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Some further comments to Nicolas Meeùs:<div><br></div><div><blockquote type="cite">Your stressing of "the framing points", your "partition principle" and "penult principle", all tend to give weight to single notes. This, I think, is a reductionist manner of presenting things (but I trust that your description is meant as pedagogical). When I stress a 6th-progression from F to D, I do not mean that its framing points, F and D, are more important, merely that the progression is an elaboration of an abstract space delimited by these notes – i.e. of a triad to which these notes belong.</blockquote><div><br></div>Your description of the roles of F and D here is synonymous to what I expressed by saying that they have greater structural weight; hence there seems to be no actual disagreement here. Of course, their significance is not limited to those single notes; nevertheless, in order for the structure to be comprehensible, these notes and their special structural status has to be expressed somehow in the musical surface. My considerations of analytical criteria concerned these ways of expression.</div><div><br></div><div><blockquote type="cite">To sum up: your criteria seem to me perfect as heuristic or pedagogical tools, and I suppose I make use of similar criteria in my own analyses or my own teaching. But at a higher level of reflexion, they should shade away in favor of more abstract considerations: we should always remind our students (and ourselves) that reductional processes are but makeshifts for unveiling elaborations.</blockquote><br></div><div>Here, our attitudes seem to differ. In my view, the relative neglect of such "heuristic tools" is a major defect in Schenkerian theory. We can construe Schenker's theory as a systemic description of syntax in tonal "masterworks" (Schenker himself compared music with language). While Schenker described with great finesse the system of structural levels that is crucial to his theory, he offered us too little to clarify how the structural positions are expressed in composition or how they are to be inferred by the listener or the analyst. In my view, the theory has nothing to lose but much to gain, if we try to supplement Schenker's accomplisment by determining principles relevant to this question. In the end, this question is not only heuristic or pedagogical, but epistemic. Insofar as we can identify what kind of compositional features are required to justify readings of structural weight, it becomes possible to test the theory empirically.</div><div><br><div><blockquote type="cite"><font face="Calibri"> (I may be wrong in that, but I cannot refrain from associating the "reductionist" view with GTTM.)<br><font class="Apple-style-span" face="Helvetica"><font class="Apple-style-span" face="Calibri"><br></font></font></font> </blockquote></div><br></div><div>I would not cite GTTM as a cautionary example but would credit it with a laudable effort to clarify the basis of structural readings. My considerations of analytical criteria are, indeed, somewhat comparable to the preference rules of GTTM. However, while I regard the aims of GTTM as quite legitimate, there are several respects in which I find its system of preference rules as unsatisfactory. It is too simplistic (Lerdhal and Jackendoff themselves admit that it does not work well with polyphonic music), and I also find some preference rules as simply wrong or given false weight. There is also the basic problem that GTTM treats each element in the prolongational structure as subordinate to a *single* element, whereas musical elaboration characteristically concerns motions from an element to another, in the manner of passing tones.</div><div><br></div><div>My points of criticism against GTTM's preference rules are too various to be discussed here (at least we should rename this thread), but one consideration may be worth presenting. GTTM places a great weight to "harmonic stability" in its determination of structural weight, in the sense that I chords are much more likely to become structurally significant just because they are I chords. In the Carnaval, this would imply that the I in m. 5 would, in terms of GTTM, be less likely to become subordinate to the surrounding IV and V4/3 of V than in Frank Samarotto's (or my) Schenkerian analysis. I believe that the criteria of prolongational weight should be more strongly independent of Roman-numeral chord identification than what GTTM asserts. Hence, prolongational patterns are created actively through composers' treatment of chords, they do not arise passively from the mere identity of chords.</div><div><br></div><div>Olli Väisälä</div><div>Sibelius Academy</div><div><a href="mailto:ovaisala@siba.fi">ovaisala@siba.fi</a></div></body></html>