As I suggested in class, it is the aspect of motion that I find most attractive about Schenker's system. The analysis is not static, in that it does not divide the work up into subsections of themes or sets, but treats the work as a whole. This has the effect of smooth forward motion, rather that the choppy segmented reading provided by (for exempla) pitch-class analysis. I would even challenge the criticism that Schenker ignores rhythm. In my limited experience, rhythm seems to play an important role in the initial critical and aesthetic choices that the analyst must make. Faster rhythms will be interpreted as sustained voices or ornamentation, medium speed will be seen as motivic or contrapuntal, while slow rhythms will be viewed as material of fundamental structure.
 I also agree with Alex in his discussion of process. I would perhaps go even further in suggesting that an added value of the method is that the process forces the analyst to reassess earlier conclusions as each level of a work is revealed. This is not the case with other note-by-note styles of analysis, which determine "meaning" of a note, and then move on. In such a case the process of analysis occurs only once, while the Schenkerian method goes over the same ground several times. Schenker's assumption of the background level (common to all works) also ensures a certain consistency in the results which is not necessarily a bad thing, as it creates a framework for the meaningful comparison of common-practice-period works.
 Any problems I may have with Schenker are the obvious ideological ones; the acceptance of the "background" as fact, the universal significance of the major triad (based on a rather selective division of the overtone series) and the inability of the system to deal with anything outside of common-practice-period (not to mention the distaste at the philosophic reasons behind it. However, I like Dr. Renwick's analogy of Christianity, in terms of recognizing the general values of a system without the acceptance of its fundamental tenets.
When it comes to Schenker, I think it's a great way to live, but don't look for me in
...'cause I won't be there.
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