Cognitive Constraints on Compositional Systems

Fred Lerdahl's "Cognitive Constraints on Compositional Systems" cites Pierre Boulez's Le Marteau sans Maître (1955) as an example of "a huge gap between compositional system and cognized result," though he "could have illustrated just as well with works by Milton Babbitt, Elliott Carter, Luigi Nono, Karlheinz Stockhausen, or Iannis Xenakis". (In semiological terms, this is a gap between the esthesic and poietic processes.) To explain this gap, and in hopes of bridging it, Lerdahl proposes the concept of a musical grammar, "a limited set of rules that can generate indefinitely large sets of musical events and/or their structural descriptions." He divides this further into compositional grammar and listening grammar, the latter being one "more or less unconsciously employed by auditors, that generates mental representations of the music". He divides the former into natural and artificial compositional grammars. While the two have historically been fruitfully mixed, a natural grammar arises spontaneously in a culture while an artificial one is a conscious invention of an individual or group in a culture; the gap can arise only between listening grammar and artificial grammars. To begin to understand the listening grammar Lerdahl and Ray Jackendoff created a theory of musical cognition, A Generative Theory of Tonal Music (1983; ISBN 0-262-62107-X). That theory is outlined in the essay. Lerdahl's constraints on artificial compositional grammars are:

Constraints on event sequences

Constraints on underlying materials

Pitch space

He concludes, "Some of these constraints seem to me binding, others optional. Constraints 9-12 are essential for the very existence of stability conditions. Constraints 13-17, on the other hand, can be variously jettisoned." Examples given are South Indian music, which doesn't modulate and isn't equally tempered (13 & 14), and music such as that of Claude Debussy, Béla Bartók, and others who "have developed consonance-dissonance patterns directly from the total chromatic" (14-17).

Comprehensibility and value

To these ends he proposes the use of the terms "complexity" and "complicatedness", complexity being hierarchical structural richness, and complicatedness being "numerous non-redundant events per unit time." On Lerdahl's view complexity has aesthetic value, while complicatedness is neutral. He writes, "All sorts of music satisfy these criteria - for example, Indian raga, Japanese koto, jazz, and most Western art music. Rock music fails on grounds of insufficient complexity. Much contemporary music pursues complicatedness as compensation for a lack of complexity. In short, these criteria allow for infinite variety but only along certain lines."

"I find this conclusion both exciting and - initially at least - alarming...the constraints are tighter than I bargained for."

"My second aesthetic claim in effect rejects this ["progressivist"] attitude in favor of the older view that music-making should be based on "nature". For the ancients, nature may have resided in the music of the spheres, but for us it lies in the musical mind."


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