Group entrainment

Introduction

The purpose of his task is a test of group entrainment. There are two different groups, and the aim is to maximise entrainment and tempo stability within groups, while minimising entrainment and influence between groups.

Protocol

Participants are divided into two groups. In each group, a group leader has a metronome. The two metronomes are set to different (non-harmonic) tempi, e.g. 85 and 100 BPM. The game has three stages.

Stage 1:

• the groups huddle to different corners of the room (or separate rooms)

• group “leaders” have metronomes (mobile app, e.g. Metronome Beats by Stonekick) are started, and the groups are instructed to internalise and embody the beat; they can clap their hands, stomp feet, snap fingers, tap their chest etc., can “choose an instrument” they want to be in the ensemble/drum kit. They are therefore not limited to just tapping/clapping etc. on the beat, but can do so also off-beat, half tempo, double tempo etc., as long as the whole group maintains their original tempo. In the instructions, improvisation should be encouraged, but it is also good to remind the participants that keeping the pattern simple will help in keeping the tempo.

• in the first stage, there is no interaction between the groups.

Stage 2:

• the groups face the other group and increase the volume of their pattern. This starts the between-groups interaction.

• metronomes are turned off, and groups try to maintain their group cohesion and resist entraining with the other group.

Stage 3: 

• the groups start moving, as groups, around the room. The groups should improvise their movement patterns, but group leaders should gently ensure their group keeps moving all the time, and not just traverse once from their side of the room to the other.

Pilot data

Here we demonstrate some of the analyses that can be useful in analysing group synchrony. These results are from just one performance, to give a taste of the type of data that the game produces. In this game, there were 10 participants that had five accelerometers each; on their left and right wrists and ankles, and on their chests. These ten participants were divided into two teams. In addition to the "captured" participants, there were two other participants. in each team.  

For the following analysis, we have extracted a 10-second sample from approximately the middle of each phase. This allows us to see how the phases differ from each other and how e.g. synchrony within and between groups evolves over the course of the game. 

Data processing 

The acceleration data from the 50 sensors is synchronised, and re-sampled to have a constant sample rate of 100 Hz. The original data consists of accelerations along three axes, with positive and negative values depending on the direction of the acceleration. However, as the accelerometers change their orientation during the recording (e.g. a wrist sensor's X-axis can point to any direction depending on the posture of the participant), these directions are not relevant. Therefore we compute the absolute acceleration, that combines the three axes and only contains positive values. Thus, the data represents acceleration to any direction, or acceleration along the trajectory of movement.  This data is then low-pass filtered so that we can get rid of the high-frequency components that are mostly noise, e.g. generated because the accelerometers or their straps can move a bit etc. As in this analysis, we want to focus on gross movements and their synchrony, we set the threshold of the filter quite low, to 2 Hz, this should emphasise the movements that occur at the beat-level at the expense of faster movements and jitters, that might be interesting for other analyses.  

Amount of movement 

A plot of the raw accelerometer data from each phase shows that the amount of movement increases in every step as is expected. In the second phase, participants start performing their rhythm louder, which requires larger accelerations. In the third phase, participants are moving around the room, which of course results in more movement (larger accelerations) still (click on the figures to embiggen them).

Figure 1. Acceleration data from all sensors, in the three sample windows.  

Let us then take a look at an individual participant, and how their five sensors are related. 

Figure 2. Individual participant; feet 

In phases one and two, participants remain still and huddled in a circle. However, many participants were using their feet for the rhythms they were creating. Figure 2 shows data from one participant. They do a stepping motion, with acceleration peaks alternating between the two sensors. In the third phase, they are walking around the room. This seems to disturb the pattern somewhat, as especially the left foot is less consistent than in the second phase. Banking the basic beat to large body parts and large muscles is a good idea. Here we can also easily estimate the tempo from the figure. In the first and second phase, there are 7 peaks per foot, in the ten-second window. This indicates a tempo of 14 * 6 = 84 beats per minute. In the third phase, the tempo has increased somewhat, as there are now clearly 15 peaks, indicating a tempo of 90 bpm. This is of course a very rough measure, kin to estimating your HR by counting heartbeats for ten seconds and multiplying this by 6. Just as we have accurate HR-monitors, we can get a more accurate tempo estimates by using autocorrelation-based periodicity analysis.   

Figure 3: Hands and chest 

Looking at the movements of hands and chests, we can see that much of the increased movement in phase three comes actually from increased hand movements, at least for this participant. While different hands and feet tend to alternate in their movements, the chest seems to be the most consistent, and clearly periodic signal from the beginning to the end. It seems to capture the main beat and ignore the "frills". This is very clear for this participant but tends to be the case more generally. Therefore for a simple synchronisation analysis, using data from chest sensors is probably a good idea. 

Periodicity of movement 

Figure 4. Periodicity as measured from individual sensors of one participant

Using the autocorrelation method to estimate periodicities, we see that different limbs move in slightly different tempi. In the left panel on figure 4, the average periodicities for the three phases, for the sensors of one participant are plotted. These are the period lengths associated with the first peaks in the autocorrelation function, or the fastest rate for each limb. We can see that e.g. for the right hand, the average tempo gets slightly faster in each phase, same goes for chest. One option for From the right panel, where the autocorrelation functions themselves are plotted, we can see that the "clearest" periodicities (highest peaks) for this participant are mostly at double the metronome tempo, or at the 1.4 second area. The feet give the clearest periodical signals overall, and as they move in an alternating pattern (see figure 2), together they form a rhythm with one step / one beat. 

Synchronisation 

When analysing "togetherness" or "matching", or "adaptation", we could very simply look how close to each other's tempo people are (e.g. standard deviation of the tempi of the group), but that is a very vague and weak measure. We should use the more complete definition of synchronisation, according to which, two systems converge in phase and/or period when they sync. So, let's look at phase synchrony. 

First of all, as we concluded above, the chest markers seem to capture the different limb patterns and sum them up into a periodic signal that is quite stable and at the frequency of the metronome. Figure 5 shows the chest accelerations of all participants, divided to the three phases, and this time also the participants are divided into the two teams or groups. 

Figure 5. Chest sensor accelerations for groups 1 and 2 (the "competing teams"), samples from the three phases of the game

If we only have two systems (two dancers in this case), we could take the acceleration of their chests, for example, and use Hilbert transform to obtain their instantaneous phases, and then get their phase difference through subtraction and then see whether it stays stable or not. If the two are synchronised, they should maintain a stable phase difference (which does not have to be zero). But, as we have ten players in two teams, we need a different method. We can use the Kuramoto model, which describes collective synchronisation of a large number of independent oscillators, spontaneously synchronising their period and phase. The model explains how the oscillators sync, and we can also use it to quantify the level at which a group of oscillators have synchronised. This can be summarised in an order parameter, an index that ranges from 0 to 1, with 0 indicating disarray and 1 perfect sync. We calculated the order parameter for group 1, group 2, and everyone together. Figure 6 shows the average OP's for each of the three phases. 

Figure 6. Average order parameters for the different phases of the game

It seems that both groups reached a similar sync level in the first phase, but group 1 somehow lost it when the groups started communicating. In the third stage, the groups get closer in terms of sync, but both are weaker than in the first stage. But, let's look at how the OP evolves in time. 

Figure 7. Order parameter evolution

The data is smoothed with a long averaging window, as the actual parameter is quite noisy, as the participants' slightly different tempi make the phase relationships somewhat unstable. The peak values at the ends of each graph are a result of the smoothing. But, these smoothed curves show some interesting features. In the first phase, the fact that participants are moving very little means that the chest signals are small, this might contribute to the jittery order parameters. In the second phase, groups seem to have a more steady state, although as we already saw in the bar graph, group 1 seems to have a difficult time, while group 2 has a very good run. In the third phase, things evolve more gradually. While group 1 improves in the middle, it seems that group 2 then gets better and better, overtaking the group 1. And as the overall order also grows towards the end, following the path of group 2, it might be that group 2 have managed to pull at least some in group 1 to sync with them. Definitely some group 1 members seem to correlate highly with group 2 especially in phase 3.  

Conclusions 

In this example, we have walked through a possible group synchronisation analysis with some accelerometer data recorded from two groups playing a sync - resist sync game. Using the Kuramoto model and the order parameter as a group synchronisation metric yields interesting information about the evolution of group synchrony. The example analysis looks at just three short windows of the original data, and is just from one group, one game. However, the whole performance could be analysed using similar methods, and for example the average OP's could be compared across different games or different groups, to compare performance within (as in pre- and post-intervention) or between participant groups. 

References:

Acebrón JA, Bonilla LL, Vicente CJP, Ritort F, Spigler R. (2005). The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of modern physics. 77(1):137–185. 

Lucas, G., Clayton, M., & Leante, L. (2011). Inter-group entrainment in Afro-Brazilian Congado ritual. Empirical Musicology Review, 6(2), 75–102.

Oullier O, de Guzman GC, Jantzen KJ, Lagarde J, Kelso JAS. (2008). Social coordination dynamics: Measuring human bonding. Social neuroscience. 3(2):178–192. 

Spiro, N. & Himberg, T. (2012). Empathy and Resisting Entrainment: Mapping the dimensions of pairwise rhythmic interaction. 16th Annual Symposium for Music Scholars in Finland, Jyväskylä, Finland.