Dataset

The dataset consisted of videos of performances of two musical pieces featured in a concert held in 2017 by the Omega Ensemble, a professional chamber music group from Australia. One piece was the Clarinet Quintet in B minor (Op. 115) written by Johannes Brahms (referred to as Quintet), and the second piece was String Quartet No. 1 in A major written by Alexander Borodin (referred to as Quartet). The Quartet is scored for violin 1, violin 2, viola, and cello. The Quintet uses the same string instruments plus a clarinet. The duration of the Quartet performance was 39 minutes and 13 seconds, while the duration of the Quintet performance was 40 minutes and 38 seconds. Both pieces contain four movements with contrasting musical characters and textural variations that enable the selection of equal numbers of homophonic and polyphonic sections of similar duration. Approval of all ethical and experimental procedures and protocols was granted by the Human Research Ethics Committee at Western Sydney University (protocol number H10487) and performed in line with the Declaration of Helsinki. Members of the Omega Ensemble were recruited in 2017. They provided written informed consent to participate in the study in the knowledge that individual participants would be identifiable because the data consisted of video recordings. A previous study using these videos [44] demonstrated that they are suitable for investigating the effects of textural variations on interpersonal coordination in musical ensemble performances from a natural concert setting. However, while our earlier analysis focused on a global measure of interpersonal coupling (phase-locking values), the current study focuses specifically on the directionality of coupling (Granger Causality).

Videos of the performances were recorded using a Canon 1DX camera body and a Canon EF 70–200 1:2.8 L zoom lens as QuickTime movies (.MOV) with dimensions 1920 × 1080 pixels at 25 frames per second. The full videos were split into parts based on textural annotations (homophonic and polyphonic) that were made in ELAN [49] based on musicological analysis of the published scores by author MB, which were checked by author PEK (both authors have university qualifications in musicology). We operationally defined musical phrases as sections of the pieces that were made up of coherent thematic material presented in a consistent texture. Alterations in both the thematic content and texture serve as phrase boundaries. Although the resulting phrase units are sometimes longer than those typically used in musicological analysis, they provide more suitable units for investigating how structural change affects the directionality of influence.

For each phrase, textural categorisation, the total number of performing instruments, and instrument roles (such as melody, counter melody, or harmonic accompaniment) were annotated in different layers within the ELAN interface. Data from each layer of the annotated ELAN file for each piece was extracted to extract video timecodes for each phrase and associated textural categorisation. The bar numbers from the score corresponding to each excerpt are provided in S1 Table (For Quintet: Brahms, J. (1892). Clarinet Quintet, Op. 115. N. Simrock.) and S2 Table (For Quartet: Borodin, A. (1884)). String Quartet No. 1. Hamburg: D. Rahter.). Based on this information, phrases that had consistent texture and predominantly all instruments playing throughout were selected for analysis. In Table 1, we present the selected phrases used for analysis in our study, and Fig 1 illustrates the specific positioning of musicians, arranged from left to right, along with appropriate labels. We made use of an equal number of homophonic and polyphonic phrases to have balanced textural classifications and similar durations (ranging from 15 to 38 s).

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Fig 1.

Images from the performance of the Quintet (Top Left) and the Quartet (Bottom Left), along with the outputs available with tracked key points using a pose estimation algorithm (Top Right and Bottom Right). The arrangement of musicians from left to right are labelled as m1 to m4 (Quartet: m1—violin1, m2—violin2, m3—viola, m4—cello) and m1 to m5 (Quintet: m1—violin1, m2—violin2, m3—viola, m4—cello, m5—clarinet).

https://doi.org/10.1371/journal.pone.0300663.g001

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Table 1. Summary statistics for all texturally consistent phrases in the Quintet and Quartet and the subset selected for analysis based on matching phrase duration.

https://doi.org/10.1371/journal.pone.0300663.t001

Computational framework and procedure

The motion data of each performer in the video recordings were extracted through a customised processing pipeline. Our previous study [44] developed the huSync computational framework utilised by this pipeline, which has been updated to include a new experimental and analytical approach that addresses the current research questions about information flow directionality. Fig 2 provides an overview of our approach, which includes four blocks, and is based on a well-established system for analysing body movements and gestures that convey expressiveness [50, 51]. The code and data pertinent to this study are openly accessible on Github. The repository contains fully commented code and detailed instructions to facilitate straightforward reproducibility. Additionally, the original huSync code is publicly accessible on Github [44].

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Fig 2. An illustration of the huSync computational framework and its system architecture as implemented in our study, showing the transition from video input signals to statistical analyses.

The accompanying images on the right delineate critical phases of the workflow and its intrinsic procedures.

https://doi.org/10.1371/journal.pone.0300663.g002

Our process was organised into a structured funnel of steps as follows:

1. After selecting videos based on our analysis criteria (see Table 1), we organised the recordings of the chosen phrases and readied them to be passed onto the second phase for feature extraction (see Fig 2(A)).
2. We use AlphaPose [52], a multi-person pose estimation algorithm to extracted motion and postural data from the chosen video recordings (see Fig 2(B)). The algorithm generates a JSON file containing the trajectory information of body parts sampled at 30 fps, with the nose key point serving as the best available representation of the head. We obtain kinematic information as a position time-series data for further analysis using the nose key point. We then used the data in the next step to quantify the directionality of influence among performers. To ensure the data are stationary, we applied first-order differencing to the log-transformed time series, a standard practice based on previous studies [53–55].
3. We employed the grangertest function from the lmtest package [56] in R Studio to evaluate the directionality of information flow. The function measures the predictive relationship between two time series (see Fig 2(C)). In our analysis, ‘X’ and ‘Y’ symbolise the time series of movements for any two given performers, respectively, and ‘order’ denotes the number of lags incorporated in the model (typically set to 1 by default). To illustrate, consider two arbitrarily chosen performers labeled as J and K; we utilised the grangertest function to investigate the extent to which the movement of performer J (X) predicts the movement of performer K (Y), and vice versa (X → Y and Y → X). This method allowed us to assess the presence of Granger causality within the pair’s interactions. It is important to note that our measurements within the video frame’s coordinates offer a parallel to each performer’s bodily movements due to the camera’s fixed orientation relative to the group. This means that the horizontal axis of our video analysis closely matches the natural horizontal axis of the performers’ body movements, thus serving as an approximate measure for lateral head movements. If the p-value yielded by the Granger test was less than .05 (our criterion for statistical significance), we rejected the null hypothesis and inferred a statistically significant predictive relationship between the two time series in the specified direction. To account for the delay between stimulus and response that is common in musical performances [27, 57], as well as in most behaviours, we performed GC tests for a lag of up to 1 second, setting the order to 30 (equal to the sampling rate) to test for multiple lag-lengths, and examine the nose key-point separately for each pair in both possible test directions (X → Y and Y → X). We extracted the GC values, including F and p values from each Granger test, and recorded the binary numbers [0, 1] indicating the outcome of each test. A value of 1 indicates a statistically significant predictive relationship (assumed to indicate influence or information flow) between the performers in the tested direction, while 0 indicates the absence of a significant predictive relationship in that direction. When GC tests in both directions were statistically significant for a given instrumentalist pair, a ‘1’ was coded for both directions. The main analyses were based on the proportion of significant GC tests among pairs of musicians for each phrase. Specifically, binary values indicating whether (1) or not (0) each Granger test was significant were averaged across all pairs of performers (separately for each test direction, X → Y and Y → X) for each phrase representing the two textures for each piece. These proportion data were then passed onto the next step to analyse the directionality of influence among co-performers to address our research questions.
4. In this stage (see Fig 2(D)), we carried out several statistical analyses on the GC values we obtained to address our hypothesis on the directionality of influence. We recorded results for all possible pairs of instrumentalists for each musical phrase. Note that the aim of these analyses was not to determine whether interaction is taking place at greater than chance levels (given that expert ensembles were intentionally coordinating highly rehearsed performances in a public concert setting), or whether GC can capture leader-follower relations in ensembles (since this has been previously demonstrated in a number of studies). Our question instead concerns the quality of interaction, specifically related to leadership relations, and whether these relations vary across conditions in relative terms. The results for all pairs for the Quintet can be found in S3 Table and those for the Quartet in S4 Table. In R, we conducted two primary statistical analyses [58, 59], one using a linear mixed-effects model (LMM) to test for general effects of musical texture on GC values, followed by an Analysis of Variance (ANOVA) to address directionality of influence effects related explicitly to melodic leadership. Musical piece (Brahms Quintet and Borodin Quartet) was included as a random effect in these analyses since we did not have hypotheses regarding the pieces (they comprised a convenience sample that were on the ensemble’s program at the time of data collection), but rather were interested effects that generalise beyond them. Shapiro-Wilk tests indicated that proportion data were not normally distributed in some conditions, even following arcsine transformation. Therefore, we report analyses on untransformed data (additional analyses with arcsin-transformed data yielded similar results). However, given these violations of the normality assumption, we also conducted binomial Generalised Linear Mixed Model (GLMM) analyses on raw binary GC values to check whether equivalent effects are obtained. Obtaining consistent outcomes for the LMM and GLMM analyses would provide evidence for the robustness and reliability of results. Such consistency was observed, and we only report the LMM and ANOVA results in the article (because these tests are standard and facilitate comparison with other studies in the literature). Due to the large number of GC tests run per musical excerpt (to assess exhaustive pairwise relations between instrumentalists), we addressed the issue of potential false positives by correcting for multiple comparisons using the Bonferroni method in supplementary analyses reported in S1 Appendix (see S1 Appendix). The results were overall consistent with those reported here.

General effect of musical texture

The hypothesis that interpersonal coupling would exhibit higher directionality in homophonic textures than polyphonic textures was tested by examining the proportion of instrumentalist pairs exhibiting statistically significant GC test values as a function of musical texture. The results in Fig 4(A) revealed a higher proportion of significant GC values for homophonic compared to polyphonic textures, thus confirming the hypothesis. To further evaluate this effect, we computed a LMM using the lme4 package in R [60], with texture as a fixed factor and piece, part, phrase, and direction of the GC test (within each pair of instrumentalists) as random effects. We included the piece as a random effect because our hypotheses were not specific to the two particular musical works featured but rather representative of Western chamber music in general.

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Fig 4.

(A—Left) Proportion of significant GC values for homophonic and polyphonic textures, averaged across the Quintet and Quartet; (B—Right) Proportion of significant GC values for four categories of musical roles adopted by co-performers, indicating the directionality of influence in the musical ensemble.

https://doi.org/10.1371/journal.pone.0300663.g004

A likelihood-ratio test indicated that the full model with texture provided a better fit to the data than a reduced model, including only the random effects (χ²(1) = 10.90, p <.001; Log Likelihood = 17.20 (full) vs 11.80 (reduced), AIC = -20.40 vs -11.50, BIC = -3.10 vs 3.37). The full model revealed a statistically significant effect of texture on GC values (Effect Estimate = -0.248, SE = 0.070, t = -3.54, p = 0.001, 95% CI [-0.388, -0.107]), indicating that the directionality of coupling was reliably higher in homophonic than polyphonic textures.

Specific effects of musical roles

The second analysis tested the hypothesis that the instrument playing the melody would exert greater influence on instrumentalists playing accompaniment material more than vice versa in homophonic textures. For this analysis, we classified the GC test outcomes based on the musical roles of the instrumentalists, which included melody, accompanying (other), or mixed (in polyphonic settings). We identified four categories of direction of influence, which can be seen in Fig 4(B): (1) melody instrument influencing accompanying instruments (Melody on Other), (2) accompanying instruments influencing the melody instrument (Other on Melody), (3) accompanying instruments influencing other accompanying instruments (Other on Other) in homophonic textures, and (4) mixed roles in polyphonic textures. GC values were entered into a LMM with the direction of influence category as a fixed factor and piece, part, and phrase as random effects. This full model provided a better fit to the data than a reduced model with only random effects, as indicated by a likelihood-ratio test (χ²(3) = 15.50, p < .01; Log Likelihood = -1.06 (full) vs -8.82 (reduced), AIC = 18.10 vs 27.60, BIC = 37.90 vs 40.00).

We conducted a follow-up ANOVA with three planned orthogonal contrasts to determine the specific effects of the direction of influence. These contrasts compared homophonic leadership categories combined (Melody on Other, Other on Melody, and Other on Other) versus the mixed polyphonic category (which is equivalent to the analysis reported above, but with different degrees of freedom), homophonic categories including a melody player (Melody on Other and Other on Melody) versus the homophonic category without a melody player (Other on Other), and the category reflecting melody instrument influence on other instruments (Melody on Other) versus accompanying instrument influence on the melody instrument (Other on Melody). This analysis indicated that GC values were significantly higher for homophonic than polyphonic textures t(45.1) = 2.849, p = .0066, 95% CI [0.212, 1.235] and for melody instrument influence on others than for other instrument influence on the melody instrument t(46.8) = 2.520, p = .015, 95% CI [0.027, 0.238]. This latter finding is consistent with our specific hypothesis about musical role. In addition, we found that GC values for homophonic pairings including a melody player were not significantly different from values for homophonic pairings without a melody player t(46.8) = −1.039, p = .304, 95% CI [-0.278, 0.089]. This post-hoc finding was not hypothesised but is informative to the extent that it indicates high directionality of influence among accompanying instrumentalists.

Links between musical texture and leadership

Regarding the effects of musical texture, finding greater directionality in coupling for homophonic textures, with information flowing from melody player to accompanying players more than vice versa, sheds light on our previous result that phase coupling was generally weaker in homophonic than polyphonic textures [44]. We previously argued that this finding could be due to coupling being more evenly distributed across all performers in polyphonic textures, whereas accompanying performers are mainly coupled to a single melodic leader in homophonic textures. Present results are generally consistent with interpretation, though the finding of directional influence among accompanying players in homophonic textures adds further nuance to the picture.

Overall, our present results suggest that coupling may be relaxed when leader-follower relations are demanded by musical structure. Such relaxation may enable leader-follower roles characterised by asymmetries in the degree to which co-performers engage in temporal adaptation and anticipation. During rhythmic interpersonal coordination, temporal adaptation processes keep interpersonal asynchronies in check by implementing reactive error correction and anticipatory processes to enable the prediction of upcoming event timing [31, 62]. Previous work on leader-follower timing suggests that greater adaptation and anticipation is observed in the follower than the leader at the level of instrumental movements [11, 36, 63, 64], and our results show that such asymmetries may generalise to ancillary body motion. Other movement features that could additionally have contributed to the present results include higher complexity of motion or greater need for self-regulation in polyphonic textures, similarly explored in studies probing effects of coordination challenges on ancillary motion [7, 34, 65]. While further investigation is necessary to confirm this using appropriate analytical techniques, the importance of body motion cues indicates that musical communication might engage coordination across multiple timescales and sensory modalities [30]. This engagement could potentially share characteristics with the multimodal nature of diverse communicative signals, as suggested by prior research [66, 67].

Questions remain about whether the effects of musical texture on leadership dynamics are affected by other aspects of musical structure, such as phrase position. Our previous study found that the effect of texture varied depending on position within the musical phrase. Coupling was stronger for polyphonic than homophonic textures at the beginning and middle portions of phrases but then decreased to similar levels at phrase endings. It was argued that leader-follower relations were adopted at phrase endings in polyphonic textures due to coordination challenges at these points. The tempo tends to slow down at phrase endings and successive phrases can be separated by silent pauses of variable duration [31]. Previous research has shown that the resulting uncertainty at phrase boundaries triggers increased communicative behavior, such as eye gaze and larger amplitude motion [17, 34, 68]. Related work has shown that leaders tend to make their timing more predictable by increasing the timing regularly and/or the amplitude of their movements [6, 10, 45, 69]. These behavioural modifications are instances of a more general phenomenon of coordination smoothers [70]. Based on these previous findings, direct influence from the melody player to accompanying players could increase at phrase endings. However, we did not investigate the effects of phrase position in the current study due to issues of time series length for reliable GC estimates (see Limitations and future work). Nevertheless, future work could investigate such effects with experimental manipulations applied over more extended musical sections (e.g., by using specially composed pieces) where coordination challenges are systematically varied. Examining patterns of information flow among accompanying players could be especially revealing in this context [71], given our finding that such interpersonal dynamics are present and measurable.

Another issue relevant to the mechanisms underlying the link between musical texture and leadership is whether the hierarchical distinction between melody and accompanying parts in homophonic textures automatically induces leader-follower relations. Previous work with piano duos has shown melody lead in keystroke asynchronies and body sway [7, 10], but the degree to which this emerges spontaneously or as a deliberate strategy still needs to be determined. The finding that leader-follower relations are more consistent at the level of keystrokes than body sway [7] suggests that the latter may serve strategic purposes or vary in order to display different expressive intentions. Relatedly, it has been found that the perception of auditory leader-follower relations, specifically the temporal lag of sound in accompanying versus melody parts, is susceptible to bottom-up effects of auditory streaming, indicating automatic processing [72], while head motion is sensitive to leadership instructions, suggesting strategic use of communicative ancillary movements [27]. In the present study, leadership was not explicitly instructed, which suggests that co-performers negotiated leadership based on structural constraints in the music. At the same time, the nature of such negotiation has proven difficult to pin down in laboratory studies [73]. Analysing verbal communication between group members during rehearsals in natural settings [74] is a promising future avenue to address such negotiation.

Regardless of whether leader-follower relations emerge spontaneously or through expressed intentions, attention plays a pivotal role in directing information flow. Ensemble performers, when employing “prioritised integrative attending,” balance the distribution of attention between their own parts and those of their co-performers, while also monitoring the overall ensemble sound [39]. Despite one’s part presumably being the highest priority [75] in the case of homophonic textures, accompanying players may allocate attentional resources disproportionally toward the melody part, as well as to parts played by other accompanying players. The melody player, while also emphasising their own part, might be receptive to these dynamics. These attentional strategies, whether intentionally implemented or automatically emergent, could influence interpersonal coupling directionally, given the established links between attention and sensory-motor coupling [31, 76, 77]. The bidirectional adjustments intrinsic to ensemble settings further add to the complexity of these interactions.

Benefits of studying natural coordination

Our study adds to the growing literature showing that body movement, including head motion, provides an valid metric to investigate interpersonal coordination and leadership dynamics in group settings [2, 27, 30]. Moreover, we demonstrate the potential of markerless motion capture technology to analyse such leader-follower dynamics in videos of music ensemble performances recorded during live concerts. Studying such performances is informative as they offer a naturalistic setting for musical communication. While this context presents an ecologically valid representation of ensemble dynamics, it may not be the only approach to investigating leadership in musical performances. Research on music and dance underscores the influence of performing “in situ” on communication quality. Factors like acoustics and audience presence can impact performers’ levels of motivation, attention, and arousal [78–80]. The nonverbal communication of emotions is a specific aspect that may benefit under these conditions, and the degree of enhancement may be reflected in increased information flow. Evidence for this link is seen in a study that found greater information flow in body sway when a trio were instructed to perform pieces with emotional expression than without emotion [81]. Heightened expressive intensity may, therefore, be associated with greater amplitude movements [82, 83] and the transmission of these cues between co-performers.

An additional advantage of using conventional video of ensemble performances is that it widens the potential pool of materials for analysis. Video-based analysis allows performances of other cultures to be studied when more specialised motion capture setups are not feasible [1], and therefore has the potential to overcome the prevailing WEIRD (Western, Educated, Industrialised, Rich, and Democratic societies) focus of research in psychology and neuroscience and subdisciplines such as music science [84]. A related practical benefit is that video is relatively neutral regarding group size, notwithstanding the issue of occlusion in large groups [44], and thus may help to accelerate the trend in the field to go beyond dyadic coordination to study groups of three or more performers [85]. An advantage of this upscaling, highlighted by the current results, is that it allowed us to examine the coupling between instrumentalists playing accompanying parts and interactions between melody and accompaniment. Our finding that the “other on other” influence was almost as strong as the “melody on other” influence in homophonic textures is noteworthy to the extent it captures the interaction between accompanying players. This finding suggests that to understand musical group dynamics, it is important to consider the interconnected network of the entire ensemble, in which subsets of performers function with some degree of independence [86]. Such independence is consistent with claims that it is necessary to balance the integration and segregation of psychological representations of “self” and “other” in ensemble performance [87–89], with the added nuance that there may be relatively high segregation between melody and accompaniment players, but a high degree of integration among the accompaniment players.

A further benefit of the current approach is conceptual. The observed effects of musical texture on leadership dynamics were not the result of an explicit experimental manipulation, nor were they post-hoc or data-driven findings. While these alternative approaches have particular strengths, experimental methods can lack ecological validity and data-driven findings can be challenging to interpret due to multiple possible contributing factors. Instead, our approach of segmenting the videoed performances based on musicological analysis of musical structure presents a middle ground that balances ecological naturalness and experimental control considerations. This feature highlights the benefit of using ensemble music from notated traditions, where the score functions as a script that constrains the actions of each performer while maintaining a degree of freedom for individual expression, as a domain to study the psychological dynamics of social interaction [3, 4].

Limitations and future work

While markerless motion analysis offers significant advantages, it also presents challenges, such as alterations in frame resolution, occlusion, and lighting conditions. Comparatively, marker-based systems yield less noisy data than their markerless counterparts despite their higher costs and potential for causing participant discomfort. This quality disparity might narrow the scope of research questions that can be effectively addressed using markerless techniques. However, these techniques provide broader opportunities for studying group interaction, offsetting their limitations to a certain extent. This trade-off is an important consideration in the choice between selecting marker-based and markerless motion analysis methods.

The huSync system, as currently designed, does not differentiate between lateral (side-to-side) and vertical (up-down) head movements. It leverages input from a multi-person human pose estimation (HPE) algorithm, and, based on the musicians’ arrangement within the scene, it solely utilises position time series along the x-axis (horizontal). However, with advancements in the HPE domain enabling data extraction in 3D space, there is potential for enhanced analysis by capturing more nuanced motion trajectories of participants in multiple directions. Research findings indicate that different types of head motion play different functional roles in ensemble music performance, exemplified by head nods being linked to timekeeping [34, 90]. Given this, it may be possible to enhance the performance analysis capabilities of future versions of HuSync by distinguishing between up-down and side-to-side head motion in relation to ensemble dynamics. The current version of HuSync also does not account for the encoding of emotional intent through head movements [91, 92]. Incorporating this aspect could provide a more nuanced understanding of interpersonal coordination in ensemble settings. It should nevertheless be acknowledged that, although we foreground head movements, they are not the exclusive, nor necessarily the paramount, metric for synchronisation in ensemble contexts.

While the current study and previous work demonstrate the capability of using GC with body motion data in providing insights on ensemble leadership dynamics, the relationship of these measures to the coordination of sounds warrants further attention. We did not include measures of auditory communication via musical sounds in our analysis, and therefore our measures focus exclusively on visual nonverbal communication exhibited by ancillary motion. Previous research has established close relations between ensemble coordination at the level of sounds and body motion [6, 7, 23] and our previous work found correspondences between overall synchrony and audio event density [44]. Although signal processing techniques exist for separating sound sources from mixed recordings [93, 94], and recent work has assessed ensemble synchrony directly from the overall group output using recurrence quantification analysis [95], the types of recordings we analysed are not well-suited for these techniques. Sound source separation can be problematic to the extent that instrumental timbres are similar (as is the case of the string sounds in our dataset). The recurrence-based technique has to date been used to distinguish between coordinated and deliberately uncoordinated sections of a musical piece (where the composer’s score instructs the performers to play at random in the uncoordinated section), rather than subtle differences in coordination, let alone leader-follower relations. An alternative viable avenue for future work is to investigate how listeners and observers perceive the directionality of effect, as has been done with overall measures of group coordination [2, 27, 65].

Another issue to address relates to the fact that the present study focused on naturalistic ensemble performance, and did not compare co-performers’ body motion to movement patterns during solo performance. Previous research has highlighted the relevance of body movements in solo performance for regulating performance and communicating musical structure and expression [82, 96]. Incorporating a solo performance condition in future studies could provide a baseline for understanding how these functions are fulfilled for different musical textures in ensemble settings [9, 97]. It also bears mention that we did not directly ascertain distinct leadership roles from the musicians but inferred them from the intrinsic musical structure. This means that related patterns of body motion could be influenced by technical demands related to coordination. A potential avenue for subsequent research is examining the extent to which homophonic textures allow for more liberal head movements due to diminished synchronisation demands.

A further limitation is that, for technical reasons (see Links between musical texture and leadership), we did not address the potential effects of position within phrases on leadership dynamics. GC assumes that time series data are stationary (i.e., free from the drift that makes summary statistics vary over time). A standard method of dealing with potential non-stationarity, higher-order differencing [53, 55], can result in the loss of information regarding serial dependencies and a reduction in sensitivity to directional information flow. Such losses may be disproportionately impactful in short time series when introducing lags to maximise the likelihood of capturing delays in information flow associated with leader-follower relations. Although it is justifiable to apply GC to short time series in contexts where there is no alternative, such as non-human animal communicative signalling, and when done in parallel with complementary methods [98], in our view, the appropriateness of doing so for human musical interaction requires further investigation. Ultimately, it will be beneficial to explore alternative metrics and modelling techniques to capture dynamics of the strength and directionality of coupling in musical groups [86, 99, 100].

Another limitation relates to sample size. Our study focuses on members of a professional ensemble performing in two constellations, a string quartet and a clarinet quintet. It is therefore best considered a proof-of-principle case study that takes advantage of the availability of data from a top international ensemble. This raises questions about the generality of findings and, in particular, how the effects of musical texture on leadership dynamics might be affected by factors such as the particular musical piece, as well as musical expertise and familiarity with co-performers. Effects of musical piece were not analysed in the current study because the quartet and quintet varied on a range of stylistic parameters beyond the number of performers involved. Examining these factors systematically across a series of studies will be necessary to disentangle their effects in future work.

Regarding familiarity, a study of piano duos found that familiarity with a co-performer part facilitates the coordination of ancillary head motion and body sway, however, not necessarily instrument keystrokes [23]. Another study found that incongruent performance goals (concerning tempo changes) were resolved with rehearsal via stylistic assimilation [73]. However, that study did not resolve how leader-follower dynamics played a role in this process. There is evidence that such relations may become less relevant with increasing familiarity. An analysis of repeat performances by a string quartet [71] revealed that, as co-performers converged on a common stylistic interpretation and their body sway became more similar across repeats, the overall degree of information flow (assessed by GC) decreased, possibly because performers came to rely on feedforward processes driven by internal models rather than actual feedback [42, 89, 101]. Our findings suggest that in future work, it would be worthwhile to examine overall information flow and the specific directionality of information flow under such conditions as a function of musical texture and performers’ roles as melody or accompanying players.