1. Sculpting musical sound David N Lee Perception-Movement-Action Research Centre University of Edinburgh Talk given at Shaping Music in Performance Workshop King’s College, London 10-11 March 2010

2. Summary of talk A theory of action control and applications to understanding moving and making music

3. Action-gaps Acting requires controlling action-gaps between current state and goal state Controlling action-gaps requires prospective sensory and intrinsic information

5. Multiple action gaps Acting generally requires controlling several action-gaps contemporaneously

7. τ The principal informational variable for controlling action-gaps is τ τ is the time-to-closure (or the time-from- closure) of an action-gap at the current rate of closing (or opening) τ of action-gap, X, equals

8. Properties of τ Action-time variable Prospective informational variable Universal variable Directly perceptible

10. τ- coupling Foundation for controlling action gaps Means the ratio of the τ s of two gaps is constant

11.  can be directly sensed through  -coupling

12. Intrinsic guiding gaps Should be simple and sufficient Should be rooted in ecological physics

13. (a) TauD guidance TauG guidance x Normalized time

15. How a gap changes under tauG - guidance

16. TauG-guidance parameters K = ‘oomph’ A = amplitude T = duration

17. tauG ‘kinetic melodies’ in the nervous system

18. Examples of tauG guidance

19. m-g

20. TauG-guidance of sucking in neonates

22. One day old infant gesture

23. TauG-guidance of pitch-glide singing Va---ne 1 s pitch (Hz)

25. TauG-guidance of attacking intensity- glide when bowing

26. Future directions We have shown how, at the few hundred millisecond level, the shape of a musical sound (pitch and intensity glides) mirrors the shape of the movement that produces it. Both follow the same tauG mathematical formula. We are now moving in two new directions: to the sub-millisecond level to explore how sound waves are sculpted to generate the timbre or quality of sound, and to the supra- second level to explore how the shapes of musical phrases are sculpted. Preliminary results suggest that tauG also features at these two levels.

27. References Schogler, B., Pepping, G-J. & Lee, D. N. (2008). TauG-guidance of transients in expressive musical performance. Experimental Brain Research, 198, 361- 372. Lee, D. N., & Schogler, B. (2009). Tau in musical expression. In S. Malloch & C. Trevarthen (Eds.), Communicative Musicality: Exploring the basis of human companionship. Oxford: Oxford U. P. Lee, D. N. (2009). General Tau Theory: evolution to date. Special Issue: Landmarks in Perception. Perception, 38, 837-858.