[Smt-talk] Classical Form and Recursion

Thomas Noll noll at cs.tu-berlin.de
Sat Mar 21 15:40:46 PDT 2009

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.
Thomas Noll

Thomas 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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