Lucas Klein

Graduate Student
McMaster Univ
Email author

Using Granger Causality to quantify information flow during a musical following task

Lucas Klein, Emily Wood, Dan Bosnyak, Laurel J. Trainor

Hi there,

Thanks for stopping by. My name is Lucas, I'm a graduate student at McMaster. I'm interested in group dynamics and improvisation in music performance. My latest project asks whether Granger causality (a measure of directed functional connectivity) can identify causal relationships between the amplitude envelopes of violin performances. Come visit my poster for the details.



Zoom Meeting ID: 771 3567 6790
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Using Granger Causality to quantify information flow during a musical following task

Lucas Klein, Emily Wood, Dan Bosnyak, Laurel J. Trainor

Group music-making requires non-verbal, interpersonal coordination. Large orchestras or bands rely on a conductor to know when and how to play, but in small ensembles, musicians must listen closely to their fellow musicians and match their playing by ear in order to create a cohesive collective musical product. Because all group members strive to play synchronously, they must anticipate what each performer will play next; if they wait to hear what sound is produced, the opportunity to play in synchrony will already have passed.

Previous research in our lab examined the role of body sway in string quartets. The body sway of secretly assigned leaders influenced that of followers as measured using Granger Causality. Granger Causality is a measure of functional directed connectivity between two time series; it quantifies how much the past of one time series can predict values of another above the beyond the predictive value of its own past. Interestingly, Chang et al. (2017) found that from the body sway time series of leaders to followers even when the musicians couldn’t see each other. This begs the question: is information that followers use to anticipate leaders’ playing also contained within the music itself?

To investigate this, we asked violinists to record themselves playing along with a recording while attempting to match it as accurately as possible in terms of expressive features like dynamic changes, expressive timing, vibrato, slurs, bowings, attack and decay, etc. These features determine the shape of a sound’s amplitude envelopes. We extracted amplitude envelopes from the musician’s performance and the recording they followed and converted them both to time series. Granger causality values from the recording to the performance a) were larger than for vice versa, and b) decreased over the course of 8 trials. As musicians became more familiar with the recording, the less predictive utility it had over their performance. The results confirm the efficacy of Granger causality to quantify causal relationships between amplitude envelopes of musical performances. They also shed light on possible planning processes that may facilitate coordination between players during group performances.