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
Summary of talk
A theory of action control
and
applications to understanding
moving
and
making 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-fromclosure) 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
 can be directly sensed through -coupling
Intrinsic guiding gaps
• Should be simple and sufficient
• Should be rooted in ecological physics
(a)
How a gap changes under
tauG - guidance
TauG-guidance parameters
K = ‘oomph’
A = amplitude
T = duration
tauG ‘kinetic melodies’ in the
nervous system
Examples of tauG guidance
m-g
m-g
TauG-guidance of sucking in neonates
One day old infant gesture
wrist position (longitudinal axis; cm)
velocity of wrist (cm/s)
80
0
60
start
-2
75
40
70
20
-4
TauG
30
velocity of wrist (cm/s)
wrist position (longitudinal axis; cm)
50
-6
10
65
-8
0
end
60
13.4
13.6
13.8
14
14.2
-10
14.4
-10
-5
-4
-3
TauA
time (s)
-2
-1
0
TauG-guidance of pitch-glide singing
Va---ne
pitch
(Hz)
1s
TauG-guidance of attacking intensityglide 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 suprasecond 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, 361372.
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.