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<div><div>On Mar 30, 2009, at 7:59 AM, Olli Väisälä wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><div>Instead of discussing Bach, I shall again present simple examples for illustrating that there may be varying degrees of evidence for prolongational structuring. Consider the following progressions in 4/4 time (soprano tones in parentheses; / = barline).</div><div><br></div><div>Progression (1). I (1^) – V (2^) – I (1^) – V (2^) / etc. / etc.</div><div><br></div><div>Progression (2). I (3^) – V (2^) – I (3^) quarter rest / V (2^) – I (1^) – V (2^) q.r. / I (1^) – V (7^) – I (1^) q.r.</div><div><br></div><div>In Progression (1), there is no empirical evidence that the "composition" is affected by any prolongational patterning beyond the most immediate level in which each V prolongs surrounding Is (as supported by the meter). Deeper-level models have no explanatory power in this case. (Trying to identify deeper levels would be as nonsensical as hierarchicizing the tones in a trill.)</div><div><br></div><div>In Progression (2), there is considerable empirical evidence that the composition is affected by a larger prolongational pattern, since meter, grouping, and regular design bring out archetypal patterns both for the harmony (I–V–I) and the top voice (3^–2^–1^). The prolongational model has considerable explanatory power for the way in which the music is shaped. Of course, one cannot "prove" that the composition manifests prolongation. The features that seem to support the 3^–2^–1^ shape <i>might</i> be a chance products or better explained by some alternative model. Given the number of such features, however, the chance explanation does not seem too likely, and it is not easy to see ways in which the prolongational model could or should be bettered. At the very least we can say that restricting ourselves to a purely concatenational model would create a high risk of losing a crucial compositional aspect.</div></div></blockquote><div><br></div><div>I realize now that I wasn't being clear enough. In the example I gave:</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>ABABA ... = (ABA)(BAB)... = ABAB "on a higher level"<br></div><div><br></div><div>There were really a pair of issues. One is grouping -- getting from ABAB... to (ABA) ... But the other is reduction -- getting from (ABA) to A. The point of the "Americans care only about Americans" example was that this latter process is also problematic: the mere presence of ABA (as in "Americans care ...") does not automatically license or motivate a reduction to A ("Americans").</div><div><br></div><div>Your distinction between Progression 1 and Progression 2 addresses the grouping issue but not the reduction issue. Here, it is clear that the harmonies should be grouped (I-V-I)(V-I-V)... But it is still not clear why we should "reduce" each unit to a single chord. You simply assert that we should -- which is fine, but it's basically presupposing an answer to the very question I'm trying to ask.</div><div><br></div><div>The point I'm trying to get at is that may be perfectly reasonable to reject a certain notion of prolongation in Progression 2. Consider two different interpretations:</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>A. Progression 2 consists of a melodic down-up-down pattern, harmonized with I and V, and repeated a step lower each time.<br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>B. Each "unit" of Progression 2 "stands for" or "represents" a single chord.<br></div><div><br></div><div>Statement (A) I think is unproblematic; statement (B) is much more so. The point is that there is no need to postulate a relation of "standing for" or "representing" in order to explain the descending melodic line, or the hierarchical relations among the units, etc. In fact, I think it's interesting to really try to see how far you can get without "representation" in the sense of statement B. My preliminary conclusion is that it's quite possible to be a good musician -- to write interesting music, to appreciate the Great Works, to perform well on an instrument -- without it. </div><div><br></div><div>There is, furthermore, an interesting-but-subtle methodological issue. Suppose you have a first-order harmonic grammar, in which each chord has a certain number of "allowable" destinations. Then, given a sequence such as ABA CDC EFE ..., you can always get a grammatical sequence by "reducing" each 3-chord unit, for example to produce ACE... The reason is that each local transition in the latter sequence is legal, because it appears as a local transition in the original. So if ABA CDC is legal than so is AC. (Which is just to say it's a first-order harmonic grammar, in which the acceptability of transitions is a local matter.) So what might *appear* to be evidence of recursive structure in a particular sequence (in this case the grammaticality of ACE) is really just a reflection of basic features of the underlying, nonrecursive harmonic grammar.</div><div><br></div><div>So in this particular case, you might think that, given </div><div><br></div><div>I (3^) – V (2^) – I (3^) quarter rest / V (2^) – I (1^) – V (2^) q.r. / I (1^) – V (7^) – I (1^) q.r.</div><div><br></div><div>It's a really interesting and remarkable fact about this particular sequence that </div><div><br></div><div>I (3^) V (2^) I (1^) </div><div><br></div><div>Is legal. But it's not -- it's just a feature of the fact that certain local transitions are commonly acceptable in tonal music.</div><div><br></div><div>Now it might be you're not interested in this sort of issue -- for you, perhaps, it's obvious that Progression (2) has recursion in the sense of statement B. That's fine, but it just means you're not interested in the question I'm interested in. I believe it's really important and interesting to ask what evidence we have for recursion in the sense of statement B. To really subject statement B to skeptical challenges, to see how well it stands up. Just repeating that we do have evidence for statement B doesn't really speak to this question.</div><br><blockquote type="cite"><div><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1; ">I am not sure whether I understand your concerns here. Tonal tradition is rich in practices in which basic skeletal progressions are subjected to diminution, variation, embellishment etc. I do not suppose you mean that you have difficulties in grasping this concept intuitively—in cases such as Progression 2 above, for example. (Naturally, when one proceeds to higher structural levels, involving more extended temporal spans, such concepts become less self-evident for intuition, but this does not seem to be your point.)</span></div></div></blockquote><div><br></div><div>The question is really about the legitimacy of extending certain sorts of unproblematic notions of embellishment to other cases. I have no problem saying that, given CEG in the harmony and a melody C-D-C, the D is a neighboring tone and that there is an "underlying" C major chord that persists throughout. I have a much harder time understanding an analogous claim where we start with a perfectly syntactic progression, like I-ii-V-I-V-I, and we say that it embellishes another syntactic question, say I-V-I. The difference is that in the one case, we transform a nonsyntactic object (like the "harmony" CEGD) into a syntactic one. In the latter case, we're trading one syntactic progression for another, and the justification for this is far less clear. This is because we cannot use the fact of nonsyntacticality as a trigger for the need for reduction.</div><div><br></div><div>Again, it may be that you're not interested in the almost-philosophical question "what does it mean to say one passage of music represents another?" Perhaps you're not at all motivated by the thought that some of our assumptions might be on shaky ground. Perhaps you want to do your reductions and get on with things. All of this is perfectly fine. But there are, I think, interesting questions here -- even if theorists often proceed as if the answers were obvious.</div><div><br></div><blockquote type="cite"><div><div>Instead of trying to describe "what it means to say" that something is prolonged, it might be more useful here to concentrate on the consequences of prolongation. If prolongational readings are capable of revealing larger patterns that seem likely to be pertinent to a certain composition (as in Progression 2 above), this should suffice for justifying the concept. </div></div></blockquote><div><br></div>Oh, but this justification works just as well for the reduction ABABAB = (ABA)(BAB) = "AB on a higher level." It's just to say, roughly, that recursive interpretation is something *we* do to music, and if we like doing it, then that's justification enough. This is the Cook/Boretz line. </div><div><br></div><div>DT</div><div><div><br></div></div><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div>Dmitri Tymoczko</div><div>Associate<span class="Apple-converted-space"> </span>Professor of Music</div><div>310 Woolworth Center</div><div>Princeton, NJ 08544-1007</div><div>(609) 258-4255 (ph), (609) 258-6793 (fax)</div><div><a href="http://music.princeton.edu/~dmitri">http://music.princeton.edu/~dmitri</a></div><div><br class="khtml-block-placeholder"></div><div><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></span><br class="Apple-interchange-newline"> </div><br></body></html>