<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear Colleagues,<div><div apple-content-edited="true"><br class="Apple-interchange-newline"> </div><div><div>On 21-Mar-09, at 6:40 PM, Thomas Noll wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "> <div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-style-span" style="-webkit-text-stroke-width: -1; "> 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). </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br></div></div></blockquote><br></div><div><!--StartFragment-->
<div class="MsoNormal">Seeing as some of my ideas were invoked at the start of this
thread, I would like to add some remarks on the topic of recursion in classical
phrase structure.<span style="mso-spacerun: yes"> </span>As has already
been pointed out, recursion in music more obviously appears in the domains of
harmony and counterpoint, and are most fully developed (as noted by Jeff Perry
and others) in Schenkerian approaches. Identifying recursion has enormous
appeal due largely to general aesthetic and theoretical goals (typically
associated with various forms of organicist thought) of unity, coherence and
the like. I would, however, urge some caution when extending such notions to
classical phrase structure and form. </div>
<div class="MsoNormal"> <o:p></o:p></div>
<div class="MsoNormal">But first, I must acknowledge that in one important sense,
formal organization is highly recursive.<span style="mso-spacerun: yes">
</span>(Warning: shameless plug to follow.) In my essay, “What are Formal
Functions?” which appears in the recently published book <i>Musical Form, Forms
& </i><span style="font-style:normal">Formenlehre</span><i>: Three
Methodological Reflections</i><span style="font-style:normal">, co-authored by
myself, James Hepokoski, and James Webster (ed. Peter Bergé; University of
Leuven Press, 2009), I present a number of “tree diagrams” (somewhat in the
manner of L&J’s GTTM) showing how the generalized temporal functions of
“beginning,” “being-in-the-middle,” and “ending” can be seen at every level in
a formal hierarchy (except the very top level, which comprises the entire
temporal extent of the musical work), and in so doing draw upon Kofi Agawu’s
notion of introversive semiosis.<span style="mso-spacerun: yes">
</span>In this (highly general) sense, formal organization is largely
recursive. I then propose that the various formal functions defined in my book </span><i>Classical
Form </i><span style="font-style:normal">are manifestations of these temporal
functions, an obvious case being the three functions of the sentence form:
presentation (a beginning), continuation (a middle), cadential (an end).<span style="mso-spacerun: yes"> </span>Seeing as the various “formal”
functions represent, or express, the generalized “temporal” functions, a sense
of formal recursion is manifest.<span style="mso-spacerun: yes">
</span>But to the extent that the various formal functions are based on widely diverse parametric criteria, the sense of recursion is less
palpable.</span></div>
<div class="MsoNormal"> <o:p></o:p></div>
<div class="MsoNormal">For example, from bottom to top, a “basic idea,” a
“presentation,” a “main theme,” and an “exposition” each express the general
notion of temporal beginning.<span style="mso-spacerun: yes"> </span>And
their being embedded within each other (again, from bottom to top) seems to be
a perfect example of recursion (when their accompanying middles and ends are
included in the picture as well).<span style="mso-spacerun: yes">
</span>But the actual structure and defining elements of these various
functions are significantly different.<span style="mso-spacerun: yes"> </span>The
structure of a presentation has little in common with the structure of a main
theme, which itself has little in common with an entire exposition.<span style="mso-spacerun: yes"> </span>Each formal function at various hierarchical levels has its own set of defining criteria, and as such, it is not
clear that the notion of recursion is applicable in these cases.<span style="mso-spacerun: yes"> </span>Indeed, I have argued elsewhere (in my
JAMS article on “The Classical Cadence”) that many misconceptions of cadence arise precisely because theorists tend to associate any type of “closure” (a generalized formal/temporal function) at any level with the
notion of “cadence,” a more specific formal function, one that (in my
opinion) is restricted to certain middle-ground formations.<span style="mso-spacerun: yes"> </span></div>
<div class="MsoNormal"> <o:p></o:p></div>
<div class="MsoNormal">My sense is that the composers of the classical style tend
to avoid form-functional recursion at successive hierarchical levels.<span style="mso-spacerun: yes"> </span>Thus, while it is very common for an
8-bar sentence type (presentation, continuation, cadential) to be embedded
within a 16-bar period (antecedent=sentence, consequent=sentence), and while it
sometimes occurs that a periodic design can be found within the presentation of
a sentence (esp. the 8-bar presentation of the compound 16-bar sentence), it is rare for a period to be embedded within a period, or a sentence, within a
sentence.<span style="mso-spacerun: yes"> </span>The case cited by Thomas
Noll, where the “model” of a developmental “core” comprises a sentence form (as
in Op. 2/1), seems to be an exception in that a sentence-like unit is embedded
within another sentence-like unit.<span style="mso-spacerun: yes">
</span>But although we can appreciate that the “grouping structure” of a core
indeed resembles that of a sentence, marked differences between them must be
acknowledged as well: in this case, the repetition of the “model” is
harmonically sequential, whereas the repetition of a basic idea within a
presentation phrase is normally tonic prolongational.<span style="mso-spacerun:
yes"> </span>These differences in fundamental harmonic organization are
not trivial, but go to the heart of why a “core” is situated where it is in the
formal organization of a work, as opposed to a more genuine “sentence,” which
has its normative placements (as main theme, or subordinate theme) within a
movement’s structure.<span style="mso-spacerun: yes"> </span></div>
<div class="MsoNormal"> <o:p></o:p></div>
<div class="MsoNormal">In short, I believe that certain elements of classical
phrase structure are regularly recursive, but a view that overemphasizes this
aspect has the potential of blurring important distinctions among units as to
their precise formal functionality.<span style="mso-spacerun: yes">
</span>I am thus more inclined to recognize the non-recursive aspects of
classical form, and in that sense I have been strongly influenced by Leonard
Meyer (as cited in an earlier posting by Nicolas Meeùs), whose notion of
“hierarchic non-uniformity” seems highly applicable to classical form.</div><div class="MsoNormal"><br></div><div class="MsoNormal">Finally, I would welcome any feedback on these ideas from members of the list, especially since I'm venturing here into terrain (i.e., recursion theory) that is not in my area of expertise.</div>
<div class="MsoNormal"> <o:p></o:p></div>
<div class="MsoNormal">William Caplin</div>
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</div><div><br></div><div><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><br class="Apple-interchange-newline">_____________________________</div><div>William E. Caplin</div><div>James McGill Professor of Music Theory</div><div><br></div><div>Schulich School of Music</div><div>McGill University</div><div>555 Sherbrooke Street West</div><div>Montreal, Quebec</div><div>Canada H3A 1E3</div><div><br class="khtml-block-placeholder"></div><div>office: (514) 398-4535 x00279</div><div>home: (514) 488-3270</div><br class="Apple-interchange-newline"></div></div></div></div></body></html>