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

preferences (Bugatti, Flammini, & Migliorati, 2002; Jun, Rho, & Hwang, 2010; Liu,
Hsieh, & Tsai, 2010; Muñoz-Expósito et al., 2007).
Musical styles, or individual musical pieces, are difficult to precisely define, and
therefore are problematic to incorporate into classical theories. “The fact that even
mature theories of music are informal is strong evidence that the performer, the
listener, and the composer do not operate principally as rule-based problem solvers”
(Loy, 1991, p. 31). That artificial neural networks are capable of classifying music in
terms of such vague categories indicates that “perhaps connectionism can show the
way to techniques that do not have the liabilities of strictly formal systems” (p. 31).
In other words, the flexibility and informality of connectionist systems allows them
to cope with situations that may be beyond the capacity of classical models. Might
not this advantage also apply to another aspect of musical cognition, composition?
Composition has in fact been one of the most successful applications of musical
connectionism. A wide variety of composing networks have been developed.
Networks have been developed to compose single-voiced melodies on the basis of
learned musical structure (Mozer, 1991; Todd, 1989); to compose harmonized melodies
or multiple-voice pieces (Adiloglu & Alpaslan, 2007; Bellgard & Tsang, 1994;
Hoover & Stanley, 2009; Mozer, 1994); to learn jazz melodies and harmonies, and
then to use this information to generate new melodies when presented with novel
harmonies (Franklin, 2006); and to improvise by composing variations on learned
melodies (Nagashima & Kawashima, 1997). The logic of network composition is that
the relationship between successive notes in a melody, or between different notes
played at the same time in a harmonized or multiple-voice piece, is not random,
but is instead constrained by stylistic, melodic, and acoustic constraints (Kohonen
et al., 1991; Lewis, 1991; Mozer, 1991, 1994). Networks are capable of learning such
constraints and using them to predict, for example, what the next note should be in
a new composition.
In keeping with musical Romanticism, however, composing networks are presumed
to have internalized constraints that are difficult to formalize or to express
in ordinary language. “Nonconnectionist algorithmic approaches in the computer
arts have often met with the difficulty that ‘laws’ of art are characteristically fuzzy
and ill-suited for algorithmic description” (Lewis, 1991, p. 212). Furthermore these
“laws” are unlikely to be gleaned from analyzing the internal structure of a network,
“since the hidden units typically compute some complicated, often uninterpretable
function of their inputs” (Todd, 1989, p. 31). It is too early to label a composing network
as an isolated genius, but it would appear that these networks are exploiting
regularities that are in some sense sublime!
This particular parallel between musical Romanticism and connectionism, that
both capture regularities that cannot be formalized, is apparent in another interesting
characteristic of musical connectionism. The most popular algorithm for training
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