<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Olli,<div><br></div><div>I suspect we're nearing that magical limit where one person's evidence is another person's reductio, so I'll be brief.</div><div><br></div><div><blockquote type="cite" class="">Owing to this property, music has, in my view, much stronger potential for extensive recursive (prolongational) structuring than has language. </blockquote><br></div><div>I'll just report that every psychologist, linguist, and evolutionary biologist I've talked to about this issue has told me that they find this suggestion implausible. They argue that language is so central to human survival that it would be extraordinary if our capacities for perceiving recursion were not utilized to their fullest extent. Consequently, they typically use limits on recursion-perception in language as a rough guide to limits on recursion-perception in music. And we know that humans sometimes do quite badly at perceiving recursion in language: the sentence "People dogs cats like hate suck" is very difficult to parse, and it involves only three levels of center embedding. More generally typical sentence lengths are on the order of 10 seconds, more than an order of magnitude shorter than typical tonal pieces. </div><div><br></div><div><div><blockquote type="cite"><div><div><div>Beginning and ending the sentence with the same word plays no role for syntactic closure in language. In your example sentence, the subject happens to be the same as the object, but this coincidence has no significance for syntax (only for semantics and rhetoric). In tonal music, by contrast, there is a norm that closed harmonic progressions begin and end with I (I hope you will agree that there is such a norm). If a phrase starts on I and proceeds to other harmonies, we are expecting a convincing return to I until this happens. (If our expectations are not fulfilled and the phrase does not return to I, we do not hear it as closed phrase, but await continuation.) This demonstrates that the referential status of a single element (tonic chord in this case) may have significance for musical syntax in a way that differs fundamentally from that of a single word for linguistic syntax. The perception of the syntax in a tonal progression may be governed by an element in that progression in a sense for which there is no linguistic counterpart. (Closed tonic-to-tonic progressions are by no means the only way to acheive such governing status, but they are a prime example.)</div></div></div></blockquote><div><br></div><div>My question was: what justifies the "reduction" of ABA to A. Your answer seems to be "there is a norm that harmonic progressions begin and end with I." But the existence of the norm is clearly insufficient. Sumo wrestling matches begin and end with bowing. The bowing is a time of lowered tension, relative to the match. But nobody takes the wrestling to "represent" or "prolong" the bowing.</div><div><br></div><div>I don't mean this to be flippant. What I want to know is what principles justify the "reduction" of ABA to A. I think this is a serious, interesting question. Many of the answers that are commonly proffered -- "we have a norm of ABA structuring," or "A is less tense than B" -- are clearly insufficient. The example of the Sumo wrestlers is silly in one sense, but it dramatizes the fact that these answers offered don't do the job. Whether you think that's important or not probably depends on whether you're convinced that there *is* a good underlying justification somewhere (as you are) or whether (like me) you are agnostic or skeptical about the issue.</div><div><br></div><blockquote type="cite"><div><div>For testing whether a listener actually perceives tonal closure in m. 3, one might consider the following experiment, though it has a deficiency. Listen to the progression (1) as written above and (2) as a truncated version, breaking of after bar 2, beat 2. If one finds (1) embodying more convincing closure than (2), this speaks to prolongational perception. The deficiency in this experiment is that (2) does not include all the information that supports perceiving bar 2, beat 2 as subordinate to the surrounding dominant, since part of this information comes retrospectively through the return of V (2^) at beat 3. Nevertheless, even without this retrospective information, I find (2) less satisfactory than (1) in terms of closure.</div></div></blockquote><div><br></div><div>The challenge is to control for the nonrecursive facts that contribute to closure. It's really a very difficult problem; just truncating progressions won't do the job, as we may have an expectation that phrases last a certain length.</div><div><br></div><div>DT</div></div><br><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></div></body></html>