Intra‐ and interbrain synchrony and hyperbrain network dynamics of a guitarist quartet and its audience during a concert

Playing music in a concert represents a multilevel interaction between musicians and the audience, where interbrain synchronization might play an essential role. Here, we simultaneously recorded electroencephalographs (EEGs) from the brains of eight people during a concert: a quartet of professional guitarists and four participants in the audience. Using phase synchronization analyses between EEG signals within and between brains, we constructed hyperbrain networks, comprising synchronized brain activity across the eight brains, and analyzed them using a graph‐theoretical approach. We found that strengths within and between brains in the delta band were higher in the quartet than in the public. Within‐brain strengths were higher and between‐brain strengths were lower in the music than in the applause condition, both particularly in the quartet group. These changes in coupling strength were accompanied by corresponding changes in the hyperbrain network topology, which were also frequency‐specific. Moreover, the network topology and the dynamical structure of guitar sounds showed specific guitar–brain, guitar–guitar, and brain–brain directional associations, indicating multilevel dynamics with upward and downward causation. Finally, the hyperbrain networks exhibit modular structures that were more stable during music performance than during applause. Our findings illustrate complex hyperbrain network interactions in a quartet and its audience during a concert.


INTRODUCTION
Making music in a concert represents a social interaction in which the musicians communicate with each other and with their audience.
in group interaction has been particularly clearly demonstrated in a study with a quartet of guitarists. 13 Specific interbrain or rather hyperbrain connectivity structures were shown to emerge during such an interaction. The most intriguing aspect of these structures is that each brain always has to communicate with three other brains and, therefore, develops different configurations depending on the interaction conditions. 13 In the current study, we examine neural group dynamics between eight brains, with two types or two groups of interaction: four guitarists playing in a quartet and four audience members, representing active and passive interactions, respectively. Since we study two different situations during the concert, namely, the music performance and the applause, active and passive interactions alternate between the groups, with the audience becoming active during the applause and the musicians being rather passive in this case. We expected that active interaction would increase the coupling strength compared to the passive form. In electroencephalographic (EEG) hyperscanning studies, it has been shown that the increase in interbrain synchrony in the audience during live music compared to baseline was dependent on emotional pleasure and closeness 22 as well as on the number of people sharing the pleasure and its strength. 23 The same pleasure and a corresponding increase in the interbrain synchrony can also be expected in the musicians, especially during applause. It is well known that hand clapping as an audience expression of appreciation for a good musical performance functions as a social self-organizing system that mostly exhibits specific dynamics with different phases (e.g., fast clapping, synchronization, and slipping back to the fast clapping) and corresponds to the trade-off between optimal synchronization and maximal applause intensity. 20,24,25 However, the neural mechanisms of clapping or applause remain unexplored. Thus, related to our previous study of the same guitarist quartet, which revealed complex hyperbrain network (HBN) interactions, 13 this study aims to demonstrate how the HBN structure extends to the audience and how musician and audience components of this structure communicate with each other during two different situations during a concert.
Previous research on neural synchrony in musical interaction has shown that intra-and interbrain synchronization is particularly enhanced during periods that put high demands on musical coordination. 7,[9][10][11][12][13]15 Moreover, it has been shown that there is a specific coupling between musicians' brains and musical instruments. 8,10,11,26 In this context, it can be expected that such coupling may also occur between audience members' brains and the instruments. However, this should not substantiate the claim that synchronization between brains is simply a result of a common perceptual input and/or a common motor output (cf. Ref. 19). As recently shown in a hyperscanning study of piano duets, keeping sensory input and movements comparable across conditions as well as during musical pauses without sensory input or movement, interbrain synchrony does not merely depend on shared sensorimotor impact but can also emerge endogenously, from aligned cognitive processes supporting social interaction. 8 Nevertheless, this relationship between brains and instruments provides important evidence that interbrain synchrony has a specific reference to the behavioral actions of musicians (cf. Refs. 9, 10, and 19).
It is also well known that music is generally self-similar, whereby structure and repetition are general features of nearly all music.
The concept of self-similarity in music is fundamental for capturing structural properties of music recordings and is provided by the self-similarity matrix (SSM) approach. 27 The repetition blocks in SSM resemble each other with respect to certain aspects, such as melody, harmony, or rhythm. Through such recurring patterns, a temporal relationship is established within the piece that can be traced by the listener and evoke a sense of familiarity and musical understanding.
Here, we use this concept to investigate the relationships between musical and brain structures in their dynamic interdependency.
Finally, a number of studies have shown that HBNs, comprising intra-and interbrain connectivity, exhibit specific modular organization during music playing and that the most important characteristic of this organization is the existence of so-called hyperbrain modules sharing electrodes or nodes from two or more brains, with strong connections or information flow within the modules and weak connections or information flow between the modules. [11][12][13]15 In a previous guitar quartet study, the HBN consisting of four guitarists' brains was shown to be a dynamic structure with nonstationary coupling dynamics and network architecture. 13 Such networks are highly adaptive to external situations requiring different network states. Moreover, Müller et al. 19 suggested a hyperbrain cell assembly hypothesis that states that cell assemblies can be formed not only within but also between brains, following roughly the same rules as within brains. The hyperbrain cell assembly, comprising the within-and between-brain connections, can lead to the joint firing of neuronal elements in these brains or in the common HBN or cell assembly. It has also been suggested that the hyperbrain module or community can be considered as a prototype of such a hyperbrain cell assembly and that this assembly should gain precedence during repeated joint activity. 19 In this context, it was hypothesized that HBNs comprising eight brains of quartet and audience members would exhibit modular organization, with hyperbrain modules or communities sharing nodes in several brains. Since musical performance is more structured than applause, it was assumed that the modular organization of the HBNs during musical performance would be more stable and less variable in their temporal dynamics than during applause. (participants E and G). Audience members E and G were familiar with each other and also knew the members of the quartet. Participants F and H were not acquainted with anyone. We only recorded four participants from the audience, as we wanted to keep the number of musicians and listeners equal with respect to common network analyses. The Ethics Committee of the Max Planck Institute for Human Development approved the study, and it was performed in accordance with the ethical standards laid down in the 1964 Declaration of Helsinki. All participants volunteered for this experiment and gave their written informed consent prior to their inclusion in the study.

Procedure and data acquisition and analysis
The concert study took place in the auditorium of the Max Planck Institute for Human Development with an audience of more than 150 people (see Figure S1 and Video S1 for details). The program of the concert consisted of eight different pieces of music for classical gui- The average number of removed ICA components was 8.6 (2.0) across participants. Thereafter, artifacts from head and body movements were rejected by visual inspection. Preprocessing of the EEG data (e.g., artifact correction and rejection) was performed using Brain Vision Analyzer 2.2 (Brain Products). The EEG was resampled at 1000 Hz and divided into 20-s epochs indicating different sequences of interest (SOIs). Three SOIs in each music piece and three SOIs during the applause, free of artifacts for all eight participants, were analyzed in terms of intra-and interbrain synchronization. For these purposes, the SOIs were band-pass filtered (using an elliptic infinite impulse response filter) within the four frequency bands: delta (0.5-4 Hz), theta (4)(5)(6)(7)(8), alpha (8)(9)(10)(11)(12)(13)(14), and beta (14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30). Thereafter, the fast Hilbert transform was applied to extract the phase of the signals in the given frequency bands, which were used for the calculation of phase synchronization by means of the Phase Synchronization Index (PSI).
The PSI was determined by the formula: where

Network construction and graph-theoretical approach measures
A graph-theoretical approach (GTA) was used to investigate HBN con- In order to fulfill the two criteria, we set the cost level to 20%, which allows for the investigation of sparse economical networks, whereby the connectivity threshold was always higher than the significance level determined by the surrogate data procedure, that is, networks at this cost or sparsity level always included significant connections and had the same number of edges (see Supplementary Materials for details). This allowed a more accurate examination of the network topology in the different musical pieces and musical sequences or SOIs.

Network and statistical analysis
The aforementioned cost level of 20% was applied to the common HBN, including all electrodes of all eight brains (224 nodes in total) in the quartet (QUA) and in the public audience (PUB). To examine the HBN topology, we determined within-and between-brain strengths (SwB and SbB, respectively), the clustering coefficient (CC), characteristic path length (CPL), local efficiency (E local ), and global efficiency (E global ). The SwB for node i was calculated as a sum of weights to this node from all other nodes within the particular brain and the Besides the common HBN analyses, comprising nodes from all eight brains, we also conducted dual HBN analyses based on all possible pairwise combinations (28 in total) between all quartet and public audience participants. There were six quartet-quartet (Q-Q), six public-public (P-P), and 16 quartet-public (Q-P) pairs, or HBNs with 56 nodes each (see Figure 1A,B for details). One can see that in contrast to the common HBN analyses, we can differentiate the impact of different connection types (i.e., Q-Q, Q-P, and P-P) here. For each of these dual HBNs, we determined the same network topology measures: SwB, SbB, CC, CPL, E local , and E global . All these measures were determined for each time window and node, and then prepared similarly as above. The data were analyzed using a three-way repeated measures ANOVA with a between-subject factor Group (Q-Q, P-P, and Q-P) and a withinsubject factors Condition (MU vs. AP) and Site (F, C, P, LT, and RT). When necessary, Greenhouse-Geisser epsilons were applied in all ANOVAs for nonsphericity correction. The Scheffé test was employed for the post-hoc testing of group differences. All statistical analyses were carried out using IBM SPSS Statistics 23.0 (SPSS Inc., Chicago, IL, USA). Furthermore, we investigated the relationships between guitar sounds and the common HBN topology indices. For these purposes, we first calculated the root mean square of the guitar signals and then constructed self-similarity matrices for each of the guitar sounds by using the moving window approach, just as this was used for the calculation of the connectivity and topology indices in the case of EEG signals R and GC were determined for the four topology measures in the delta frequency band: SwB, SbB, E local , and E global . We limited our analyses to these four topology measures because the E local and E global represent network topology properties that are relatively similar to CC and CPL, but unlike the last, are equidirectional. The delta band was chosen because it was only here that the between-brain connections showed significant differences between groups and conditions. In addition to MSD-NTD relationships, MSD-MSD and NTD-NTD were also captured by R and GC indices. The same analyses were then performed with individual music pieces comprising only 1365 data points.

Common HBN topology
Results of the ANOVAs for the six GTA metrics across the four frequency bands are collated in Table 1 and Figures 2 and 3. The most significant differences, besides the factor Site, which indicates topology variation across different electrode sites, were found for the factor Condition and its interaction with the factor Group. The main effect Group was significant only for the three GTA measures (SbB, CPL, and E global ) in the delta band, whereby SbB and E global were higher and CPL correspondingly shorter in QUA than in PUB (see Figure 2 for details). Interestingly, SwB was higher and SbB was lower in the MU as compared to the AP condition, both above all in the QUA group. In addition, the CPL was shorter during AP than during MU, especially in the QUA group and particularly at the frontocentral and left-temporal sites  (see Figure 2 for details). The other three GTA measures (SwB, CC, and E local ) in the theta, alpha, and partly also in the beta band, reflecting local processes and processes within the brains, were higher during MU than during AP, especially in the QUA group (see Figure 3 and Table 1 for details). As common HBN analyses cannot provide information on which relationships (Q-Q, P-P, or Q-P) play a more important role, dual analyses were conducted to clarify this issue.

Dual HBN topology
Results of a three-way repeated measures ANOVAs with a betweensubject factor Group (Q-Q, P-P, and Q-P) and a within-subject factors Condition (MU vs. AP) and Site (F, C, P, LT, and RT) for the six GTA measures are presented in Table 2

Relationships between guitar sound structures and the common HBN topology
The results of these analyses at the 99% significance level (p < 0.01) are presented in Figure 5. As can be seen, R and GC were expectedly    Figure 7A under the similarity matrices) by paired t-test showed the significantly lowest similarity during applause in comparison to music conditions (all ps < 0.001, Bonferroni-corrected).

Modular organization of the common HBNs and its stability
As shown in Figure 7B, there were also significant differences between music pieces, indicating different similarity or stability of community structures within these pieces (all ps < 0.001). We also calculated F I G U R E 6 Exemplary representation of the hyperbrain modularity or community structure with intra-and interbrain connectivity.
(A) Within-brain connectivity maps and topological distribution of strengths within the eight brains. (B) Between-brain connectivity maps and topological distribution of strengths for the between-brain connections. The strength of the nodes (sum of all outgoing connections) in the brain connectivity maps is coded by circle size, and the strength of edges is coded by line thickness. The different modules are coded by color. Please note that only the strongest within-and between-brain connections are displayed. The guitarists' brains are denoted A, B, C, and D, and the audience members' brains are denoted E, F, G, and H. modularity values, providing a statistic that quantifies the degree to which the network may be subdivided into clearly delineated groups or modules. As shown in Figure 7C, the modularity values show a similar pattern of differences between conditions as the similarity values, with a significantly lowest modularity during applause as compared to music conditions (all ps < 0.001). This indicates that the partitioning of the HBNs into modules or communities was more stable during music conditions than during applause. There were also significant differences between music conditions or pieces (all ps < 0.01; see Figure 7C for details). Here, it should be noted that all conditions (also the AP condition) showed high modularity values (more than 0.28), indicating a good partition of HBNs into modules or communities.

F I G U R E 7
Similarity and modularity of community structures within the three music pieces and during applause. (A) Similarity matrices determined by MI between all community structures within the three music pieces and during the applause. Community structures were calculated for each time window across three SOIs (273 time windows in total). Under the matrices, mean MI values averaged across the rows are presented. (B) Box plots of the mean MI values for the three music piece and applause conditions. (C) Box plots of the modularity values for the three music piece and applause conditions. Modularity values were determined for each community structure as a statistic for the degree to which the common HBN may be subdivided into clearly delineated groups or modules. Note that the differences in the similarity (MI) and modularity (Q) were highly significant (p < 0.001) between all four conditions.

DISCUSSION
The primary objective of this study was to investigate the intra-and interbrain dynamics and hyperbrain architecture and dynamics emerging in a quartet of guitarists and the audience during a concert. The main findings are that: (1) practically all GTA measures in the common and especially in the dual HBNs showed significant differences between the quartet and audience members during music performance and the applause, which were also frequency-specific in the common HBNs; (2) in the delta band, SwB was higher and SbB was lower in the MU as compared to the AP condition, both mostly in the QUA group and for the Q-Q relations; (3) guitar sounds not only correlated with, or predicted each other, but this correlation or prediction in the Granger sense also concerned guitar-brain and brain-brain relations with respect to the dynamics of corresponding structures; and (4) the HBNs exhibit modular structures with hyperbrain modules or communities, comprising nodes across several brains, and the dynamics of these community structures was much more stable during the music performance than during the applause.
In the common HBN analyses, the factor Group was significant for SbB, CPL, and E global (only in the delta band), indicating higher SbB and E global and shorter CPL in the QUA as compared to the PUB group. In contrast, the Condition factor and the Group-by-Condition interaction were significant for SwB, CC, and E local in the theta and alpha frequency ranges, which were higher in the MU than in the AP condition, especially in the QUA group (see Figure 3). This discrepancy indicates that the low frequency (delta band) is responsible for group differences with respect to the interbrain connectivity and HBN integration, whereas the faster theta and alpha frequencies support condition differences with respect to the intrabrain connectivity and HBN segregation. Thus, the common HBNs have two different modes (i.e., global with enhanced interbrain connectivity and network integration, and local with strong intrabrain connectivity and network segregation), which are working at different frequencies with respect to group and condition differences. Interestingly, the factor Condition was also significant for SbB and CPL in the delta band, but in contrast to SwB, SbB was higher and CPL was shorter in the AP as compared to the MU condition. Thus, the delta band is also sensitive to condition differences but in different way than local processes at faster theta and alpha frequencies, which were higher in MU than AP condition. This differentiation for frequency and topology measures or modes (local vs. global) is very interesting and probably characteristic for HBNs with different functional units (e.g., musicians and audience).
As mentioned above, the SbB in the common HBN includes Q-Q and Q-P connections in the case of the QUA group and P-P and Q-P connections in the case of the PUB group. Accordingly, the dual HBN analyses, which allowed us to separate these three types of connections (i.e., Q-Q, P-P, and Q-P), showed generally higher SbB (also only in the delta band) in the Q-Q than in the Q-P and P-P groups, and higher SbB in the Q-P than in the P-P group. Like the common HBNs, SbB in the dual HBNs was also lower in the MU than in the AP condition, especially in the Q-Q group. In contrast to this and to the common HBN analyses, CPL in the dual networks was shorter in the MU than in the AP condition, especially in the Q-P and P-P dual networks. In addition, other GTA measures (SwB, CC, E local , and E global ) were highest in the Q-Q and lowest in the P-P groups, and generally higher during the music performance than during the applause, especially in the Q-Q and Q-P dual networks. Moreover, this relationship also holds for other frequency bands (i.e., theta, alpha, and beta). All this suggests that active interaction (making music) evokes stronger connections within and between brains in musicians during a concert than in the audience and changes the topology of the HBNs toward the small-world networks with higher segregation (higher CC and E local ) and integration (shorter CPL and higher E global ) of neural processes. There is neurophysiological evidence that neural networks generally exhibit "small-world" structures (i.e., high levels of clustering and short path lengths) that support efficient information segregation and integration with low energy and wiring costs as well as a high rate of information transmission and communication. [35][36][37][38] The small-world structure of HBNs suggests a more efficient and effective communication between brains when interaction demands are higher. This confirms the findings made previously in a guitarist quartet 13 and guitarist duets, 12,15 which showed small-world properties of the HBNs and an increase in small-worldness with higher frequency. However, it has also been shown that low frequencies (e.g., delta and theta) play an essential role in interbrain dynamics. 9,10,12,13,15 Interestingly, significant differences between the groups and conditions in the SbB (both in common and dual networks) were found only in the delta band, supporting the previous findings. In EEG hyperscanning studies, it has been shown that an increase in interbrain synchrony in an audience during live music was dependent on emotional pleasure and closeness as well as on the number of people sharing pleasure and its strength. 22,23 Whether the greater pleasure of musicians than of audience members or a certain degree of asynchrony in the audience during applause or other factors are responsible for the differences in SbB at the delta frequency between musicians and the audience during applause remains to be seen. However, it is obvious that musicians and listeners behave differently during the concert and that this influences the different brain The observed significant correlation between guitar sounds was not surprising, even though the guitarists played different parts of the music. However, the musical structures (MSD) determined by the SSMs were relatively similar and, therefore, showed strong correlations. However, the correlation between the MSD of guitar sounds and the NTD of the guitarists' and audience members' brains was relatively low, but did reach the significance level in some cases. Most interestingly, MSD and NTD predicted each other in a Granger sense, especially in the case of SwB, but also in the case of other topology measures. A synchronization between brains and instruments was reported previously. 8,10,11,26 Here, we show another level of synchrony or prediction, where structures of music (MSD) and brain dynamics (NTD) are related to each other or predict each other, and this concerns not only the guitarists' but also the audience members' brains. In the hyperscanning study on guitarist duets with a directed synchronization measure, it has been shown that the relations between brains and instruments are unidirectional or bidirectional. 11 As suggested, "the instrument's sound is a result of the musician's behavior, which is based on sensorimotor synchronization and action. At the same time, this sound influences the behavior of musicians through auditory sensory pathways and is in this sense an actor" (Müller and Lindenberger 11 ).
Moreover, the directional coupling from brains to instruments can be considered as an anticipation process, predicting a specific or expected It has been suggested that hyperbrain modules can be considered as a prototype of so-called hyperbrain cell assemblies and that hyperbrain cell assemblies that are formed during an interaction should gain precedence during repeated joint activity. 19 Here, we have shown that the hyperbrain community structure is more stable in the music condition than during applause. This can indicate that some hyperbrain cell assemblies or a specific configuration of brain activity are favored during music and occur repeatedly, thus contributing a certain stability to the aforementioned hyperbrain community structures emerging across time. Such recovery of a specific neural activity configuration can be induced via a self-similar musical structure that evokes certain self-similarity in the HBNs or cell assemblies that can be reinforced or modulated by the emotional pleasure of musicians and audience members. [41][42][43] The concept of recurrence is prominent in many disciplines or approaches and is strictly related to the temporal evolution of complex dynamical systems indicating periodic behavior. 39,44,45 Applause is definitely a periodic and recurrent action but is, presumably, not as well organized as making music or listening to it, which might explain the higher variability (or lower stability) of the hyperbrain community structure across time in the AP as compared to the MU condition.
The results of this study may have implications for real-world music playing and group interaction. As proposed by Hasson and Frith,46 ". . . interactions with other members of a group can fundamentally shape the way we behave in the world, and alignment is a ubiquitous feature of such interactions." Our study shows that such an alignment presupposes different types of synchronization and network dynamics with different modes for different parts of the system or HBN (e.g., musicians and/or audience), depending on the situation (music making or applause). As noted by D'Ausilio et al., 3 "group-level musical coordination can be considered as a microcosm of social interaction.
Individual musicians function as processing units within a complex dynamical system (the ensemble) whose goal is to communicate musical meaning (which is aesthetic and affective in nature) to an audience.
Information flows simultaneously to and from each unit, and the system as a whole relies upon predictive models and adaptive mechanisms to meet the real-time demands of interpersonal coordination. As in more general forms of social interaction, co-performers behave in complex but formalized (rule-based) ways that are constrained by the tools they use (musical instruments), conventions (genre-specific performance styles and leader-follower roles), and often a script (the musical score)." The results of our study confirm this view and suggest some further implications in terms of HBN dynamics and their relations to instruments or instrument sounds during a real concert.

LIMITATIONS
The present study has limitations and leaves room for questions to be addressed in future research. First, the sample size of our study was small, which has implications for generalizability. However, the main patterns of HBN connectivity and network organization were comparable across different musical pieces and frequency bands.
Second, our analyses were limited to phase synchronization within single-frequency bands. Cross-frequency coupling is likely to provide further information about functionally relevant network properties and NTD. 19,47,48 Thus, further sophisticated research is needed to shed light on neuronal mechanisms of concert interaction and behavior.

CONCLUSION
Our results showed that intra-and interbrain synchrony and resulting HBN topology differ in the quartet and audience members during the music performance and applause in a concert of a quartet. The HBN topology and MSD of guitar sounds showed specific guitar-brain, guitar-guitar, and brain-brain directional associations, suggesting multilevel dynamics with upward and downward causation. The HBN architecture exhibits a modular organization with hyperbrain modules or communities that are more stable during music performance than during applause. Thus, observation of dynamic changes in synchronization and network architecture seems to be essential to achieve a profound understanding of group dynamics and social interaction.