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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'>Thomas--<BR>
OK, I’ll be the simpleton who asks, “has Bierwisch ever heard of Schenker?” <BR>
Of course, I’m at a disadvantage—by speaking about “true” recursion B. seems to have something more rigorous ans formalized in mind than the everyday definitions of recursion that satisfy mere musicians like myself. Furthermore, is Schenker’s concept of structural levels interesting because it’s recursive, or because it helps us (using something like recursion) understand music that’s important to us? <BR>
Best,<BR>
jp<BR>
Jeff Perry<BR>
Associate Professor of Music Theory<BR>
School of Music<BR>
Louisiana State University<BR>
jperry@lsu.edu / (225) 578-3556 (voice) / (225) 578-3333 (fax)<BR>
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On 3/21/09 5:40 PM, "Thomas Noll" <noll@cs.tu-berlin.de> wrote:<BR>
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</SPAN></FONT><BLOCKQUOTE><FONT SIZE="4"><FONT FACE="Helvetica, Verdana, Arial"><SPAN STYLE='font-size:14.0px'>Dear Colleagues,<BR>
last summer I participated in a cross-disciplinary workshop on "Recursion in Logics, Language and Art" in Berlin, organized by the logician Ingolf Max.<BR>
One participant was the well-recognized linguist Manfred Bierwisch, who argued in favor of a particular difference between natural language and music in the light of the concept of recursion.<BR>
He said that music exhibits repetition in a variety of ways, but – unlike language – it lacks instances of true recursion. My feeling is that Bierwisch has a point. But I nevertheless feel the obligation to challenge this assertion. <BR>
My own contribution to this workshop addressed a transformational approach to the theory of well-formed modes, and thereby implied a potential counter-argument on a mathematical level. But I started to think of other possible counter-arguments to Bierwisch's denial of recursion in music. 20th century fractal composition techniques come to mind, but they are still music-theoretical wall-flowers and wouldn't easily overthrow Bierwisch's position with respect to common practice repertoire. Event hierarchies in the sense of Lerdahl and Jackdoff's GTTM are candidates for recursive structures, but their music-theoretical meaning cannot compete with the grammatical meaning of derivation trees in linguistics. In the workshop I spontaneously summarized William Caplin's analysis (Classical Form, p. 149) of the core of the development of the 1st movement of Beethoven's F-minor sonata (Op. 2, No.1). Recall that Caplin interprets formal syntagmatic units with formal functions, such as presentation, continuation, cadence (closing function). If we understand the core in terms of a loosely organized "super-sentence", we find units with the functions presentation and continuation in recursive embedding - even if only with depth 2. In particular the presentation of the model involves a large portion of the secondary theme (including its presentation phrase and the first bars of its continuation phrase). <BR>
I would be glad to share this discussion with the list and to later forward the thread to the participants of the workshop.<BR>
Sincerely<BR>
Thomas Noll <BR>
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Thomas Noll<BR>
<a href="http://flp.cs.tu-berlin.de/~noll">http://flp.cs.tu-berlin.de/~noll</a><BR>
noll@cs.tu-berlin.de<BR>
Escola Superior de Musica de Catalunya, Barcelona <BR>
Departament de Teoria i Composició <BR>
Tel (priv.): +34 93 268 75 19<BR>
Tel (mobil): +34 66 368 12 02<BR>
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