Syntax

Parameters Defining Branching of Tones or Chords

Several parameters intervene to define the branching of tones or chords in this tree. Some of them deal with rhythmic aspects, others with perceptual salience, and others with the Western tonal hierarchy. In Western tonal music, this last parameter plays an important role, and has received a considerable refinement in Fred Lerdahl's tonal pitch space theory. Tonal hierarchies are expressed as distances separating events: the less related the events in Western music, the more distant they are in tonal pitch space. Pitch space distances are experienced as feelings of tension and relaxation by the listeners, so that the greater the distance between two events, the stronger the tension. By combining both theories, Lerdahl allows considerably refining the syntactic-like function of events in the prolongational tree, by quantifying the tensing or relaxing value of each event as a function of both its distance toward the local tonic in TPST and its embedding in the prolongational tree. The syntactic-like function of a musical event may thus be formalized by a precise quantification of tension or relaxation. The most embedded events in the prolongational tree usually instill the strongest tension values.

Lerdahl and Jackendoff formalized syntactic processes in music in a way that allows some comparison with language. Understanding sentences requires assigning to each word a specific functional relationship with the other words of the sentence. Similarly, understanding music requires assigning to each event a specific function of elaboration or prolongation in relation to the other events. A key feature for comparing music and language is that these functions are context-dependent. For example, the chord G is likely to act as an elaboration of the C major chord in a piece in C major key, but as a prolongation in a piece in G major key. A given musical event may thus lead to entirely different tree structures, depending on the key context in which it is occurring. This strong context dependency of musical function is reminiscent of the context dependency of the syntactic functions of words in sentences. Because of this similarity, it has been suggested that music and language processing might share cognitive and neural resources.

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