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Hi Panos,<div><div><br><div><div><blockquote type="cite"><div>One important distinction must be made: recursive vs non- recursive is a property of the <b>grammar (i.e. the model)</b>, not of the <b>corpus</b>. <i>Any</i> finite corpus can be modeled with a non-recursive grammar, even if it contains strings like</div><div><br></div><div>ABCDCBA</div><div><br></div><div>This is because, if the corpus is finite, you'll never have to deal with infinite depth of recursion. Of course, if recursive structures keep occurring with high frequency and at deep levels of embedding, it will be rather forced and unnatural to insist on a non-recursive model. The real question therefore becomes one of the model's <b>economy, explanatory power, ability to relate to other disciplines </b>(e.g. cognition) etc.</div><div><br></div><div>To summarize, in my mind recursive vs non-recursive is a question of <b>model selection</b>, not a question of what the music <b>is<span class="Apple-style-span" style="font-weight: normal; "> </span>intrinsically</b>.</div></blockquote><div><br></div><div>You're right, I was speaking too loosely. Typically, in both music and linguistics, we have an open-ended corpus in mind. We might be interested in sequences such as:</div><div><br></div><div>{ABA, ABCBA, ABCDCBA, "and so on"}</div><div>{I-V-I, I-ii-V-I, I-vi-IV-ii-V-vi-IV-I, "and so on"}</div><div><br></div><div>It's the "and so on" that causes problems.</div><div><br></div><div>Furthermore, since we believe these sequences to be caused by human beings following some sort of rules, we're really asking questions about the causal structure of the universe, rather than about sequences themselves. </div><div><br></div><div>That said, the points I was making can be translated into this more precise language. We may have sequences that can be modeled very nicely with a nonrecursive grammar, such as </div><div><br></div><div>AB, ABAB, ABABAB, "and so on"</div><div><br></div><div>Which we still perceive and organize recursively. </div><div><br></div></div><div>DT</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></div></div></div></body></html>