups, each individual has a decreased influence on the group, both less potential to destabilize the group and lower requirements to keep the group stable. We also found that higher node strength was associated with better overall performance, both in terms of variability and tempo accuracy.

Group timing tasks address some of the foundations of human social interaction. This area of research has been labeled the ‘dark matter’ of social neuroscience (Dumas et al., 2014; Insel, 2010; Schilbach et al., 2013) because it has not received enough attention despite the fact that large parts of the human cortex respond to social stimuli (Frith and Frith, 2001). The temporal regularities in music make it an ideal stimulus to promote synchronous and cooperative movement, providing evidence as to why music is often present at emotional social gatherings such as weddings, funerals, parties, and political rallies. Feelings of affiliation and cooperation increase between people who have experienced synchronous movement with each other, even during infancy (Cirelli et al., 2014; Cirelli et al., 2016; Hove and Risen, 2009; Mogan et al., 2017; Trainor and Cirelli, 2015; Valdesolo et al., 2010). The ability of music to strengthen social bonds within a group may have evolutionary roots that enhance survival capabilities of the group (Huron, 2001; Savage et al., 2020; Trainor, 2015). Arguably, the presence of a convergent regular rhythm defined over the ensemble allows individuals of varying skill level to perform together without having to predict each note they play, an idea that remained largely untested in the present study because of the relative simplicity of the isochronous stimulus.

Participants in group activities sometimes report a so-called state of flow characterized by absorption, loss of sense of control, loss of self-consciousness, togetherness, and effortless action toward a shared goal (Csikszentmihalyi, 1990; Gaggioli et al., 2017; Hart et al., 2014). Little is known about the underlying group processes that enable such experiences. Some of the required conditions have been studied in the context of group musical performance (Bishop et al., 2019; D’Amario et al., 2018). Collective intentionality is often seen as an extrapolation of single-person cognitive processes in that individuals predict other individuals’ goals and actions (Tomasello, 2000, Tomasello, 2014). Yet, the neural and cognitive mechanisms historically identified in single-person paradigms do not always map onto the ontology of social behavior (Przyrembel et al., 2012). Collective intentionality can stand for an independent mode of social cognition (Satne and Salice, 2018; Zahavi and Satne, 2015). Social cognition theory can even be turned upside-down by observing cases where individual agency arises from social interaction (De Jaegher and Froese, 2009; Froese et al., 2014). The present work shows how collective dynamics can absorb individual action.

The current manuscript is a computational study, so no data have been generated for this manuscript.

1. 1. Alderisio F
   2. Bardy BG
   3. di Bernardo M

   (2016) Entrainment and synchronization in networks of rayleigh-van der pol oscillators with diffusive and haken-kelso-bunz couplings

   Biol Cybern 110:151–169.

   https://doi.org/10.1007/s00422-016-0685-7

   • PubMed
   • Google Scholar
2. 1. Bardy BG
   2. Calabrese C
   3. De Lellis P
   4. Bourgeaud S
   5. Colomer C
   6. Pla S
   7. di Bernardo M

   (2020) Moving in unison after perceptual interruption

   Scientific Reports 10:1–13.

   https://doi.org/10.1038/s41598-020-74914-z

   • PubMed
   • Google Scholar
3. 1. Barrat A
   2. Barthélemy M
   3. Pastor-Satorras R
   4. Vespignani A

   (2004) The architecture of complex weighted networks

   PNAS 101:3747–3752.

   https://doi.org/10.1073/pnas.0400087101

   • PubMed
   • Google Scholar
4. 1. Bates D
   2. Mächler M
   3. Bolker B
   4. Walker S

   (2015) Fitting linear mixed-effects models using lme4

   Journal of Statistical Software 67:1–48.

   https://doi.org/10.18637/jss.v067.i01

   • Google Scholar
5. 1. Bégel V
   2. Demos AP
   3. Wang M
   4. Palmer C

   (2022) Social interaction and rate effects in models of musical synchronization

   Frontiers in Psychology 13:865536.

   https://doi.org/10.3389/fpsyg.2022.865536

   • PubMed
   • Google Scholar
6. 1. Ben M
   2. Lüdecke D
   3. Makowski D

   (2020) Effectsize: estimation of effect size indices and standardized parameters

   Journal of Open Source Software 5:2815.

   https://doi.org/10.21105/joss.02815

   • Google Scholar
7. 1. Benadon F
   2. McGraw A
   3. Robinson M

   (2018) Quantitative analysis of temporal structure in cuban guaguancó drumming

   Music & Science 1:205920431878264.

   https://doi.org/10.1177/2059204318782642

   • Google Scholar
8. 1. Berdahl AM
   2. Kao AB
   3. Flack A
   4. Westley PAH
   5. Codling EA
   6. Couzin ID
   7. Dell AI
   8. Biro D

   (2018) Collective animal navigation and migratory culture: from theoretical models to empirical evidence

   Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 373:20170009.

   https://doi.org/10.1098/rstb.2017.0009

   • PubMed
   • Google Scholar
9. 1. Bishop L
   2. Cancino-Chacón C
   3. Goebl W

   (2019) Moving to communicate, moving to interact

   Music Perception 37:1–25.

   https://doi.org/10.1525/mp.2019.37.1.1

   • Google Scholar
10. 1. Breakspear M
    2. Heitmann S
    3. Daffertshofer A

    (2010) Generative models of cortical oscillations: neurobiological implications of the kuramoto model

    Frontiers in Human Neuroscience 4:190.

    https://doi.org/10.3389/fnhum.2010.00190

    • PubMed
    • Google Scholar
11. 1. Brown J
    2. Bossomaier T
    3. Barnett L

    (2020) Information flow in finite flocks

    Scientific Reports 10:3837.

    https://doi.org/10.1038/s41598-020-59080-6

    • PubMed
    • Google Scholar
12. 1. Burger B
    2. Thompson MR
    3. Luck G
    4. Saarikallio S
    5. Toiviainen P

    (2013) Influences of rhythm- and timbre-related musical features on characteristics of music-induced movement

    Frontiers in Psychology 4:183.

    https://doi.org/10.3389/fpsyg.2013.00183

    • PubMed
    • Google Scholar
13. 1. Chang A
    2. Livingstone SR
    3. Bosnyak DJ
    4. Trainor LJ

    (2017) Body sway reflects leadership in joint music performance

    PNAS 114:E4134–E4141.

    https://doi.org/10.1073/pnas.1617657114

    • PubMed
    • Google Scholar
14. 1. Chang A
    2. Kragness HE
    3. Livingstone SR
    4. Bosnyak DJ
    5. Trainor LJ

    (2019) Body sway reflects joint emotional expression in music ensemble performance

    Scientific Reports 9:1–11.

    https://doi.org/10.1038/s41598-018-36358-4

    • PubMed
    • Google Scholar
15. 1. Chaté H
    2. Ginelli F
    3. Grégoire G
    4. Peruani F
    5. Raynaud F

    (2008) Modeling collective motion: variations on the vicsek model

    The European Physical Journal B 64:451–456.

    https://doi.org/10.1140/epjb/e2008-00275-9

    • Google Scholar
16. 1. Chauvigné LAS
    2. Walton A
    3. Richardson MJ
    4. Brown S

    (2019) Multi-person and multisensory synchronization during group dancing

    Human Movement Science 63:199–208.

    https://doi.org/10.1016/j.humov.2018.12.005

    • PubMed
    • Google Scholar
17. 1. Cirelli LK
    2. Einarson KM
    3. Trainor LJ

    (2014) Interpersonal synchrony increases prosocial behavior in infants

    Developmental Science 17:1003–1011.

    https://doi.org/10.1111/desc.12193

    • PubMed
    • Google Scholar
18. 1. Cirelli LK
    2. Wan SJ
    3. Trainor LJ

    (2016) Social effects of movement synchrony: increased infant helpfulness only transfers to affiliates of synchronously moving partners

    Infancy 21:807–821.

    https://doi.org/10.1111/infa.12140

    • Google Scholar
19. 1. Cirelli LK
    2. Trehub SE
    3. Trainor LJ

    (2018) Rhythm and melody as social signals for infants

    Annals of the New York Academy of Sciences 1423:66–72.

    https://doi.org/10.1111/nyas.13580

    • PubMed
    • Google Scholar
20. 1. Conard NJ
    2. Malina M
    3. Münzel SC

    (2009) New flutes document the earliest musical tradition in southwestern Germany

    Nature 460:737–740.

    https://doi.org/10.1038/nature08169

    • PubMed
    • Google Scholar
21. 1. Couzin ID

    (2018) Synchronization: the key to effective communication in animal collectives

    Trends in Cognitive Sciences 22:844–846.

    https://doi.org/10.1016/j.tics.2018.08.001

    • PubMed
    • Google Scholar
22. 1. Csardi G
    2. Nepusz T

    (2006)

    The igraph software package for complex network research

    InterJournal Complex Systems 1695:1–9.

    • Google Scholar
23. Book

    1. Csikszentmihalyi M

    (1990)

    Flow: The Psychology of Optimal Experience

    Harper & Row.

    • Google Scholar
24. 1. D’Amario S
    2. Daffern H
    3. Bailes F

    (2018) Synchronization in singing DUO performances: the roles of visual contact and leadership instruction

    Frontiers in Psychology 9:1208.

    https://doi.org/10.3389/fpsyg.2018.01208

    • PubMed
    • Google Scholar
25. 1. D’Ausilio A
    2. Novembre G
    3. Fadiga L
    4. Keller PE

    (2015) What can music tell us about social interaction?

    Trends in Cognitive Sciences 19:111–114.

    https://doi.org/10.1016/j.tics.2015.01.005

    • PubMed
    • Google Scholar
26. 1. Davies M
    2. Madison G
    3. Silva P
    4. Gouyon F

    (2013) The effect of microtiming deviations on the perception of groove in short rhythms

    Music Perception 30:497–510.

    https://doi.org/10.1525/mp.2013.30.5.497

    • Google Scholar
27. Book

    1. Dayan P
    2. Abbott LF

    (2001)

    Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems

    MIT Press.

    • Google Scholar
28. 1. Dean RT
    2. Dunsmuir WTM

    (2016) Dangers and uses of cross-correlation in analyzing time series in perception, performance, movement, and neuroscience: the importance of constructing transfer function autoregressive models

    Behavior Research Methods 48:783–802.

    https://doi.org/10.3758/s13428-015-0611-2

    • PubMed
    • Google Scholar
29. 1. De Jaegher H
    2. Froese T

    (2009) On the role of social interaction in individual agency

    Adaptive Behavior 17:444–460.

    https://doi.org/10.1177/1059712309343822

    • Google Scholar
30. Software

    1. Dobromir D

    (2022) Group_sync_elife, version swh:1:rev:6479ed2e3409ebc156fbc917a246cf4c4edf4f44

    Software Heritage.

    https://archive.softwareheritage.org/swh:1:dir:a203ffdbf29ac2532c1625c7aa397e43fbdb6eb4;origin=https://gitlab.com/dodo_bird/group_sync_elife;visit=swh:1:snp:7d9f1691d935937d923f4090877180af0adc599b;anchor=swh:1:rev:6479ed2e3409ebc156fbc917a246cf4c4edf4f44
31. 1. Dotov D
    2. Froese T

    (2018) Entraining chaotic dynamics: a novel movement sonification paradigm could promote generalization

    Human Movement Science 61:27–41.

    https://doi.org/10.1016/j.humov.2018.06.016

    • PubMed
    • Google Scholar
32. 1. Dotov DG
    2. Cochen de Cock V
    3. Geny C
    4. Ihalainen P
    5. Moens B
    6. Leman M
    7. Bardy B
    8. Dalla Bella S

    (2019) The role of interaction and predictability in the spontaneous entrainment of movement

    Journal of Experimental Psychology. General 148:1041–1057.

    https://doi.org/10.1037/xge0000609

    • PubMed
    • Google Scholar
33. 1. Dumas G
    2. de Guzman GC
    3. Tognoli E
    4. Kelso JAS

    (2014) The human dynamic clamp as a paradigm for social interaction

    PNAS 111:E3726–E3734.

    https://doi.org/10.1073/pnas.1407486111

    • PubMed
    • Google Scholar
34. 1. Farine DR
    2. Strandburg-Peshkin A
    3. Couzin ID
    4. Berger-Wolf TY
    5. Crofoot MC

    (2017) Individual variation in local interaction rules can explain emergent patterns of spatial organization in wild baboons

    Proceedings. Biological Sciences 284:20162243.

    https://doi.org/10.1098/rspb.2016.2243

    • PubMed
    • Google Scholar
35. 1. Frank TD
    2. Daffertshofer A
    3. Peper CE
    4. Beek PJ
    5. Haken H

    (2000) Towards a comprehensive theory of brain activity

    Physica D 144:62–86.

    https://doi.org/10.1016/S0167-2789(00)00071-3

    • Google Scholar
36. 1. Friston K
    2. Frith C

    (2015) A duet for one

    Consciousness and Cognition 36:390–405.

    https://doi.org/10.1016/j.concog.2014.12.003

    • PubMed
    • Google Scholar
37. 1. Frith U
    2. Frith C

    (2001) The biological basis of social interaction

    Current Directions in Psychological Science 10:151–155.

    https://doi.org/10.1111/1467-8721.00137

    • Google Scholar
38. 1. Froese T
    2. Iizuka H
    3. Ikegami T

    (2014) Embodied social interaction constitutes social cognition in pairs of humans: a minimalist virtual reality experiment

    Scientific Reports 4:3672.

    https://doi.org/10.1038/srep03672

    • PubMed
    • Google Scholar
39. 1. Gaggioli A
    2. Chirico A
    3. Mazzoni E
    4. Milani L
    5. Riva G

    (2017) Networked flow in musical bands

    Psychology of Music 45:283–297.

    https://doi.org/10.1177/0305735616665003

    • Google Scholar
40. 1. Galton F

    (1907) Vox populi (the wisdom of crowds)

    Nature 75:450–451.

    https://doi.org/10.1038/075450a0

    • Google Scholar
41. 1. Gamba M
    2. Torti V
    3. Estienne V
    4. Randrianarison RM
    5. Valente D
    6. Rovara P
    7. Bonadonna G
    8. Friard O
    9. Giacoma C

    (2016) The indris have got rhythm! timing and pitch variation of a primate song examined between sexes and age classes

    Frontiers in Neuroscience 10:249.

    https://doi.org/10.3389/fnins.2016.00249

    • PubMed
    • Google Scholar
42. 1. Goldstone RL
    2. Roberts ME

    (2006) Self-organized TRAIL systems in groups of humans

    Complexity 11:43–50.

    https://doi.org/10.1002/cplx.20135

    • Google Scholar
43. 1. Gourévitch B
    2. Eggermont JJ

    (2007) Evaluating information transfer between auditory cortical neurons

    Journal of Neurophysiology 97:2533–2543.

    https://doi.org/10.1152/jn.01106.2006

    • PubMed
    • Google Scholar
44. 1. Greenfield MD
    2. Marin-Cudraz T
    3. Party V

    (2017) Evolution of synchronies in insect choruses

    Biological Journal of the Linnean Society 122:487–504.

    https://doi.org/10.1093/biolinnean/blx096

    • Google Scholar
45. 1. Greenfield MD
    2. Aihara I
    3. Amichay G
    4. Anichini M
    5. Nityananda V

    (2021) Rhythm interaction in animal groups: selective attention in communication networks

    Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 376:20200338.

    https://doi.org/10.1098/rstb.2020.0338

    • PubMed
    • Google Scholar
46. 1. Hart Y
    2. Noy L
    3. Feniger-Schaal R
    4. Mayo AE
    5. Alon U

    (2014) Individuality and togetherness in joint improvised motion

    PLOS ONE 9:e87213.

    https://doi.org/10.1371/journal.pone.0087213

    • PubMed
    • Google Scholar
47. 1. Heggli OA
    2. Cabral J
    3. Konvalinka I
    4. Vuust P
    5. Kringelbach ML

    (2019) A kuramoto model of self-other integration across interpersonal synchronization strategies

    PLOS Computational Biology 15:e1007422.

    https://doi.org/10.1371/journal.pcbi.1007422

    • PubMed
    • Google Scholar
48. 1. Heggli OA
    2. Konvalinka I
    3. Kringelbach ML
    4. Vuust P

    (2021) A metastable attractor model of self-other integration (MEAMSO) in rhythmic synchronization

    Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 376:20200332.

    https://doi.org/10.1098/rstb.2020.0332

    • PubMed
    • Google Scholar
49. 1. Honing H
    2. ten Cate C
    3. Peretz I
    4. Trehub SE

    (2015) Without it no music: cognition, biology and evolution of musicality

    Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 370:20140088.

    https://doi.org/10.1098/rstb.2014.0088

    • PubMed
    • Google Scholar
50. 1. Hove MJ
    2. Risen JL

    (2009) It’s all in the timing: interpersonal synchrony increases affiliation

    Social Cognition 27:949–960.

    https://doi.org/10.1521/soco.2009.27.6.949

    • Google Scholar
51. 1. Hove MJ
    2. Marie C
    3. Bruce IC
    4. Trainor LJ

    (2014) Superior time perception for lower musical pitch explains why bass-ranged instruments lay down musical rhythms

    PNAS 111:10383–10388.

    https://doi.org/10.1073/pnas.1402039111

    • PubMed
    • Google Scholar
52. 1. Hove MJ
    2. Martinez SA
    3. Stupacher J

    (2020) Feel the bass: music presented to tactile and auditory modalities increases aesthetic appreciation and body movement

    Journal of Experimental Psychology. General 149:1137–1147.

    https://doi.org/10.1037/xge0000708

    • PubMed
    • Google Scholar
53. 1. Huron D

    (2001) Is music an evolutionary adaptation?

    Annals of the New York Academy of Sciences 930:43–61.

    https://doi.org/10.1111/j.1749-6632.2001.tb05724.x

    • PubMed
    • Google Scholar
54. 1. Insel TR

    (2010) The challenge of translation in social neuroscience: a review of oxytocin, vasopressin, and affiliative behavior

    Neuron 65:768–779.

    https://doi.org/10.1016/j.neuron.2010.03.005

    • PubMed
    • Google Scholar
55. 1. Ispolatov Y

    (2015) Computing in fish schools

    eLife 5:e12852.

    https://doi.org/10.7554/eLife.12852

    • PubMed
    • Google Scholar
56. 1. Ito S
    2. Hansen ME
    3. Heiland R
    4. Lumsdaine A
    5. Litke AM
    6. Beggs JM

    (2011) Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model

    PLOS ONE 6:e27431.

    https://doi.org/10.1371/journal.pone.0027431

    • PubMed
    • Google Scholar
57. 1. Jacobs PA
    2. Lengauer CC
    3. Bruschi CV
    4. Garre M
    5. Gjuracic K
    6. Mccoy EE

    (2007) From disorder to order in marching locusts

    Science 317:490–494.

    https://doi.org/10.5061/dryad.5t110.Supplementary

    • Google Scholar
58. 1. Keller PE
    2. Novembre G
    3. Hove MJ

    (2014) Rhythm in joint action: psychological and neurophysiological mechanisms for real-time interpersonal coordination

    Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 369:20130394.

    https://doi.org/10.1098/rstb.2013.0394

    • PubMed
    • Google Scholar
59. 1. Keller PE
    2. König R
    3. Novembre G

    (2017) Simultaneous cooperation and competition in the evolution of musical behavior: sex-related modulations of the singer’s formant in human chorusing

    Frontiers in Psychology 8:1559.

    https://doi.org/10.3389/fpsyg.2017.01559

    • PubMed
    • Google Scholar
60. 1. Kelso JAS

    (2021) Unifying large- and small-scale theories of coordination

    Entropy 23:537.

    https://doi.org/10.3390/e23050537

    • PubMed
    • Google Scholar
61. 1. Konvalinka I
    2. Vuust P
    3. Roepstorff A
    4. Frith CD

    (2010) Follow you, follow me: continuous mutual prediction and adaptation in joint tapping

    Quarterly Journal of Experimental Psychology 63:2220–2230.

    https://doi.org/10.1080/17470218.2010.497843

    • PubMed
    • Google Scholar
62. Book

    1. Kugler PN
    2. Turvey MT

    (1987)

    Information, Natural Law, and the Self-Assembly of Rhythmic Movement

    New Jersey: Lawrence Erlbaum Associates, Inc.

    • Google Scholar
63. Conference

    1. Kuramoto Y

    (1975)

    Self-entrainment of a population of coupled non-linear oscillators

    International Symposium on Mathematical Problems in Theoretical Physics.

    • Google Scholar
64. 1. Kuznetsova A
    2. Brockhoff PB
    3. Christensen RHB

    (2017) lmertest package: tests in linear mixed effects models

    Journal of Statistical Software 82:1–26.

    https://doi.org/10.18637/jss.v082.i13

    • Google Scholar
65. 1. Liebermann-Jordanidis H
    2. Novembre G
    3. Koch I
    4. Keller PE

    (2021) Simultaneous self-other integration and segregation support real-time interpersonal coordination in a musical joint action task

    Acta Psychologica 218:103348.

    https://doi.org/10.1016/j.actpsy.2021.103348

    • PubMed
    • Google Scholar
66. Book

    1. Linson A
    2. Clarke EF

    (2017)

    Distributed cognition, ecological theory, and group improvisation

    In: Clarke EF, Doffman M, editors. Distributed Creativity: Collaboration and Improvisation in Contemporary Music. New York: Oxford University Press. pp. 52–69.

    • Google Scholar
67. 1. Lucas G
    2. Clayton M
    3. Leante L

    (2011) Inter-group entrainment in afro-brazilian congado ritual

    Empirical Musicology Review 6:75–102.

    https://doi.org/10.18061/1811/51203

    • Google Scholar
68. 1. Lungarella M
    2. Pegors T
    3. Bulwinkle D
    4. Sporns O

    (2005) Methods for quantifying the informational structure of sensory and motor data

    Neuroinformatics 3:243–262.

    https://doi.org/10.1385/NI:3:3:243

    • PubMed
    • Google Scholar
69. 1. Lungarella M
    2. Sporns O

    (2006) Mapping information flow in sensorimotor networks

    PLOS Computational Biology 2:e144.

    https://doi.org/10.1371/journal.pcbi.0020144

    • PubMed
    • Google Scholar
70. 1. MacDougall HG
    2. Moore ST

    (2005) Marching to the beat of the same drummer: the spontaneous tempo of human locomotion

    Journal of Applied Physiology 99:1164–1173.

    https://doi.org/10.1152/japplphysiol.00138.2005

    • PubMed
    • Google Scholar
71. 1. Madison G
    2. Karampela O
    3. Ullén F
    4. Holm L

    (2013) Effects of practice on variability in an isochronous serial interval production task: asymptotical levels of tapping variability after training are similar to those of musicians

    Acta Psychologica 143:119–128.

    https://doi.org/10.1016/j.actpsy.2013.02.010

    • PubMed
    • Google Scholar
72. 1. Mann RP
    2. Faria J
    3. Sumpter DJT
    4. Krause J

    (2013) The dynamics of audience applause

    Journal of the Royal Society, Interface 10:20130466.

    https://doi.org/10.1098/rsif.2013.0466

    • PubMed
    • Google Scholar
73. 1. Manning FC
    2. Harris J
    3. Schutz M

    (2017) Temporal prediction abilities are mediated by motor effector and rhythmic expertise

    Experimental Brain Research 235:861–871.

    https://doi.org/10.1007/s00221-016-4845-8

    • PubMed
    • Google Scholar
74. 1. McAuley JD
    2. Jones MR
    3. Holub S
    4. Johnston HM
    5. Miller NS

    (2006) The time of our lives: life span development of timing and event tracking

    Journal of Experimental Psychology. General 135:348–367.

    https://doi.org/10.1037/0096-3445.135.3.348

    • Google Scholar
75. 1. Miller N
    2. Garnier S
    3. Hartnett AT
    4. Couzin ID

    (2013) Both information and social cohesion determine collective decisions in animal groups

    PNAS 110:5263–5268.

    https://doi.org/10.1073/pnas.1217513110

    • PubMed
    • Google Scholar
76. Conference

    1. Moelants D
    2. Stevens C
    3. Burnham D
    4. McPherson G
    5. Schubert E
    6. Renwick J

    (2002)

    Preferred tempo reconsidered

    Proceedings of the 7th International Conference on Music Perception and Cognition. pp. 580–583.

    • Google Scholar
77. 1. Mogan R
    2. Fischer R
    3. Bulbulia JA

    (2017) To be in synchrony or not? A meta-analysis of synchrony’s effects on behavior, perception, cognition and affect

    Journal of Experimental Social Psychology 72:13–20.

    https://doi.org/10.1016/j.jesp.2017.03.009

    • Google Scholar
78. Book

    1. Newman MEJ
    2. Barabási AL
    3. Watts DJ

    (2011) The Structure and Dynamics of Networks

    Princeton University Press.

    https://doi.org/10.1515/9781400841356

    • Google Scholar
79. 1. Noori R
    2. Park D
    3. Griffiths JD
    4. Bells S
    5. Frankland PW
    6. Mabbott D
    7. Lefebvre J

    (2020) Activity-dependent myelination: A glial mechanism of oscillatory self-organization in large-scale brain networks

    PNAS 117:13227–13237.

    https://doi.org/10.1073/pnas.1916646117

    • PubMed
    • Google Scholar
80. 1. Novembre G
    2. Sammler D
    3. Keller PE

    (2016) Neural alpha oscillations index the balance between self-other integration and segregation in real-time joint action

    Neuropsychologia 89:414–425.

    https://doi.org/10.1016/j.neuropsychologia.2016.07.027

    • PubMed
    • Google Scholar
81. 1. Okano M
    2. Shinya M
    3. Kudo K

    (2017) Paired synchronous rhythmic finger tapping without an external timing cue shows greater speed increases relative to those for solo tapping

    Scientific Reports 7:43987.

    https://doi.org/10.1038/srep43987

    • PubMed
    • Google Scholar
82. 1. Oullier O
    2. de Guzman GC
    3. Jantzen KJ
    4. Lagarde J
    5. Kelso JAS

    (2008) Social coordination dynamics: measuring human bonding

    Social Neuroscience 3:178–192.

    https://doi.org/10.1080/17470910701563392

    • PubMed
    • Google Scholar
83. 1. Parrish JK
    2. Viscido SV
    3. Grünbaum D

    (2002) Self-organized fish schools: an examination of emergent properties

    The Biological Bulletin 202:296–305.

    https://doi.org/10.2307/1543482

    • PubMed
    • Google Scholar
84. 1. Patel AD
    2. Iversen JR

    (2014) The evolutionary neuroscience of musical beat perception: the action simulation for auditory prediction (ASAP) hypothesis

    Frontiers in Systems Neuroscience 8:57.

    https://doi.org/10.3389/fnsys.2014.00057

    • PubMed
    • Google Scholar
85. Book

    1. Prokopenko M
    2. Polani D
    3. Ay N

    (2014) On the cross-disciplinary nature of guided self-organisation

    In: Prokopenko M, editors. In Guided Self-Organization: Inception. Berlin, Heidelberg: Springer. pp. 3–15.

    https://doi.org/10.1007/978-3-642-53734-9

    • Google Scholar
86. 1. Przyrembel M
    2. Smallwood J
    3. Pauen M
    4. Singer T

    (2012) Illuminating the dark matter of social neuroscience: considering the problem of social interaction from philosophical, psychological, and neuroscientific perspectives

    Frontiers in Human Neuroscience 6:190.

    https://doi.org/10.3389/fnhum.2012.00190

    • PubMed
    • Google Scholar
87. Conference

    1. Puckette MS

    (1997)

    Pure Data

    Proceedings of the International Computer Music Conference.

    • Google Scholar
88. 1. Ragert M
    2. Fairhurst MT
    3. Keller PE

    (2014) Segregation and integration of auditory streams when listening to multi-part music

    PLOS ONE 9:e84085.

    https://doi.org/10.1371/journal.pone.0084085

    • PubMed
    • Google Scholar
89. 1. Ravignani A
    2. Bowling DL
    3. Fitch WT

    (2014) Chorusing, synchrony, and the evolutionary functions of rhythm

    Frontiers in Psychology 5:1–15.

    https://doi.org/10.3389/fpsyg.2014.01118

    • PubMed
    • Google Scholar
90. 1. Ravignani A
    2. Verga L
    3. Greenfield MD

    (2019) Interactive rhythms across species: the evolutionary biology of animal chorusing and turn-taking

    Annals of the New York Academy of Sciences 1453:12–21.

    https://doi.org/10.1111/nyas.14230

    • PubMed
    • Google Scholar
91. 1. Repp BH

    (2005) Sensorimotor synchronization: a review of the tapping literature

    Psychonomic Bulletin & Review 12:969–992.

    https://doi.org/10.3758/bf03206433

    • PubMed
    • Google Scholar
92. 1. Rio KW
    2. Dachner GC
    3. Warren WH

    (2018) Local interactions underlying collective motion in human crowds

    Proceedings of the Royal Society Biological Sciences 285:20180611.

    https://doi.org/10.1098/rspb.2018.0611

    • PubMed
    • Google Scholar
93. 1. Roman IR
    2. Washburn A
    3. Large EW
    4. Chafe C
    5. Fujioka T

    (2019) Delayed feedback embedded in perception-action coordination cycles results in anticipation behavior during synchronized rhythmic action: a dynamical systems approach

    PLOS Computational Biology 15:e1007371.

    https://doi.org/10.1371/journal.pcbi.1007371

    • PubMed
    • Google Scholar
94. 1. Rosenthal SB
    2. Twomey CR
    3. Hartnett AT
    4. Wu HS
    5. Couzin ID

    (2015) Revealing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion

    PNAS 112:4690–4695.

    https://doi.org/10.1073/pnas.1420068112

    • PubMed
    • Google Scholar
95. 1. Salimpoor VN
    2. Benovoy M
    3. Larcher K
    4. Dagher A
    5. Zatorre RJ

    (2011) Anatomically distinct dopamine release during anticipation and experience of peak emotion to music

    Nature Neuroscience 14:257–262.

    https://doi.org/10.1038/nn.2726

    • PubMed
    • Google Scholar
96. Book

    1. Satne G
    2. Salice A

    (2018)

    Shared intentionality and the cooperative evolutionary hypothesis

    In: Fiebich A, editors. Minimal Cooperation and Shared Agency. Springer. pp. 71–92.

    • Google Scholar
97. 1. Savage PE
    2. Brown S
    3. Sakai E
    4. Currie TE

    (2015) Statistical universals reveal the structures and functions of human music

    PNAS 112:8987–8992.

    https://doi.org/10.1073/pnas.1414495112

    • PubMed
    • Google Scholar
98. 1. Savage PE
    2. Loui P
    3. Tarr B
    4. Schachner A
    5. Glowacki L
    6. Mithen S
    7. Fitch WT

    (2020) Music as a coevolved system for social bonding

    The Behavioral and Brain Sciences 44:e59.

    https://doi.org/10.1017/S0140525X20000333

    • PubMed
    • Google Scholar
99. 1. Schilbach L
    2. Timmermans B
    3. Reddy V
    4. Costall A
    5. Bente G
    6. Schlicht T
    7. Vogeley K

    (2013) Authors’ response: a second-person neuroscience in interaction

    The Behavioral and Brain Sciences 36:441–462.

    https://doi.org/10.1017/s0140525x12002452

    • PubMed
    • Google Scholar
100. 1. Schmidt RC
     2. Carello C
     3. Turvey MT

     (1990) Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people

     Journal of Experimental Psychology. Human Perception and Performance 16:227–247.

     https://doi.org/10.1037//0096-1523.16.2.227

     • PubMed
     • Google Scholar
101. 1. Schmidt RC
     2. O’Brien B

     (1997) Evaluating the dynamics of unintended interpersonal coordination

     Ecological Psychology 9:189–206.

     https://doi.org/10.1207/s15326969eco0903_2

     • Google Scholar
102. 1. Schreiber T

     (2000) Measuring information transfer

     Physical Review Letters 85:461–464.

     https://doi.org/10.1103/PhysRevLett.85.461

     • PubMed
     • Google Scholar
103. 1. Seth AK
     2. Edelman GM

     (2004) Environment and behavior influence the complexity of evolved neural networks

     Adaptive Behavior 12:5–20.

     https://doi.org/10.1177/105971230401200103

     • Google Scholar
104. 1. Seth AK
     2. Barrett AB
     3. Barnett L

     (2011) Causal density and integrated information as measures of conscious level

     Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences 369:3748–3767.

     https://doi.org/10.1098/rsta.2011.0079

     • PubMed
     • Google Scholar
105. 1. Shahal S
     2. Wurzberg A
     3. Sibony I
     4. Duadi H
     5. Shniderman E
     6. Weymouth D
     7. Davidson N
     8. Fridman M

     (2020) Synchronization of complex human networks

     Nature Communications 11:3854.

     https://doi.org/10.1038/s41467-020-17540-7

     • PubMed
     • Google Scholar
106. 1. Silverberg JL
     2. Bierbaum M
     3. Sethna JP
     4. Cohen I

     (2013) Collective motion of humans in mosh and circle pits at heavy metal concerts

     Physical Review Letters 110:228701.

     https://doi.org/10.1103/PhysRevLett.110.228701

     • PubMed
     • Google Scholar
107. Book

     1. Singer JD
     2. Willett JB

     (2003) Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence

     Oxford University Press.

     https://doi.org/10.1093/acprof:oso/9780195152968.001.0001

     • Google Scholar
108. 1. Stoffregen TA
     2. Villard S
     3. Kim CG
     4. Ito K
     5. Bardy BG

     (2009) Coupling of head and body movement with motion of the audible environment

     Journal of Experimental Psychology. Human Perception and Performance 35:1221–1231.

     https://doi.org/10.1037/a0014251

     • PubMed
     • Google Scholar
109. 1. Strogatz SH

     (2000) From kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

     Physica D 143:1–20.

     https://doi.org/10.1016/S0167-2789(00)00094-4

     • Google Scholar
110. 1. Sumpter DJT

     (2006) The principles of collective animal behaviour

     Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 361:5–22.

     https://doi.org/10.1098/rstb.2005.1733

     • PubMed
     • Google Scholar
111. Book

     1. Surowiecki J

     (2005)

     The Wisdom of Crowds

     Anchor.

     • Google Scholar
112. 1. Thomson M
     2. Murphy K
     3. Lukeman R

     (2018) Groups clapping in unison undergo size-dependent error-induced frequency increase

     Scientific Reports 8:808.

     https://doi.org/10.1038/s41598-017-18539-9

     • PubMed
     • Google Scholar
113. Book

     1. Tomasello M

     (2000) The Cultural Origins of Human Cognition

     Cambridge: Harvard University Press.

     https://doi.org/10.4159/9780674044371

     • Google Scholar
114. Book

     1. Tomasello M

     (2014) A Natural History of Human Thinking

     Harvard University Press.

     https://doi.org/10.4159/9780674726369

     • Google Scholar
115. 1. Torney C
     2. Neufeld Z
     3. Couzin ID

     (2009) Context-dependent interaction leads to emergent search behavior in social aggregates

     PNAS 106:22055–22060.

     https://doi.org/10.1073/pnas.0907929106

     • PubMed
     • Google Scholar
116. 1. Trainor LJ

     (2015) The origins of music in auditory scene analysis and the roles of evolution and culture in musical creation

     Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 370:20140089.

     https://doi.org/10.1098/rstb.2014.0089

     • PubMed
     • Google Scholar
117. 1. Trainor LJ
     2. Cirelli L

     (2015) Rhythm and interpersonal synchrony in early social development

     Annals of the New York Academy of Sciences 1337:45–52.

     https://doi.org/10.1111/nyas.12649

     • PubMed
     • Google Scholar
118. Book

     1. Trainor LJ
     2. Marsh-Rollo S

     (2019) Rhythm, meter, and timing: the heartbeat of musical development

     In: Thaut MH, Hodges DA, editors. The Oxford Handbook of Music and the Brain. Oxford Academic. pp. 591–622.

     https://doi.org/10.1093/oxfordhb/9780198804123.013.24

     • Google Scholar
119. 1. Valdesolo P
     2. Ouyang J
     3. DeSteno D

     (2010) The rhythm of joint action: synchrony promotes cooperative ability

     Journal of Experimental Social Psychology 46:693–695.

     https://doi.org/10.1016/j.jesp.2010.03.004

     • Google Scholar
120. 1. van der Steen MCM
     2. Keller PE

     (2013) The adaptation and anticipation model (ADAM) of sensorimotor synchronization

     Frontiers in Human Neuroscience 7:253.

     https://doi.org/10.3389/fnhum.2013.00253

     • PubMed
     • Google Scholar
121. 1. Vicsek T
     2. Czirók A
     3. Ben-Jacob E
     4. Cohen I
     5. Shochet O

     (1995) Novel type of phase transition in a system of self-driven particles

     Physical Review Letters 75:1226–1229.

     https://doi.org/10.1103/PhysRevLett.75.1226

     • PubMed
     • Google Scholar
122. 1. Vilar L
     2. Araújo D
     3. Davids K
     4. Bar-Yam Y

     (2013) Science of winning soccer: emergent pattern-forming dynamics in association football

     Journal of Systems Science and Complexity 26:73–84.

     https://doi.org/10.1007/s11424-013-2286-z

     • Google Scholar
123. 1. Warren WH

     (2018) Collective motion in human crowds

     Current Directions in Psychological Science 27:232–240.

     https://doi.org/10.1177/0963721417746743

     • PubMed
     • Google Scholar
124. Book

     1. Wiener N

     (1956)

     The theory of prediction

     In: Wiener N, editors. In Modern Mathematics for Engineers. Dover Publications. pp. 323–329.

     • Google Scholar
125. 1. Wolf T
     2. Vesper C
     3. Sebanz N
     4. Keller PE
     5. Knoblich G

     (2019) Combining phase advancement and period correction explains rushing during joint rhythmic activities

     Scientific Reports 9:9350.

     https://doi.org/10.1038/s41598-019-45601-5

     • PubMed
     • Google Scholar
126. 1. Wolpert DM
     2. Doya K
     3. Kawato M

     (2003) A unifying computational framework for motor control and social interaction

     Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 358:593–602.

     https://doi.org/10.1098/rstb.2002.1238

     • PubMed
     • Google Scholar
127. 1. Zahavi D
     2. Satne G

     (2015)

     Beyond the Analytic-Continental Divide: Pluralist Philosophy in the Twenty-First Century

     Varieties of shared intentionality: tomasello and classical phenomenology, Beyond the Analytic-Continental Divide: Pluralist Philosophy in the Twenty-First Century, Taylor and Francis, 10.4324/9781315766621.

     • Google Scholar
128. 1. Zentner M
     2. Eerola T

     (2010) Rhythmic engagement with music in infancy

     PNAS 107:5768–5773.

     https://doi.org/10.1073/pnas.1000121107

     • PubMed
     • Google Scholar
129. 1. Zhang M
     2. Beetle C
     3. Kelso JAS
     4. Tognoli E

     (2019) Connecting empirical phenomena and theoretical models of biological coordination across scales

     Journal of the Royal Society, Interface 16:20190360.

     https://doi.org/10.1098/rsif.2019.0360

     • PubMed
     • Google Scholar

Author details

1. Dobromir Dotov

   1. LIVELab, McMaster University, Hamilton, Canada
   2. Psychology, Neuroscience and Behaviour, McMaster University, Hamilton, Canada
   3. Department of Biomechanics, University of Nebraska Omaha, Omaha, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   ddotov@unomaha.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-5543-360X

2. Lana Delasanta

   1. Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs, United States
   2. Department of Psychological Sciences, University of Connecticut, Storrs, United States

   Contribution

   Formal analysis, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

3. Daniel J Cameron

   1. LIVELab, McMaster University, Hamilton, Canada
   2. Psychology, Neuroscience and Behaviour, McMaster University, Hamilton, Canada

   Contribution

   Conceptualization, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5543-9836

4. Edward W Large

   1. Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs, United States
   2. Department of Psychological Sciences, University of Connecticut, Storrs, United States
   3. Department of Physics, University of Connecticut, Storrs, United States
   4. CT Institute for Brain and Cognitive Sciences, University of Connecticut, Storrs, United States

   Contribution

   Conceptualization, Software, Formal analysis, Supervision, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3909-3518

5. Laurel Trainor

   1. LIVELab, McMaster University, Hamilton, Canada
   2. Psychology, Neuroscience and Behaviour, McMaster University, Hamilton, Canada
   3. Rotman Research Institute, Toronto, Canada

   Contribution

   Conceptualization, Formal analysis, Supervision, Funding acquisition, Methodology, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3397-2079

• 939

  views

• 145

  downloads

• 9

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.