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<TITLE>Re: [Smt-talk] Classical Form and Recursion</TITLE>
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<FONT FACE="Verdana, Helvetica, Arial"><SPAN STYLE='font-size:12.0px'>Rick Cohn does this sort of thing in “Dramatization...” <I>19thCM</I> 15/3 (1992).<BR>
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Scott<BR>
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Scott Murphy<BR>
Associate Professor, Music Theory<BR>
University of Kansas<BR>
smurphy@ku.edu<BR>
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on 3/25/09 9:20 AM, Dmitri Tymoczko at dmitri@Princeton.EDU wrote:<BR>
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</SPAN></FONT><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>It is typically possible to interpret a sequence of symbols recursively. For instance, we could take the sequence<BR>
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</SPAN></FONT><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>ABABABABAB...<BR>
</SPAN></FONT></FONT><FONT FACE="Verdana, Helvetica, Arial"><SPAN STYLE='font-size:12.0px'><BR>
</SPAN></FONT><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>And group it as follows:<BR>
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</SPAN></FONT><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>(ABA)(BAB)(ABA)(BAB) ...<BR>
</SPAN></FONT></FONT><FONT FACE="Verdana, Helvetica, Arial"><SPAN STYLE='font-size:12.0px'><BR>
</SPAN></FONT><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>Then, by asserting that (ABA) "stands for" (or "represents" or "prolongs") A, while (BAB) "represents" B, we could come up with a "higher level" version of the same pattern<BR>
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</SPAN></FONT><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>ABABABAB ...<BR>
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</SPAN></FONT><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>(Here each symbol stands for 3 symbols in our original.) We might take this to demonstrate that there is recursive structure in our sequence. It is even possible that this sort of procedure could represent a psychologically accurate description of the way some particular person perceives or organizes the sequence.</SPAN></FONT></FONT><FONT FACE="Verdana, Helvetica, Arial"><SPAN STYLE='font-size:12.0px'><BR>
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