Collective dynamics support group drumming, reduce variability, and stabilize tempo drift

  1. Dobromir Dotov
  2. Lana Delasanta
  3. Daniel J Cameron
  4. Edward W Large
  5. Laurel Trainor

  • Curated by eLife

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    Evaluation Summary:

    The paper will be of great interest to scientists looking for new approaches to understanding group behavior, especially within the fields of human cognition, neurosciences, and musicology. Taking joint drumming as a model of collective dynamics, and combining several quantitative methods, the authors characterize how human behavior changes, at the individual- and group-level, as a function of group numerosity. An important take home message of this work is that not everything we know from studies involving dyads should be necessarily generalized to larger groups.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name with the authors.)

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Abstract

Humans are social animals who engage in a variety of collective activities requiring coordinated action. Among these, music is a defining and ancient aspect of human sociality. Human social interaction has largely been addressed in dyadic paradigms, and it is yet to be determined whether the ensuing conclusions generalize to larger groups. Studied more extensively in non-human animal behavior, the presence of multiple agents engaged in the same task space creates different constraints and possibilities than in simpler dyadic interactions. We addressed whether collective dynamics play a role in human circle drumming. The task was to synchronize in a group with an initial reference pattern and then maintain synchronization after it was muted. We varied the number of drummers from solo to dyad, quartet, and octet. The observed lower variability, lack of speeding up, smoother individual dynamics, and leader-less inter-personal coordination indicated that stability increased as group size increased, a sort of temporal wisdom of crowds. We propose a hybrid continuous-discrete Kuramoto model for emergent group synchronization with a pulse-based coupling that exhibits a mean field positive feedback loop. This research suggests that collective phenomena are among the factors that play a role in social cognition.

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  1. Version published to 10.7554/elife.74816 on eLife
  2. eLife

    Author Response

    Reviewer #1 (Public Review):

    Dotov et al. took joint drumming as a model of human collective dynamics. They tested interpersonal synchronization across progressively larger groups composed of 1, 2, 4 and 8 individuals. They conducted several analyses, generally showing that the stability of group coordination increases with group numerosity. They also propose a model that nicely mirrors some of the results.

    The manuscript is very clear and very well written. The introduction covers a lot of relevant literature, including animal models that are very relevant in this field but often ignored by human studies. The methods cover a wide range of distinct analyses, including modelling, giving a comprehensive overview of the data. There are a few small technical differences across the experiments conducted with small vs. large groups, but I think this is to some extent unavoidable (yet, future studies might attempt to improve this). Furthermore, the currently adopted model accounts well for behaviors where all individuals produce a similar output and therefore are "equally important". However, it might be interesting to test to what extent this can be generalized to situations where each individual produces a distinct sound (as in a small orchestra) and therefore might selectively adapt to (more clearly) distinguishable individuals.

    We agree that this is important. We discuss this in a new section (4.1) at the end of the discussion. We suggest that heterogeneity makes it possible for other modes of organization to compete with the attractive tendency towards the global average. We also point out that factors such as individual skill, task difficulty, delays, and selective attention enable such heterogeneity in the ensemble.

    Similarly, it would be interesting to test to what extent the current results (and model) can be generalized to interactions that more strongly rely on predictive behavior (as there is not much to predict here given that all participants have to drum at a stable, non-changing tempo).

    We can only speculate that the present results are less relevant to interactions that rely strongly on predicitive behavior, as behaviour in our simple task could be modeled well by our hybrid single oscillator Kuromoto model. We inserted the idea that the presence of a group rhythm can diminish the demands for individuals to predict each other’s notes, the end of paragraph 1, page 27.

    An important implication of this study is that some well-known behaviors typically studied in dyadic interaction might be less prominent when group numerosity increases. I am specifically referring to "speeding up" (also termed "joint rushing") and "tap-by-tap error correction" (Wolf et al., 2019 and Konvalinka et al., 2010, also cited in the manuscript, are two recent examples). I am not sure whether this depends on how the data is analyzed (e.g. averaging the behavior of multiple drummers), yet this might be an important take-home message.

    Thank you for the suggestion. We edited to emphasize that the relevant part of the analysis of the drumming data was performed at the individual level and using the same methods as typically done in dyadic tapping (first sentences of Section 2.7.2). Speeding up was the only variable where we used group-averages. For consistency, and to avoid confusion, in the present version we re-did the stats (the changed statistical parameters are highlighted) and figures using the individual data points and we did not observe major changes.

    I am confident that this study will have a significant impact on the field, bringing more researchers close to the study of large groups, and generally bridging the gap between human and animal studies of collective behavior.

    Reviewer #2 (Public Review):

    In this manuscript Dotov et al. study how individuals in a group adjust their rhythms and maintain synchrony while drumming. The authors recognize correctly that most investigation of rhythm interaction examines pairs (dyads) rather than larger groups despite the ubiquity of group situations and interactions in human as well as non-human animals. Their study is both empirical, using human drummers, and modeling, evaluating how well variations of the Kuramoto coupled-oscillator describe timing of grouped drummers. Based on temporal analyses of drumming in groups of different sizes, it is concluded that this coupled oscillator model provides a 'good fit' to the data and that each individual in a group responds to the collective stimulus generated by all neighbors, the 'mean field'.

    I have concerns about 1) the overall analysis and testing in the study and about 2) specific aspects of the model and how it relates to human cognition. Because the study is largely empirical, it would be most critical for the authors to propose two - or more - alternative hypotheses for achieving and maintaining synchrony in a group. Ideally, these alternatives would have different predictions, which could be tested by appropriate analyses of drummer timing. For example, in non-human animals, where the problem of rhythm interaction in groups has been examined more thoroughly than in humans, many acoustic species organize their timing by attending largely to a few nearby neighbors and ignoring the rest. Such 'selective attention' is known to occur in species where dyads (and triads) keep time with a Kuramoto oscillator, but the overall timing of the group does not arise from individual responses to the mean field. Can this alternative be evaluated in the drumming data ? Would this alternative fit the drumming data as well as, or better than , the mean field, 'wisdom of the crowd' model ?

    These are very important points. The present paper is restricted to a simple task where participants are instructed to synchronize with each other. However, we now more explicitly acknowledge the limitations of our study and include a new section, “Beyond the group average” at the end of the Discussion that is dedicated to this issue and discussed other organizing tendencies that are particularly relevant in larger and more diverse ensembles. In the context of the present task, the relative difference between local and global interactions was likely negligible because of the small differences in timing, from 4 to 16 ms, between the closest and most distant pairs.

    It will be interesting in future studies to introduce acoustic heterogeneity by varying the timbre of the instruments, for example. In the present study, the instruments had the same timbre with narrowly varying fundamental frequencies (117-129 Hz in the duets/quartets and 249-284 Hz in the octets), a situation that encourages integration of all the acoustic information. We do point out that the present approach needs to be expanded to be able to account for competitive pressure and selective attention.

    The well-known Vicsek model (discussed briefly in paragraph 2, page 15), related to the Kuramoto under certain assumptions, can account for a variety of dynamic behaviors in flocking animals. The ability for selective attention in the form of a heterogeneous coupling matrix, combined with the existence of competitive pressure in the form of negative coupling terms can result in spontaneous formation of clusters and spatiotemporal patterns of movement. This is consistent with prior research in chorusing animals (insects and anurans). Large musical ensembles also involve groupings of instruments such as separate sections that change their relative loudness across time. Typically these are not spontaneous but composed and conducted, yet they may satisfy the same constraints.

    We also pointed out that we see these as complementary organizing principles. Even in the Vicsek model, there is a notion of a ‘local order parameter’ whereby individuals are coupled to a group average within a narrow interaction radius. The relative importance of other organization tendencies depends on the layout of the acoustic environment and the competitive and collaborative aspects of the task. Hence, parameters such as delay and individual heterogeneity could act as symmetry breaking terms that enable different stabilities from the basic global group synchrony.

    A second concern arises from relying on a hybrid, continuous - pulsed version of the Kuramoto coupled oscillator. If the human drummers in the test could only hear but not see their neighbors, this hybrid model would seem appropriate: Each drummer only receives sensory input at the exact moment when a neighbor's drumstick strikes the drum. But the drummers see as well as hear their neighbors, and they may be receiving a considerable amount of information on their neighbors' rhythms throughout the drum cycle. Can this potential problem be addressed? In general, more attention should be paid to the cognitive aspects of the experiment: What exactly do the individual drummers perceive, and how might they perceive the 'mean field' ?

    This is all very relevant. We instructed participants to focus on X’s in the centers of their drums and not look at their peers (edited to mention that in at the end of Section 2.4, page 9). Additionally, the pattern of results for tempo change, cross-correlations, and variability in the dyadic condition was consistent with previous studies that involved purely auditory tapping tasks (emphasized in the begging of paragraph 2, page 26). The best way to address this limitation would be to repeat the study and block the visual contact among participants, as well as include a condition emphasizing visual contact.

    It is beyond the scope of the present paper to make model-based predictions of effects of coupling and information availability, but this should be done in future work. For the present paper, we now include a simulation involving continuous coupling (end of section 2.9.2, page 16) and Supplementary Figure 8A) which fails to reproduce the results for variability, results that are well captured by the hybrid continuous-pulsed model we developed, see the Supplementary Materials.

    Reviewer #3 (Public Review):

    The contribution provides approaches to understanding group behaviour using drumming as a case of collective dynamics. The experimental design is interestingly complemented with the novel application of several methods established in different disciplines. The key strengths of the contribution seem to be concentrated in 1) the combination of theoretical and methodological elements brought from the application of methods from neurosciences and psychology and 2) the methodological diversity and creative debate brought to the study of musical performance, including here the object of study, which looks at group drumming as a cultural trait in many societies.

    Even though the experimental design and object of study do not represent an original approach, the proposed procedures and the analytical approaches shed light on elements poorly addressed in music studies. The performers' relationships, feedbacks, differences between solo and ensemble performance and interpersonal organization convey novel ideas to the field and most probably new insights to the methodological part.

    It must be mentioned that the authors accepted the challenge of leaving the nauseatic no-frills dyadic tests and tapping experiments in the direction of more culturally comprehensive (and complex) setups. This represents a very important strength of the paper and greatly improves the communication with performers and music studies, which have been affected by the poor impact of predictable non-musical experimental tasks (that can easily generate statistical significant measurements). More specifically, the originality of the experiment-analysis approach provided a novel framework to observe how the axis from individual to collective unfolds in interaction patterns. In special, the emergence of mutual prediction in large groups is quite interesting, although similar results might be found elsewhere.

    Thank you for these comments.

    On another side, important issues regarding the literature review, experimental design and assumptions should be addressed.

    I miss an important part of the literature that reports similar experiments under the thematic framework of musical expressivity/expression, groove, microtiming and timing studies. From the participatory discrepancies proposed in 1980's Keil (1987) to the work of Benadon et al (2018), Guy Madison, colleagues and others, this literature presents formidable studies that could help understand how timing and interactions are structured and conceptualized in the music studies and by musicians and experts. (I declare that I have no recent collaborations with the authors I mentioned throughout the text and that I don't feel comfortable suggesting my own contributions to the field). This is important because there are important ontological concerns in applying methods from sciences to cultural performances.

    Thank you for the suggestions. We included a brief discussion in the newly added “Beyond the group average” section at the end of the Discussion, specifically the first paragraph, pages 27-8. We think that expressive timing naturally fits in continuation with the other reviewers’ concerns about how much the idea of the group average generalizes to real musical situations. By design and instruction, we stripped individual expression from the present task. Specific cultural contexts and performance styles may want to escape or at least expressively tackle this constraint of our task, and we believe that now that we have established the mean field as one factor affecting group behaviour, further studies can take on the challenge of developing models that make predictions in more complex situations closer to real musical interactions – and testing those models empirically.

    One ontological issue that different cultural phenomena differ from, for example, animal behaviour. For example, the authors consider timing and synchrony in a way that does not comply with cultural concepts: p.4 "Here we consider a musical task in which timing consistency and synchrony is crucial". A large part of the literature mentioned above and evidence found in ethnographic literature indicate that the ability to modulate timing and synchrony-asynchrony elements are part of explicit cultural processes of meaning formation (see, for example, Lucas, Glaura and Clayton, Martin and Leante, Laura (2011) 'Inter-group entrainment in Afro-Brazilian Congado ritual.', Empirical musicology review., 6 (2). pp. 75-102.). Without these idiosyncrasies, what you listen to can't be considered a musical task in context and lacks basic expressivity elements that represent musical meaning on different levels (see, for example, the Swanwick's work about layers/levels of musical discourse formation).

    Indeed, this is an important issue. We often use cultural phenomena merely as a motivation but do not dive in the relevant details. Here, in addition to the previous discussion, we now reiterate that the tendency towards the group average is one organizing tendency but there are additional ones, enabled by individual heterogeneity and context. For example, marching bands and chanting crowds probably impose different constraints than individual artistic expression by skillful musicians.

    Such plain ideas about the ontology of musical activities (e.g. that musical practice is oriented by precision or synchrony) generate superficial constructs such as precision priority, dance synchrony, imaginary internal oscillators, strict predictive motor planning that are not present in cultural reports, excepting some cultures of classical European music based on notation and shaped by industrial models. The lack of proper cultural framing of the drumming task might also have induced the authors to instruct the participants to minimize "temporal variability" (musical timing) and maintain the rate of the stimulus (musical tempo), even though these limiting tasks mostly take part of musical training in some societies (examples of social drumming in non-western societies barely represent isochronous tempo or timing in any linguistic or conceptual way). The authors should examine how this instruction impacts the validity of results that describe the variability since it was affected by imposed conditions and might have limited the observed behaviour. The reporting of the results in the graphs must also allow the diagnosis of the effect of timing in such small time frame windows of action.

    We agree totally. We made changes and tried to be more specific about the cultural framing, delineating contexts where the present ideas are more relevant and where they are less relevant, or at least incomplete (the bottom of page 3, and pages 27-8).

  3. Version published to 10.1101/2021.09.16.458206v2 on bioRxiv
  4. eLife

    Evaluation Summary:

    The paper will be of great interest to scientists looking for new approaches to understanding group behavior, especially within the fields of human cognition, neurosciences, and musicology. Taking joint drumming as a model of collective dynamics, and combining several quantitative methods, the authors characterize how human behavior changes, at the individual- and group-level, as a function of group numerosity. An important take home message of this work is that not everything we know from studies involving dyads should be necessarily generalized to larger groups.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name with the authors.)

  5. eLife

    Reviewer #1 (Public Review):

    Dotov et al. took joint drumming as a model of human collective dynamics. They tested interpersonal synchronization across progressively larger groups composed of 1, 2, 4 and 8 individuals. They conducted several analyses, generally showing that the stability of group coordination increases with group numerosity. They also propose a model that nicely mirrors some of the results.

    The manuscript is very clear and very well written. The introduction covers a lot of relevant literature, including animal models that are very relevant in this field but often ignored by human studies. The methods cover a wide range of distinct analyses, including modelling, giving a comprehensive overview of the data. There are a few small technical differences across the experiments conducted with small vs. large groups, but I think this is to some extent unavoidable (yet, future studies might attempt to improve this). Furthermore, the currently adopted model accounts well for behaviors where all individuals produce a similar output and therefore are "equally important". However, it might be interesting to test to what extent this can be generalized to situations where each individual produces a distinct sound (as in a small orchestra) and therefore might selectively adapt to (more clearly) distinguishable individuals. Similarly, it would be interesting to test to what extent the current results (and model) can be generalized to interactions that more strongly rely on predictive behavior (as there is not much to predict here given that all participants have to drum at a stable, non-changing tempo).

    An important implication of this study is that some well-known behaviors typically studied in dyadic interaction might be less prominent when group numerosity increases. I am specifically referring to "speeding up" (also termed "joint rushing") and "tap-by-tap error correction" (Wolf et al., 2019 and Konvalinka et al., 2010, also cited in the manuscript, are two recent examples). I am not sure whether this depends on how the data is analyzed (e.g. averaging the behavior of multiple drummers), yet this might be an important take-home message.

    I am confident that this study will have a significant impact on the field, bringing more researchers close to the study of large groups, and generally bridging the gap between human and animal studies of collective behavior.

  6. eLife

    Reviewer #2 (Public Review):

    In this manuscript Dotov et al. study how individuals in a group adjust their rhythms and maintain synchrony while drumming. The authors recognize correctly that most investigation of rhythm interaction examines pairs (dyads) rather than larger groups despite the ubiquity of group situations and interactions in human as well as non-human animals. Their study is both empirical, using human drummers, and modeling, evaluating how well variations of the Kuramoto coupled-oscillator describe timing of grouped drummers. Based on temporal analyses of drumming in groups of different sizes, it is concluded that this coupled oscillator model provides a 'good fit' to the data and that each individual in a group responds to the collective stimulus generated by all neighbors, the 'mean field'.

    I have concerns about 1) the overall analysis and testing in the study and about 2) specific aspects of the model and how it relates to human cognition. Because the study is largely empirical, it would be most critical for the authors to propose two - or more - alternative hypotheses for achieving and maintaining synchrony in a group. Ideally, these alternatives would have different predictions, which could be tested by appropriate analyses of drummer timing. For example, in non-human animals, where the problem of rhythm interaction in groups has been examined more thoroughly than in humans, many acoustic species organize their timing by attending largely to a few nearby neighbors and ignoring the rest. Such 'selective attention' is known to occur in species where dyads (and triads) keep time with a Kuramoto oscillator, but the overall timing of the group does not arise from individual responses to the mean field. Can this alternative be evaluated in the drumming data ?
    Would this alternative fit the drumming data as well as, or better than , the mean field, 'wisdom of the crowd' model ?

    A second concern arises from relying on a hybrid, continuous - pulsed version of the Kuramoto coupled oscillator. If the human drummers in the test could only hear but not see their neighbors, this hybrid model would seem appropriate: Each drummer only receives sensory input at the exact moment when a neighbor's drumstick strikes the drum. But the drummers see as well as hear their neighbors, and they may be receiving a considerable amount of information on their neighbors' rhythms throughout the drum cycle. Can this potential problem be addressed? In general, more attention should be paid to the cognitive aspects of the experiment: What exactly do the individual drummers perceive, and how might they perceive the 'mean field' ?

  7. eLife

    Reviewer #3 (Public Review):

    The contribution provides approaches to understanding group behaviour using drumming as a case of collective dynamics. The experimental design is interestingly complemented with the novel application of several methods established in different disciplines. The key strengths of the contribution seem to be concentrated in 1) the combination of theoretical and methodological elements brought from the application of methods from neurosciences and psychology and 2) the methodological diversity and creative debate brought to the study of musical performance, including here the object of study, which looks at group drumming as a cultural trait in many societies.

    Even though the experimental design and object of study do not represent an original approach, the proposed procedures and the analytical approaches shed light on elements poorly addressed in music studies. The performers' relationships, feedbacks, differences between solo and ensemble performance and interpersonal organization convey novel ideas to the field and most probably new insights to the methodological part.
    It must be mentioned that the authors accepted the challenge of leaving the nauseatic no-frills dyadic tests and tapping experiments in the direction of more culturally comprehensive (and complex) setups. This represents a very important strength of the paper and greatly improves the communication with performers and music studies, which have been affected by the poor impact of predictable non-musical experimental tasks (that can easily generate statistical significant measurements). More specifically, the originality of the experiment-analysis approach provided a novel framework to observe how the axis from individual to collective unfolds in interaction patterns. In special, the emergence of mutual prediction in large groups is quite interesting, although similar results might be found elsewhere.

    On another side, important issues regarding the literature review, experimental design and assumptions should be addressed.
    I miss an important part of the literature that reports similar experiments under the thematic framework of musical expressivity/expression, groove, microtiming and timing studies. From the participatory discrepancies proposed in 1980's Keil (1987) to the work of Benadon et al (2018), Guy Madison, colleagues and others, this literature presents formidable studies that could help understand how timing and interactions are structured and conceptualized in the music studies and by musicians and experts. (I declare that I have no recent collaborations with the authors I mentioned throughout the text and that I don't feel comfortable suggesting my own contributions to the field). This is important because there are important ontological concerns in applying methods from sciences to cultural performances. One ontological issue that different cultural phenomena differ from, for example, animal behaviour. For example, the authors consider timing and synchrony in a way that does not comply with cultural concepts: p.4 "Here we consider a musical task in which timing consistency and synchrony is crucial". A large part of the literature mentioned above and evidence found in ethnographic literature indicate that the ability to modulate timing and synchrony-asynchrony elements are part of explicit cultural processes of meaning formation (see, for example, Lucas, Glaura and Clayton, Martin and Leante, Laura (2011) 'Inter-group entrainment in Afro-Brazilian Congado ritual.', Empirical musicology review., 6 (2). pp. 75-102.). Without these idiosyncrasies, what you listen to can't be considered a musical task in context and lacks basic expressivity elements that represent musical meaning on different levels (see, for example, the Swanwick's work about layers/levels of musical discourse formation). Such plain ideas about the ontology of musical activities (e.g. that musical practice is oriented by precision or synchrony) generate superficial constructs such as precision priority, dance synchrony, imaginary internal oscillators, strict predictive motor planning that are not present in cultural reports, excepting some cultures of classical European music based on notation and shaped by industrial models. The lack of proper cultural framing of the drumming task might also have induced the authors to instruct the participants to minimize "temporal variability" (musical timing) and maintain the rate of the stimulus (musical tempo), even though these limiting tasks mostly take part of musical training in some societies (examples of social drumming in non-western societies barely represent isochronous tempo or timing in any linguistic or conceptual way). The authors should examine how this instruction impacts the validity of results that describe the variability since it was affected by imposed conditions and might have limited the observed behaviour. The reporting of the results in the graphs must also allow the diagnosis of the effect of timing in such small time frame windows of action.

  8. Version published to 10.1101/2021.09.16.458206v1 on bioRxiv