Musical Synchrony and Interpersonal Coordination

You are a researcher at an academy of music in Ontario. You would like to understand how musicians in a string quartet coordinate and synchronize with one another. To do this, you recruit two groups of musicians to the Large Interactive Virtual Environment laboratory (LIVELab, https://livelab.mcmaster.ca) at McMaster University where the musician’s live behavioural data can be recorded. Specifically, body sway was measured using an infrared optical motion capture system, which requires each musician to wear a felt cap with reflective markers.

The two groups of musicians are two string quartets. A string quartet consists of a first violinist (labeled as M1), a second violinist (M2), one violist (M3), and one cellist (M4). Both string quartets performed the same 2-minute musical excerpt three times (i.e., three trials). One string quartet performed the excerpt in the same room (the “sight” condition), while the other string quartet performed in a room where there were dividers between the musicians to prevent them from seeing one another (the “no sight” condition).

Body sway was measured as the change of position in millimeters in the anterior-posterior direction. The data can be found below. Measurements were taken at a frequency of 8hz (i.e., 8 time samples per second). A 2-minute recording will therefore yield 960 time sample data points per musician.

Musical synchrony and interpersonal coordination can be analyzed by comparing how similar a musician’s body sway time series is to another musician’s time series (i.e., a cross-correlation between two time series) as well as whether one musician’s time series is able to predict another musician’s time series (i.e., granger causality analysis between time series), which is also known as the information flow.

As a researcher of the academy of music, you would like to understand the following questions:

• Do the string quartets in both the sight and no-sight conditions become more synchronized with each successive trial?
• Is the string quartet in the sigh condition more synchronized than the string quartet in the no-sight condition?
• Does the first violinist time series “forecast” the time series of the other musicians?

To answer the above question, please complete the following statistical analyses:

1. Plot a line graph time series for each musician in each trial. Visually compare the line series between the quartets in the sight condition vs. the no-sight condition.

2. Convert the timeline data of each musician to z-scores.

3. Run a window cross-correlation analysis between the following pairs of musicians in each trial and in each condition (there are six possible pair combinations):

• • M1 and M2
  • M1 and M3
  • M1 and M4
  • M2 and M3
  • M2 and M4
  • M3 and M4

4. Run a granger causality analysis between the following pairs of musicians in each trial and each condition (there are 12 possible pair combinations)

• • M1 -> M2 and M2 <-M1
  • M1 -> M3 and M3 <- M1
  • M1 -> M4 and M4 <- M1
  • M2 -> M3 and M3 <- M2
  • M2 -> M4 and M4 <- M2
  • M3 -> M4 and M3 <- M3

Files to Download:

1. P09_dataset.csv

References for further reading

Wood, E. A., Chang, A., Bosnyak, D., Klein, L., Baraku, E., Dotov, D., & Trainor, L. J. (2022). Creating a shared musical interpretation: Changes in coordination dynamics while learning unfamiliar music together. Annals of the New York Academy of Sciences, 1516(1), 106-113.