Mind, Body, World- Foundations of Cognitive Science, 2013a

of fifths. In other words, if one ignores the sublime nature of networks and seeks to
interpret their internal structures, one can discover new kinds of formal representations
that could easily become part of a classical theory.
Other, more direct integrations can be made between connectionist and classical
approaches to music. For example, NetNeg is a hybrid artificial intelligence
system for composing two voice counterpoint pieces (Goldman et al., 1999). It
assumes that some aspects of musical knowledge are subsymbolic and difficult to
formalize, while other aspects are symbolic and easily described in terms of formal
rules. NetNeg incorporates both types of processes to guide composition. It includes
a network component that learns to reproduce melodies experienced during a training
phase and uses this knowledge to generate new melodies. It also includes two
rule-based agents, each of which is responsible for composing one of the voices that
make up the counterpoint and for enforcing the formal rules that govern this kind
of composition.
There is a loose coupling between the connectionist and the rule-based agents
in NetNeg (Goldman et al., 1999), so that both co-operate, and both place constraints,
on the melodies that are composed. The network suggests the next note in
the melody, for either voice, and passes this information on to a rule-based agent.
This suggestion, combined with interactions between the two rule-based agents
(e.g., to reach an agreement on the next note to meet some aesthetic rule, such as
moving the melody in opposite directions), results in each rule-based agent choosing
the next note. This selection is then passed back to the connectionist part of the
system to generate the next melodic prediction as the process iterates.
Integration is also possible between connectionist and embodied approaches
to music. For example, for a string instrument, each note in a composition can be
played by pressing different strings in different locations, and each location can
be pressed by a different finger (Sayegh, 1989). The choice of string, location, and
fingering is usually not specified in the composition; a performer must explore a
variety of possible fingerings for playing a particular piece. Sayegh has developed
a connectionist system that places various constraints on fingering so the network
can suggest the optimal fingering to use. A humorous—yet strangely plausible—
account of linking connectionist networks with actions was provided in Garrison
Cottrell’s (1989) proposal of the “connectionist air guitar.”
Links also exist between classical and embodied approaches to musical cognition,
although these are more tenuous because such research is in its infancy. For example,
while Leman (2008) concentrated on the direct nature of musical experience that
characterizes the embodied approach, he recognized that indirect accounts—such as
verbal descriptions of music—are both common and important. The most promising
links are appearing in work on the cognitive neuroscience of music, which is beginning
to explore the relationship between music perception and action.
Classical Music and Cognitive Science 311