<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">
<div>The main attitude in my posting yesterday was a paradigmatic view on tonal functions. Dmitri's emphasis of the classification of chords into pre-dominant, dominant, tonic, and other implies a syntagmatic attitude and reminds of a the study of co-occurrences in corpus linguistics. To my mind both approaches are valuable and there is no reason to play one off against the other. In particular in this thread it is interesting to see how secondary dominants show up under both perspectives. Furthermore I believe my unorthodox proposal is also sound with the Neo-Riemannian concept of D (dominant) as an operator on triads. </div><div>Suppose again, we would like to understand harmonic analysis as an approach to the investigation of a semiotic system.</div><div>In a common and elementary understanding of sign systems we would associate chords and chord sequences with a syntactical layer and the harmonic designators such as I, ii, V/V, ... or T, S, D, or D(D(D(X)))) with expressions of a semantic metalanguage for harmony. In a less common understanding I propose to exchange the roles of syntax and semantics. The reason is first of all technical. In logical semantics one evaluates (syntactical) formulas in sets or some other category. Remember, in Neo-Riemannian theory we deal with group actions on sets of chords. Thus, the design of this description level looks more like a semantic domain. The expressions like D(D(D(X)))), however, where recursions become manifest through brackets, remind more of a syntactic domain of some predicate logics, say. My problem is to understand the ontological consequences of this technical switch. </div><div>Sincerely </div><div>Thomas Noll</div><div><div><div><br><div><div>Am 25.03.2009 um 14:21 schrieb Dmitri Tymoczko:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><blockquote type="cite"><div>Normally we might tend to say that the tonal functions should be meanings of chords. </div></blockquote><div><br></div><div>The philosophers and linguists I know would be pretty unhappy with this description. An alternative way to think about functions is as grammatical categories like "noun" and "verb." To say two chords are "predominants" is to say that they behave similarly. This leads to the North American view of functions whereby ii and IV are predominants, viio and V are dominants, I is a tonic, and iii and vi are each in their own categories -- neither tonic, nor dominant, nor subdominant. I find this view more congenial than orthodox function theory, where iii is sometimes D and sometimes T.</div><div><br></div><div>DT</div></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div>Dmitri Tymoczko</div><div>Associate<span class="Apple-converted-space"> </span>Professor of Music</div><div>310 Woolworth Center</div><div>Princeton, NJ 08544-1007</div><div>(609) 258-4255 (ph), (609) 258-6793 (fax)</div><div><a href="http://music.princeton.edu/~dmitri">http://music.princeton.edu/~dmitri</a></div><div><br class="khtml-block-placeholder"></div><div><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></span><br class="Apple-interchange-newline"> </div><br><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Smt-talk mailing list</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:Smt-talk@societymusictheory.org">Smt-talk@societymusictheory.org</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org">http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org</a></div> </blockquote></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>*********************************************************</div><div>Thomas Noll</div><div><a href="http://flp.cs.tu-berlin.de/~noll">http://flp.cs.tu-berlin.de/~noll</a></div><div><a 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"></div><br class="Apple-interchange-newline"></span></span> </div><br></div></div></div></body></html>