[Smt-talk] Classical Form and Recursion

matralab matralab at gmail.com
Sun Mar 22 02:42:51 PDT 2009

Two first off-hand responses:

1) to say that fractal composition techniques are not a musical practice
worthy of analysis because of its theoretical wall-flower status is not a
statement about music but about social/historical contingencies in
reception. It would be like stating that linguistics is not a valid
intellectual practice because most people do not read linguistic theory
books and most writers of novels have no clue about linguistics. Or like
stating that English is a better language than Hebraic because more people
use and speak it...

2) the limitation you encounter may be repertoire-based. Without having any
concrete example in mind I would suggest to look   - rather than to
Beethoven (whose variations (op.111 or 120) might still be promising
material) -  to (naming only well-established and widely performed and
discussed) composers such as Brian Ferneyhough, Clarence Barlow, Matthias
Spahlinger, Steve Reich, James Tenney, Kaikoshru Sorabji, Tom Johnson,
Gerhard Winkler, Arvo Pârt etc. My own early (student) work is replete with
recursion. Indeed, recursion/self-referentiality (prompted no doubt by
Hofstadters "Goedel Escher Bach") almost seemed to be a compositional fad at
the time of my composition studies in late 1980s Germany. Another promising
field for the study of recursive practices in music would seem to be Gamelan
music and South Indian rhythm theory.

Sorry for the vagueness - I write this far from my library and cannot verify
- but I am sure there is some literature out there on this subject.

Hope it helps


PS If the Bierwisch statement is about the comparison "natural languages"
/music, what does this assume re the "naturalness' of music ? Just as there
is no language without implicit grammar (the self-reflection on its usage
undertook mostly by poets (and only sometimes by grammatrians and
linguists)), there is no musical practice without implicit theory (where
again the musicians/composers do more work on changing and defining
grammatical usage than do the theoreticians). In this sense, there is no
"unnatural" music or - inversely - there is no such thing as a "natural"
language: usage already is applied linguistics/music theory, and usually
predates any analysis that would define its "naturalness" by centuries.

Sandeep Bhagwati
Canada Research Chair for Inter-X Art
Concordia University Montreal

2009/3/21 Thomas Noll <noll at cs.tu-berlin.de>

> 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 <http://flp.cs.tu-berlin.de/%7Enoll>
> 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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