< previous page page_308 next page >

Page 308with grammaticality, music theory is much more concerned with preference among a considerable number of competing well-formed (grammatical) structures. The closest analog to linguistic grammaticality in music theory is adherence to well-formedness rules. These rules resemble linguistic rules in that they either establish a branching or hierarchical structure (likephrase-structure rules in syntax) or characterize permissible distortions of the branching structure (like transformations). Thissuggests that the bulk of a linguistic grammar consists of well-formedness rulesfrom phonology through syntax to semantics.Even the lexicon can be considered a part of the well-formedness rule component, in that it establishes well-formed matchingsbetween phonological, syntactic, and semantic form at the terminal nodes of branching structures. The well-formedness rules formusic, even considering all four components of the musical grammar, hardly approach the linguistic well-formedness rules incomplexity. This reflects the much greater role of grammaticality in language than in music.

The question thus arises as to whether linguistic theory contains any rule systems comparable to preference rules in music. Itturns out that a number of phenomena discussed in the linguistic literature have properties appropriate to such rules. We presentthree of these briefly.

Relative Scope of Quantifiers

Within the rules relating syntactic form to semantic representation, there is a subsystem that deals with establishing thecorrespondence between the syntactic position of quantifier words such as every, all, some, and many and their scope in logicalform. The effect of scope difference is illustrated in the following pair of sentences, discussed in many places in the linguisticliterature. (Emphasizing two languages in example 12.1b aids interpretation.)

12.1

a. Every person in this room knows at least two languages.

b. At least two languages are known by every person in this room.

In 12.1a each person may know a different two languages, but in 12.1b two particular languages are known to everyone in theroom. The difference is notated formally in terms of relative embedding of quantifiers; the "logical forms" of 12.1a and 12.1bare (informally) 12.2a and 12.2b, respectively.

12.2

a. Every person x in this room is such that [there are two languages y and z such that [x knows at least y and z]].

b. There are two languages y and z such that [every person x in this room is such that [x knows at least y and z]].

< previous page page_308 next page >