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Related to Tonal music: Modal music, Functional tonality
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11) According to Schenker, tonal music in our classical tradition is (or ought to be) organized in such a way that the musical surface is derived by "composing out" a basic harmonic and scalar progression.
12) Such rules have a place in tonal music, for example, the rule that designated pitches come from a set of twelve octave-equivalent semitones.
One of the strengths of Lerdahl and Jackendoff's A Generative Theory of Tonal Music is that it emphasizes these long-term relations, and the way in which the listener--especially the listener to the masterworks of our listening culture--hears the music as going somewhere, fulfilling at a later stage expectations subliminally aroused at an earlier one.
13) And it is the existence of this extended common practice that gives credibility to the hypothesis that there is a unified generative grammar of tonal music.
More recently, Longuet-Higgins has developed a geometrical model of tonal relations, and Lerdahl, in a formidably difficult work, has recast the findings of A Generative Theory of Tonal Music in terms of paths taken through "tonal pitch space," although, as he here and there acknowledges, his model is numerical rather than spatial, and talk of "regions" of "pitch space" involves a kind of metaphor.
Tonal music shows a preference for "conjunct melodic motion" (that is, small intervals and fluent movement across them); it exhibits a widespread use of "acoustic consonance," with octave, fifth, and fourth assuming prominent melodic and harmonic roles; there is a tendency to "harmonic consistency" (consonant sequences or dissonant sequences, but not a scrambled mixture of both); pitches are organized as scales within the octave; and certain notes are singled out as more important or central than others (for instance, the tonic, the dominant, the leading note) (p.
As he shows, the basic sonorities of Western tonal music arise from efficient voice-leading, harmonic consistency, and acoustic consonance, and these three features are woven together in the extended common practice.
All of the intervals in tonal music can be defined on this space, in which they appear as vectors.
In principle, then, the notes of tonal music lie at the points of a discrete three-dimensional space which extends infinitely in all directions away from any starting point.
he presents a transformational interpretation for hearing tonal music with tonal intentions: "the listener/performer/analyst relates sounding chords to the tonic in various ways.
The next article, by Eytan Agmon, attempts to "reconcile" the theory of structural levels with harmonic theory by presenting an alternate reductive model based on what he calls a "prolongation-hierarchical" analysis that is based, in many ways, on the models proposed in Fred Lerdahl and Ray Jackendoff's A Generative Theory of Tonal Music (Cambridge: MIT Press, 1983).
Finally, a more accurate title might be "Modeling the Cognition of Basic Tonal Music Structures.