Function and Pitch Hierarchy in Movement II of Bartok's Fifth Quartet

I mean this short essay to serve as a simple demonstration of how one may apply certain notions of harmonic function and of pitch hierarchy to a mature work by Bela Bartok. The essay begins with a brief description of the basic concepts needed in the demonstration and then proceeds to an analysis of several passages from the second movement of Bartok's String Quartet No. 5. Four harmonic functions are important to the analysis, and each of them is defined in relation to a particular role or activity within a musical context, activities which themselves are most fully exemplified in tonal music. The present functions are thus analogues of tonal harmonic function by virtue of musical action, rather than, for example, because of some precompositionally defined interval distance or similarly abstract pitch-class relationship. Some time ago I concluded that Bartok's music does not show any uniformly reliable one-to-one correspondence between harmonic behavior and precompositional intervallic relationships. But it does feature, as is common knowledge, pitch classes and harmonic events which behave in ways analogous to tonal harmonic functions. It thus seems reasonable to recognize and evaluate such functions behaviorally in context, rather than to try to predict their specific meaning on some precompositional basis. The four functions involved are named as follows: initiating tones or events, goal tones or events, local dominant tones or events, and large-scale interior tonal centers. The behavioral implications of these terms are clear enough so that I can proceed to use them in the analysis without pausing over a separate example of each one. But one should note that a harmonic goal event which can only be identified within a specific musical context must obviously rely for its intelligibility upon many musical elements other than pure pitch relationships. When goal events are identified in the essay, I will not bother to spell out the reasons for each such identification, but those reasons, including phrase structure, melodic contour, dynamics, duration, and other familiar aspects of the music, do exist and can easily be recognized in each case. The conception of pitch hierarchy to be used here grows out of combining these contextual harmonic functions with two general conditions, conditions which I believe to be sufficient to produce some kind of hierarchical structure in music. The conditions are, first, that some differentiation of structural weight be apparent within the succession of musical events in a context and, second, that we be able to discern within that musical context some kind of consistent design among such structural