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<div class="moz-text-html" lang="x-western"> <font size="-1"><font
face="Georgia">One major difference between
linguistics and music theory, with respect to recursion, is that
linguistic syntax deals with phrases (sentences) only, not with
discourses as does music semiotics. It is to be expected that a
semiotic system based on such limited functionality as that of phrases
will evidence a higher level of (formal) recursion than a system of
discourses. It could be argued that natural languages evidence so to
say no recursion at the level of discourses (except, perhaps, in some
poetic discourses; but those probably </font></font><font size="-1"><font
face="Georgia">would </font></font><font size="-1"><font
face="Georgia">be more adequately treated by musical than by
linguistic theory). <br>
<br>
To state that "music – unlike language – lacks instances of true
recursion" begs several questions, not only that of the definition of
'recursion', but also that of the extent, and the conditions, to which
any language evidences recursion. Some of the messages posted in this
thread explicitly or inplicitly refer to intertextuality, which indeed
may be considered a form of external (or extrinsic) recursion. Some
stress Schenkerian theory as a theory of recursion – which it is, in my
opinion, to a larger (or, at least, to a more interesting) extent than
GTTM.<br>
<br>
The whole discussion is biased, in my opinion, by the fact that it
started with an assumption that natural languages evidence <b><i>*true*</i></b>
recursion: if natural languages must be the true yardstick of
[semiotic] recursion, then indeed music lacks it and the discussion is
not worth pursuing. If, however, one engages the discussion without
preconcieved idea of where the "truth" lies, then a cross-disciplinary
approach might become possible. This is a recurrent problem with
general semiotics, that it claims cross-disciplinarity, but hardly can
free itself from the model of natural languages.<br>
<br>
I don't know whether all natural languages evidence recursion, but I
would easily agree with the idea that not evey type of music in the
world does – or, to say it otherwise, I am not sure that all types of
music can be considered semiotic. But I do believe that our Occidental
music, probably one among the most semiotized ones in the world, must
be included in any thorough reflexion about [true?] recursion.<br>
<br>
Yours,<br>
<br>
Nicolas Meeùs<br>
<a class="moz-txt-link-abbreviated"
href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
<a class="moz-txt-link-freetext" href="http://www.plm.paris-sorbonne.fr">http://www.plm.paris-sorbonne.fr</a><br>
<br>
<br>
</font></font><font size="-1"><font face="Georgia"><br>
</font></font><br>
Thomas Noll a écrit :
<blockquote
cite="mid:BD554D7E-0BF9-47E4-BB71-3C81D950CD77@cs.tu-berlin.de"
type="cite">
<div>Dear Richard, dear all</div>
<div>many thanks for the vivid resonance to my posting and for the
particular links, examples and hints. </div>
<div>it was the intention of the organizer of the workshop in Berlin
to have concepts like iteration, repetition, hierarchy, recursion,
self-similarity etc. on the table and to consider their manifestations
in various fields with participants from various fields. The challenge
was of course to search for related meanings in different fields.</div>
<div><br class="webkit-block-placeholder">
</div>
<div>With regard to the connection with computer programming and
music let me mention the rhythmic trees in the software "OpenMusic" (as
they occur in the voice-objects of OM) as a nice instance: The very
elegant(!) implementation is based on a recursive concept of musical
duration. Simply speaking, a duration is a pair (d L), where d is a
number and L a (possibly empty) sequence of durations. I like this
example because it embodies essential syntactic aspects of traditional
rhythmic notation in terms of a context free Chomsky LL1-grammar,
namely the programing language LISP. I even tend to believe that the OM
developers noticed that traditional rhythmic notation with embedded
beams intellectually predates(!) the invention of derivation trees by
the 20th century grammarians.</div>
<div><br class="webkit-block-placeholder">
</div>
<div>
<div>it seems useful, but is not that easy, to formulate satisfactory
conditions of fulfillment for what might be called "true recursion" in
music.</div>
<div>In order to agree upon an instance of recursion it is perhaps
necessary to enter a formalized metalanguage. In a second phase of the
discussion different applications of recursive definitions to musical
objects would have to be compared and distinguished. A quite general
and flexible kind of concept with embodied recursion is what Guerino
Mazzola in "Topos of Music" (section 6.7) calls circular denotators.
The above definition of rhythmic tree in OM is circular, for example.
If we take Mazzola's attempt seriously we should say: Whenever a music
theorist deliberately uses a circular denotator in order to identify
a musical object, he/she takes responsibility for involving an instance
of recursion. But which ones are the "truly" interesting cases for a
cross-disciplinary discourse? That's my question in this thread. </div>
<div> </div>
</div>
<div>Following a common subdivision of syntactics we may decide to
distinguish between paradigmatic and syntagmatic recursion. David
Lewin's K-Net-tutorial (on the "Choral" in Schoenbergs Op.11 No.2 is an
instance of paradigmatic recursion, while formalized approaches to
Schenkerian Analysis (a recent one was presented by Alan Marsden and
Geraint Wiggins, CIM08, Thessaloniki) are candidates for instances of
syntagmatic recursion. </div>
<div>I fear a comparison with natural language cannot bypass the
differences in the constitution of paradigms and syntagms and the
particularities of their interaction.</div>
<div><br class="webkit-block-placeholder">
</div>
<div>Sincerely,</div>
<div>Thomas Noll </div>
<div><br class="Apple-interchange-newline">
<blockquote type="cite"> Dear all,
<div><br>
</div>
<div><span class="Apple-tab-span" style="white-space: pre;"> </span>I
find this thread less interesting than it might be because the term
"recursion" has many different meanings attached to it in different
fields. My first exposure was in computer programming, and descriptions
of "recursion" in Schenkerian thought made little sense to me at first
because of my initial exposure to the term. In such circumstances, it
is easy to pull out a definition that will tank someone else's
position. I believe philosophers call this "equivocation of terms."</div>
<div><span class="Apple-tab-span" style="white-space: pre;"> </span>Thomas,
how was this problem addressed at the conference? It must have been
very stimulating.<br>
</div>
<div><br>
</div>
<div>Best,</div>
<div><br>
</div>
<div>Richard Hermann, Prof. of Music</div>
<div>Univ. of New Mexico</div>
<div><br>
<div>
<div>On Mar 22, 2009, at 5:19 AM, Dave Headlam wrote:</div>
<br class="Apple-interchange-newline">
<blockquote type="cite"> <font face="Verdana, Helvetica, Arial"><span
style="font-size: 14px;">Dear Thomas: I would suggest a few things,
of couRsE starting with not a CURSery romp through the Inimitable
VolumE “Godel Escher Bach” by Hofstadter:<br>
<br>
In an article I wrote for Spectrum 7 I noted the affinity between the
opening Rhythm of Beethoven’s 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 “tries” to get to the secondary key
three times, and gets bogged down the first two times in a stubborn D
minor, reflecting the rhythm’s inability to break free until it’s third
measure. (It was Ed Hantz who pointed out the “Satz” connection to me
when I arrived in Rochester.)<br>
<br>
<br>
If you are versed in Knets and Gretchen Foley’s writings, you will find
that recursive sum / difference combinations are the essence of George
Perle’s music — even Michael Buchler would be satisfied with the
rationale for recursion in this setting, I would wager.<br>
<br>
<br>
Dave Headlam<br>
<br>
<br>
<br>
On 3/21/09 6:40 PM, "Thomas Noll" <<a moz-do-not-send="true"
href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a>> wrote:<br>
<br>
</span></font>
<blockquote type="cite"><font size="4"><font
face="Helvetica, Verdana, Arial"><span style="font-size: 18px;">Dear
Colleagues,<br>
last summer I participated in a cross-disciplinary workshop on
"Recursion in Logics, Language and Art" in Berlin, organized by the
logician Ingolf Max.<br>
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.<br>
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. <br>
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). <br>
I would be glad to share this discussion with the list and to later
forward the thread to the participants of the workshop.<br>
Sincerely<br>
Thomas Noll <br>
</span></font></font><font face="Verdana, Helvetica, Arial"><span
style="font-size: 14px;"><br>
<br>
</span><font size="2"><span style="font-size: 12px;">*********************************************************<br>
Thomas Noll<br>
<a moz-do-not-send="true"
href="http://flp.cs.tu-berlin.de/%7Enoll">http://flp.cs.tu-berlin.de/~noll</a><br>
<a moz-do-not-send="true" href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a><br>
Escola Superior de Musica de Catalunya, Barcelona <br>
Departament de Teoria i Composició <br>
Tel (priv.): +34 93 268 75 19<br>
Tel (mobil): +34 66 368 12 02<br>
<br>
*********************************************************<br>
<br>
<br>
<br>
<br>
</span></font><span style="font-size: 14px;"> <br>
<br>
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<span style="font-size: 14px;"><font face="Monaco, Courier New"><br>
<br>
</font><font face="Verdana, Helvetica, Arial">-----------------------<br>
<br>
Dave Headlam<br>
Professor of Music Theory<br>
<br>
Eastman School of Music<br>
26 Gibbs St<br>
Rochester, NY 14604<br>
(585) 274-1568 office<br>
<a moz-do-not-send="true" href="mailto:dheadlam@esm.rochester.edu">dheadlam@esm.rochester.edu</a><br>
<a moz-do-not-send="true"
href="http://theory.esm.rochester.edu/dave_headlam">http://theory.esm.rochester.edu/dave_headlam</a><br>
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<div>*********************************************************</div>
<div>Thomas Noll</div>
<div><a moz-do-not-send="true"
href="http://flp.cs.tu-berlin.de/%7Enoll">http://flp.cs.tu-berlin.de/~noll</a></div>
<div><a moz-do-not-send="true" href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a></div>
<div>Escola Superior de Musica de Catalunya, Barcelona </div>
<div>Departament de Teoria i Composició </div>
<div>Tel (priv.): +34 93 268 75 19</div>
<div>Tel (mobil): +34 66 368 12 02</div>
<div><br class="khtml-block-placeholder">
</div>
<div>*********************************************************</div>
<div><br class="khtml-block-placeholder">
</div>
<div><br>
<br class="khtml-block-placeholder">
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