1. Musical rhythm, bodily movement and the emergence of metre Martin Clayton Entrainment III, Milton Keynes 9 December 2005 with thanks to Udo Will, Devin McAuley, Laura Leante and Nikki Moran

2. Context Justin London, Hearing in Time (2004): our ability to follow musical metre is a specific instance of our capacity to entrain Ed Large, On synchronizing movements to music (Human Movement Science 19, 2000): “a model of meter perception is proposed in which a musical stimulus provides input to a pattern-forming dynamical system”

3. Outline of presentation Brief summary of analysis presented in the paper ‘Observing entrainment’ Discussion points arising

4. Video-based analysis Temporal processes are manifested in bodily movement as well as in sound waves Video-based observational analysis can be used to extract timing data from this movement What does analysis of video data tell us about the temporal organisation of performance? This example: north Indian jor, said to possess pulse but no metre

5. Veena Sahasrabuddhe – jor – Shree Rag

6. Observer plot – tanpura (string 1)

7. Periods – tanpura (string 1)

8. Tanpura patterns – average periods and phase relationships Singer (VS)Tanpura LTanpura R Ave Period (secs)2.032.723.00 Singer vs Tanpura L  no evidence of entrainment Singer vs Tanpura R stable phase relationship Tanpura R vs Tanpura L  no evidence of entrainment

9. Tanpura patterns – entrainment Analysis of the phase relationships between each pair of players suggests entrainment between the singer and tanpura R: the periods – of 2 sec and 3 sec respectively – alternate in and out of phase Tanpura L is not entrained to either of the others, but does realign her phase at a cadence

10. Observer plot – performers tapping

11. Periodicities – performers tapping

12. The average periods of both singer’s and harmonium player’s beat marking gestures are 1.35 sec in the middle portion and 0.67 sec at the beginning and end There is a consistent relationship between the phases of the two sets of beat markers, indicating entrainment.

13. Relative phase of singer’s beat markers and tanpura patterns The relative phase plots suggest only self-entrainment between the singer’s beat markers and her own tanpura playing, with periods in a 1:3 ratio Singer’s beat vs Singer’s tanpura stable phase relationship Singer’s beat vs Tanpura R  no evidence of entrainment Singer’s beat vs Tanpura L  no evidence of entrainment

14. Periodicities (sec) and their relationships Beat0.67 1:2 1:3 Beat1.35 VS tanpura2.03 2:3 Tanpura R3.00

15. Conclusion: entrainment and rhythmic structure Analysis of bodily movements in this jor extract reveal the existence of a complex hierarchical time organisation This emergent temporal organisation seems to be the result of unconscious entrainment processes occurring both within and between performers

16. Coda: Can this temporal organisation be heard? Tapping studies suggest that some expert listeners can perceive the faster beat (as tapped by the singer) even in the preceding (theoretically unpulsed) section However, others tap at different rates (in 3:2, 2:3 and 4:3 relationship to the above)… … and others deny the existence of any beat at all No evidence that the relationships between pulses – other than that between fast and slow beat markers – is either intentional or perceived by listeners

17. Discussion points What is the relationship between the organisation described here and musical metre? Does this study provide evidence that proto-metrical behaviour can emerge spontaneously when individuals engage in cooperative activities? If so, what are the conditions under which this organisation will emerge?