A simple mathematical equation explains how people synchronize when tapping out rhythms together

12. November 2019

When two people tap out a simple rhythm together, they choose different strategies to synchronize. Sometimes one person becomes a leader, and the other becomes a follower, and sometimes there is no leader at all. These strategies can be explained using a simple mathematical equation, shown by researchers from the DNRF’s Center for Music in the Brain at Aarhus University. The study was published in the scientific journal PLOS Computational Biology.

Musicians play on African drums.
Musicians play on African drums. Photo: Lee Pigott/Unsplash

Most people interact with others daily, and often, we effortlessly synchronize our movements with others’ movements across various kinds of interactions. However, a rather simple interaction such as tapping out a rhythm with others is shown to be quite complex.

According to a new study from the DNRF’s Center for Music in the Brain (MIB) at Aarhus University, there are fundamental strategies as to how people synchronize when tapping out rhythms together. The answer lies in a simple mathematical equation. Behind the study are post-doc Ole Heggli, post-doc Joana Cabral, Professor Morten Kringelbach, and head of center Peter Vuust from MIB, together with Ivana Konvalinka, assistant professor at the Technical University of Denmark. The study was recently published in the scientific journal PLOS Computational Biology.

Two different strategies can be used to coordinate movements when two people tap out the same rhythm together. For instance, one person can choose to be a leader and thereby force the other person to be a follower. Or, both persons can choose to follow each other at the same time.

“In very rare cases we may also see two persons both trying to be a leader, for instance, by pairing a drummer with another drummer,” said Heggli, who is the lead author behind the study.

According to the researchers, these different synchronization strategies occur because of differences in how people decode and use the information coming from the person with whom they are tapping out a rhythm. To test this hypothesis, the research team from MIB and the Technical University of Denmark built a computer model using a simple mathematical equation using so-called coupled oscillators. Coupled oscillations are used to describe repetitive processes, such as the movement of your finger when tapping out a rhythm. With this computer model, the research team made a comparative study where data created by the model were compared with data from real people tapping together.

“The key difference between previous studies and this one is that we used two oscillators for each person, rather than just one,” said post-doc Heggli.

Using data from more than one person, the researchers constructed a model that more precisely reproduces what happens in the brain when people tap together.

The results from the interdisciplinary study showed that the different synchronization strategies vary depending on how people treat information coming from one another. If both parts are attentive to each other, they tend to follow one another simultaneously, whereas a so-called leader-follower interaction occurs when one person is not attentive to the other.

The results are important in providing more information on human interaction and how we can improve them in the future.

Read the scientific article from MIB in PLOS Computational Biology here