[Smt-talk] Classical Form and Recursion

[Thomas Noll]

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.
Sincerely
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.
>
> DT
>
> Dmitri Tymoczko
> Associate Professor of Music
> 310 Woolworth Center
> Princeton, NJ 08544-1007
> (609) 258-4255 (ph), (609) 258-6793 (fax)
> http://music.princeton.edu/~dmitri
>
>
>
>
>
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*********************************************************
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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