[Smt-talk] Classical Form and Recursion

Ildar Khannanov solfeggio7 at yahoo.com
Wed Mar 25 18:14:43 PDT 2009

Dear Thomas,
I think I am getting this, little by little. Something similar has been done in literary analysis under the term "juxtaposition of metaphor on metonymy." Derrida and Paul de Man liked to talk about this. In fact, they tried to use rhetoric en lieu of grammar and vice versa. In other words, to do paradigmatic analysis (tropes, figures) as if they were dealing with syntax, and to treat syntax as a kind of metaphorical expression. I have to say that it did work.
North American understanding of tonal functions is, indeed, purely syntactic. That is why Riemann is hastily discarded with his Tonvorstellungen. Pradigmatic, or, in your words, semantic understanding of tonal functions is not common in the US. I would add my two cents by saying that paradigmatic perception of tonal functions is not inborn. It comes with special training (ear training) directed at hearing them phenomenally, but in my years of training in a pro-Riemannian land I have not heard a clear explanation of what tags the T, S, and D together (syn-tags them).  Are you trying to explain it by using recursion?
Ildar Khannanov
Peabody Conservatory

--- On Wed, 3/25/09, Thomas Noll <noll at cs.tu-berlin.de> wrote:

From: Thomas Noll <noll at cs.tu-berlin.de>
Subject: Re: [Smt-talk] Classical Form and Recursion
To: "smt-talk Talk" <smt-talk at societymusictheory.org>
Date: Wednesday, March 25, 2009, 4:37 PM

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.    
Suppose again, we would like to understand harmonic analysis as an approach to the investigation of a semiotic system.
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.      
Thomas Noll

Am 25.03.2009 um 14:21 schrieb Dmitri Tymoczko:

Normally we might tend to say that the tonal functions should be meanings of chords. 

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.


Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)

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Thomas 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
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