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

eing created. Importantly, the well-formedness rules provide psychological principles
for organizing musical stimuli, as one would expect in a classical theory. The
rules “define a class of grouping structures that can be associated with a sequence
of pitch-events, but which are not specified in any direct way by the physical signal
(as pitches and durations are)” (p. 39). Lerdahl and Jackendoff take care to express
these rules in plain English so as not to obscure their theory. However, they presume
that the well-formedness rules could be translated into a more formal notation,
and indeed computer implementations of their theory are possible (Hamanaka,
Hirata, & Tojo, 2006).
Lerdahl and Jackendoff’s (1983) well-formedness rules are not sufficient to
deliver a unique “parsing” of a musical piece. One reason for this is because, unlike
language, a musical parsing cannot be deemed to be correct; it can only be described
as having a certain degree of coherence or preferredness. Lerdahl and Jackendoff
supplement their well-formedness rules with a set of preference rules. For instance,
one preference rule for grouping structure indicates that symmetric groups are to
be preferred over asymmetric ones. Once again there is a different set of preference
rules for each of the four hierarchies of musical structure.
The hierarchical structures defined by the generative theory of tonal music
(Lerdahl & Jackendoff, 1983) describe the properties of a particular musical event.
In contrast, the hierarchical arrangement of musical tones (Krumhansl, 1990) is a
general organizational principle that applies to musical pitches in general, not to
an event. Interestingly, the two types of hierarchies are not mutually exclusive. The
generative theory of tonal music has been extended (Lerdahl, 2001) to include tonal
pitch spaces, which are spatial representations of tones and chords in which the
distance between two entities in the space reflects the cognitive distance between
them. Lerdahl has shown that the properties of tonal pitch space can be used to aid
in the construction of the time-span reduction and the prolongational reduction,
increasing the power of the original generative theory. The theory can be used to
predict listeners’ judgments about the attraction and tension between tones in a
musical selection (Lerdahl & Krumhansl, 2007).
Lerdahl and Jackendoff’s (1983) generative theory of tonal music shares another
characteristic with the linguistic theories that inspired it: it provides an account of
musical competence, and it is less concerned with algorithmic accounts of music
perception. The goal of their theory is to provide a “formal description of the musical
intuitions of a listener who is experienced in a musical idiom” (p. 1). Musical
intuition is the largely unconscious knowledge that a listener uses to organize, identify,
and comprehend musical stimuli. Because characterizing such knowledge is the
goal of the theory, other processing is ignored.
Instead of describing the listener’s real-time mental processes, we will be concerned
only with the final state of his understanding. In our view it would be fruitless to
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