[Smt-talk] Classical Form and Recursion

[Lodewijk Muns]

Dear Thomas Noll,
 
thanks for drawing attention to this issue.
 
Discussions around the theme of music compared to language often suffer from
faulty generalizations. Different kinds of music are structured in diverse
ways, and there is no "natural music" in the sense that there is "natural
language".
 
As to classical tonal music, I think recursion is a key concept to
understanding its (much discussed but poorly understood) "language-like"
(sprachähnlich) character.
 
I am currently working on a PhD dissertation (also Berlin, Humboldt
Universität) about "Recursion and Quotation in Classical Music". Basic
thesis is, that in the classical style the tonal language is shaped in such
a way as to enhance music's language-like character (Sprachähnlichkeit).
This facilitates a specific practice of quotation, which is an exemplary
recursive device.
 
To investigate this further, the concept of hierarchy should be elucidated,
as it is present e.g. in GTTM to which you refer and (dubiously) in
Schenkerism. One key question is to which extent the harmonic process
creates levels, or is, as in common prejudice, "linear".
 
This is not a good moment to summarize my ideas, to which I will gladly come
back later. A preliminary attempt at addressing some of the issues is
contained in my Schenker-essay, earlier posted to this list, which can be
found on my website (http://www.xs4all.nl/~lmuns/WhyIamNotaSchenkerian.pdf).
 
Best regards,
 
Lodewijk Muns
 <mailto:lmuns at xs4all.nl> lmuns at xs4all.nl 
 <http://www.xs4all.nl/~lmuns> www.xs4all.nl/~lmuns

 

  _____  

From: smt-talk-bounces at societymusictheory.org
[mailto:smt-talk-bounces at societymusictheory.org] On Behalf Of Thomas Noll
Sent: zaterdag 21 maart 2009 23:41
To: smt-talk Talk
Subject: [Smt-talk] Classical Form and Recursion


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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