ï~~Distal Learning of Musical Instrument
Control Parameters
Michael A. Casey
Perceptual Computing Group
MIT Media Laboratory
Cambridge, MA 02139
mkc@media.mit.edu
Abstract
This paper describes a parameter estimation
method for sound generating environments based
on distal supervised learning techniques using
muli-layer neural networks. The paradigm we have
chosen for investigation is that of learning to control a musical instrument in order to produce an
intended sound. We present the general framework of distal learning from contemporary control
theory literature and show that musical instrument
control is a distal learning problem. Examples of
the application of distal learning to the control
of various sound synthesis environments are discussed. We also consider representational issues
for signal-based learning in neural networks.
1 Introduction
When performers play musical instruments
they realize a mapping from an internal representation of sound intentions to a set of motor actions that, when applied to the instrument, create the intended sounds. Clearly this
mapping is learned over a significant amount
of time during which the performer practices
many musical passages and many forms of articulation appropriate to their instrument. After much training the musician is able to realize novel intentions without having to practice
every possible situation in advance. Such is
the case in improvisation, for example, where
the performer draws on previously learned
skills to create new musical outcomes.
In this paper we are primarily concerned
with the issue of timbral control of a musical instrument and in modeling the learning
process that allows a performer to produce a
sound outcome from a sound intention. Space
dictates that we limit the discussion to the
modeling of static control environments. However, the methods presented here can also be
applied to dynamic control environments. We
first introduce the distal learning problem and
show that it is appropriate for learning to control a musical instrument.
2 Distal Learning
The distal learning problem is illustrated in
Figure 1. The Learner controls a set of distal
variables via a set of proximal variables. The
proximal variables are inputs to an environment that produces a distal outcome. Musical
performers directly control action parameters
such as bow pressure, bowing speed and finger positions. These control parameters pass
through the musical instrument, which is a
complex dynamical system, and the resulting sound is a transformation of these inputs.
Thus the performer has indirect control over
the sound outcome. The learner holds an internal representation of the sound that they
want to produce, i.e. a sound intention, and
it is the difference between this and the sound
outcome that is used to drive the learning of
the control parameters to the instrument. We
refer to the sound output as y, and the sound
intention as y*. Thus the error term for learning can simply be stated as:
E = (y*-y)
(1)
The musical instrument is referred to as a
plant or physical environment to which the
learner has to find an inverse model that maps
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240
ICMC Proceedings 1993
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