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Sculpting musical sound
David N LeePerception-Movement-Action Research Centre
University of Edinburgh
Talk given atShaping Music in Performance Workshop
King’s College, London10-11 March 2010
Summary of talk
A theory of action controland
applications to understandingmoving
andmaking music
Action-gaps
• Acting requires controlling action-gaps between current state and goal state
• Controlling action-gaps requires prospective sensory and intrinsic information
Multiple action gaps
• Acting generally requires controlling several action-gaps contemporaneously
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 X / &X
Properties of τ
• Action-time variable• Prospective informational variable• Universal variable• Directly perceptible
τ-coupling
• Foundation for controlling action gaps
• Means the ratio of the τ s of two gaps is constant
τ can be directly sensed through τ-coupling
Intrinsic guiding gaps
• Should be simple and sufficient• Should be rooted in ecological physics
(a)
How a gap changes undertauG - guidance
TauG-guidance parameters
K = ‘oomph’ A = amplitudeT = duration
tauG ‘kinetic melodies’ in the nervous system
Examples of tauG guidance
m-g
m-g
TauG-guidance of sucking in neonates
-10
-8
-6
-4
-2
0
-5 -4 -3 -2 -1 0
TauG
TauA
60
65
70
75
80
-10
0
10
20
30
40
50
60
13.4 13.6 13.8 14 14.2 14.4
wrist position (longitudinal axis; cm)
velocity of wrist (cm/s)
wrist position (longitudinal axis; cm)
velocity of wrist (cm/s)
time (s)
start
end
One day old infant gesture
TauG-guidance of pitch-glide singing
Va---ne
1 s
pitch (Hz)
TauG-guidance of attacking intensity- glide when bowing
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.
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.