[Smt-talk] Classical Form and Recursion

[Dave Headlam]

Dear Thomas:   I would suggest a few things, of couRsE starting with not a
CURSery romp through the Inimitable VolumE ³Godel Escher Bach² by
Hofstadter:

In an article I wrote for Spectrum 7 I noted the affinity between the
opening Rhythm of Beethoven¹s opus 59, no. 1 / II and the exposition, both
of which (I now think) are sentence-structure based in a (IMO) clear case of
recursion ‹ the expos ³tries² to get to the secondary key three times, and
gets bogged down the first two times in a stubborn D minor, reflecting the
rhythm¹s inability to break free until it¹s third measure.  (It was Ed Hantz
who pointed out the ³Satz² connection to me when I arrived in Rochester.)


If you are versed in Knets and Gretchen Foley¹s writings, you will find that
recursive sum / difference combinations are the essence of George Perle¹s
music ‹ even Michael Buchler would be satisfied with the rationale for
recursion in this setting, I would wager.


Dave Headlam



On 3/21/09 6:40 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


-----------------------

Dave Headlam
Professor of Music Theory

Eastman School of Music
26 Gibbs St
Rochester, NY 14604
(585) 274-1568 office
dheadlam at esm.rochester.edu
http://theory.esm.rochester.edu/dave_headlam


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