[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.
Sincerely
Thomas Noll
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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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