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

and stored in memory in a form different from sensory codes” (Krumhansl, 1990,
p. 281). The tonal hierarchy is one such mental organization of musical tones.
In music, tones are not the only elements that appear to be organized by psychological
hierarchies. “When hearing a piece, the listener naturally organizes the
sound signals into units such as motives, themes, phrases, periods, theme-groups,
and the piece itself” (Lerdahl & Jackendoff, 1983, p. 12). In their classic work A
Generative Theory of Tonal Music, Lerdahl and Jackendoff (1983) developed a classical
model of how such a hierarchical organization is derived.
Lerdahl and Jackendoff ’s (1983) research program was inspired by Leonard
Bernstein’s (1976) Charles Eliot Norton lectures at Harvard, in which Bernstein
called for the methods of Chomskyan linguistics to be applied to music. “All musical
thinkers agree that there is such a thing as a musical syntax, comparable to
a descriptive grammar of speech” (p. 56). There are indeed important parallels
between language and music that support developing a generative grammar of
music (Jackendoff, 2009). In particular, systems for both language and music must
be capable of dealing with novel stimuli, which classical researchers argue requires
the use of recursive rules. However, there are important differences too. Most notable
for Jackendoff (2009) is that language conveys propositional thought, while
music does not. This means that while a linguistic analysis can ultimately be evaluated
as being true or false, the same cannot be said for a musical analysis, which has
important implications for a grammatical model of music.
Lerdahl and Jackendoff ’s (1983) generative theory of tonal music correspondingly
has components that are closely analogous to a generative grammar for language
and other components that are not. The linguistic analogs assign structural
descriptions to a musical piece. These structural descriptions involve four different,
but interrelated, hierarchies.
The first is grouping structure, which hierarchically organizes a piece into
motives, phrases, and sections. The second is metrical structure, which relates the
events of a piece to hierarchically organized alternations of strong and weak beats.
The third is time-span reduction, which assigns pitches to a hierarchy of structural
importance that is related to grouping and metrical structures. The fourth is prolongational
reduction, which is a hierarchy that “expresses harmonic and melodic
tension and relaxation, continuity and progression” (Lerdahl & Jackendoff, 1983,
p. 9). Prolongational reduction was inspired by Schenkerian musical analysis
(Schenker, 1979), and is represented in a fashion that is very similar to a phrase
marker. As a result, it is the component of the generative theory of tonal music that
is most closely related to a generative syntax of language (Jackendoff, 2009).
Each of the four hierarchies is associated with a set of well-formedness rules
(Lerdahl & Jackendoff, 1983). These rules describe how the different hierarchies are
constructed, and they also impose constraints that prevent certain structures from
276 Chapter 6