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<div><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I am, indeed, of the opinion that music – complex art music, at least – typically accommodates different and even "conflicting" aspects of organization. The relationship between prolongational (recursive) and "concatenational" aspects of common practice harmony and voice leading is one example of this phenomenon. [...] <span class="Apple-style-span" style="-webkit-text-stroke-width: -1; ">Let us state, in somewhat simplistic terms, that Schenker made the following two claims. (1) Prolongation—or multilevel patterning of harmony and voice leading—is an important aspect of organization in tonal masterworks. (2) It is the all-embracing aspect to which all other aspects are strictly subordinate. Now (1), of course, does not imply (2). I think many if not most present-day Schenkerians (such as me) would approve of (1) but not of (2).</span></div></blockquote><div><br></div><div>Very good point! I describe this view as "compatibilism." I completely agree that most present-day Schenkerians are compatibilists. Schenker and Salzer (and maybe Beach and Rothgeb) weren't/aren't. So there's been a pretty big shift here -- with hardly a single music-theoretical publication about the subject. In fact, the only relevant writing I know of is an excellent unpublished paper by Bill Rothstein, who's also a compatibilist. I wish he'd publish it, because I think it's a really important issue.</div><br><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><span class="Apple-style-span" style="-webkit-text-stroke-width: -1; ">I did not want to deny the significance of psychology. There are wide variances in what we perceive or fail to perceive depending on circumstances, predispositions, conscious efforts etc. What I wanted to point out is that the ways in which chords and tones relate with other parameters (meter, design, register, etc.) (1) offer empirical evidence of the ways in which composers perceived the relationships between the chords and tones (2) affect the probabilities of the ways in which the listeners will perceive these relationships.</span></div></blockquote><br></div><div>I think the deep question is this: is "prolongational structure" a quasi-syntactical, more-or-less objective feature of the music, the way TSDT harmonic structure (arguably) is, or is it something we (perceivers, analysts, etc.) impose on the music from outside -- as when we interpret ABABAB... as (ABA)(BAB) = ABABA... </div><div><span class="Apple-tab-span" style="white-space:pre"> </span>It seems like you're claiming the former; someone like Nicholas Cook (or maybe Ben Boretz) might favor the latter view. Panos and Ioannis, by contrast, would almost seem to want to erase the distinction entirely, claiming that "recursivity" is *entirely* an interpretive matter, having nothing to do with the underlying stimulus. </div><div><span class="Apple-tab-span" style="white-space:pre"> </span>To my mind, there are a host of complicated issues relevant here. For instance:</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>1. Representation. I understand why someone would say that the melody (C4-E4-D4-C4)-(D4-F4-E4-D4) has a hierarchical, quasi-recursive structure: a single motive is repeated at two different pitch levels, and similar concepts ("up by step") apply at both. I am much less clear about what it means to say that (C4-E4-D4-C4) "represents" or "stands for" (or "prolongs" or "embellishes") a single note on "a higher structural level." (This gets at a point raised by Ioannis in a previous email.) The claim that certain sequences of notes "represent"/"embellish"/"stand for" others, and that this standing-for is ubiquitous in tonal music, is very complex and thorny. It's almost a philosophy or linguistics issue, as Mark DeBellis has been suggesting.<br></div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>2. Surface accent vs. Depth. Schenker emphasized that chords could be accented and emphasized by the musical surface in all sorts of ways, and yet not belong to deeper levels of structure. Olli's claim seems to be that accent (meter, design, register) in general provide a definitive recursive interpretation.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Personally, I don't see why differences in strength and weakness necessarily imply the need for recursive interpretation. Nor does the presence of simple ABA patterns. For example, the sentence "Americans care only about Americans" does not "prolong" or "represent" or "embellish" the word "Americans" even though it has the structure ABA. Nor do differences of emphasis, or pauses: imagine reading "Americans care only about Americans" while strongly stressing the first and last words, or drawing them out in length. </div><div><span class="Apple-tab-span" style="white-space:pre"> </span>The question is -- do we think that differences in stress and accent create a need for recursive interpretation of music? To take your example, suppose someone tells us they hear a particular I-ii-V-I-ii-V-I passage as a sequence of chords, with some strong and some weak, some short and some long, but no "embedding" or "representing" or "prolongation?" Can we really say that this hearing is *wrong* -- that it misses objective syntax-like features of the music?</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Offhand, I'm more inclined to think that recursive conceptualization is optional rather than required -- a feature of the way many people like to think about music, rather than an interpretation mandated by the music itself. This is perhaps the way Nicholas Cook thinks about Schenkerian interpretation.<br></div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>3. "Hearing" vs. "hearing as." <span class="Apple-tab-span" style="white-space:pre"> </span>We know that it is possible to be wrong about what one hears -- for instance, one might incorrectly think that one could hear long-range tonal closure. And we also know that there's an important difference between "hearing as" (knowing through perception that X) and "hearing plus thinking" (hearing while thinking "that's X"). So how could we establish that Olli (or other listeners) hears the sequence in the way he's described, rather than just hearing it while thinking "this prolongs that"? In other words, what reason do we have to believe in the reliability of statements like "I hear these chords as prolonging this one?" </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: 12.0px Helvetica"><span class="Apple-tab-span" style="white-space:pre"> </span>I don't mean this rhetorically, by the way. I'm very interested in whether there could be empirical tests of this very issue. I've tried to come up with some, without much success.</font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">In any case, I don't think I have the answers to these questions, but I do think they're really interesting and not-much-discussed. They almost lie at the border of philosophy, cognitive science, and music. The role of recursion in tonal music is really, really fundamental here ... and it would be great if we as a community could work toward some clarity about the issues involved. There's clearly a huge amount of interest in the subject, judging by the flurry of email activity on the list.</div><div><br></div><div>DT</div><div><br></div><div><br></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>