[Smt-talk] Classical Form and Recursion

Jeffrey Perry jperry at lsu.edu
Sun Mar 22 07:13:36 PDT 2009

    OK, I¹ll be the simpleton who asks, ³has Bierwisch ever heard of
    Of course, I¹m at a disadvantage‹by speaking about ³true² 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 Schenker¹s concept of structural levels interesting because
it¹s recursive, or because it helps us (using something like recursion)
understand music that¹s important to us?
Jeff Perry
Associate Professor of Music Theory
School of Music
Louisiana State University
jperry at lsu.edu / (225) 578-3556 (voice) / (225) 578-3333 (fax)

On 3/21/09 5:40 PM, "Thomas Noll" <noll at cs.tu-berlin.de> wrote:

> Dear Colleagues,
> last summer I participated in a cross-disciplinary workshop on "Recursion in
> Logics, Language and Art" in Berlin, organized by the logician Ingolf Max.
> 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.
> 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. 
> 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). 
> I would be glad to share this discussion with the list and to later forward
> the thread to the participants of the workshop.
> Sincerely
> Thomas Noll      
> *********************************************************
> Thomas Noll
> http://flp.cs.tu-berlin.de/~noll
> noll at cs.tu-berlin.de
> Escola Superior de Musica de Catalunya, Barcelona 
> Departament de Teoria i Composició 
> Tel (priv.):   +34 93 268 75 19
> Tel (mobil): +34 66 368 12 02
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> rg

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