[Smt-talk] Classical Form and Recursion

[Thomas Noll]

What does "X is Dominant of Y" mean (in the paradigmatic sense)? Is X  
a chord and Y a region? Under such an assumption it would be  
impossible to speak of secondary dominants without an additional  
operation of "typecasting" wherein chords are turned into regions.  
What is the basis for such a "typecasting" operation: Something like  
the recursivity of the Tonnetz -  as mentioned by Nicolas Meeùs? It  
seems that the acceptance of secondary dominants as instances of  
recursion has strong consequences for the entire theory.
A typical syntagmatic trace for the chord-as-region-casting is a ii -  
V/V progression. If we assume recursion we assume that behind the  
scene the "V" in "V/I" is casted as the "V" in "I/V".
Analogously we have the reverse direction, the V - ii/IV progression  
(think of Chopin's E-minor prelude). Here the "IV" in "IV/I" is  
casted as "IV" in "I/IV" behind the scene.
What are other typical syntagmatic traces for such chord-as-region- 
castings?

Sincerely
Thomas Noll

> The Tonnetz would appear to me as an example of recursion, in that  
> it can be taken to represent pitches (as in Euler), or chords (as  
> at times in Riemann), or tonalities (Schoenberg's regions). This  
> exemplifies the assumption that functions are the same or similar  
> at these three embedded levels. Some may remember that at one of  
> the early OxMac conferences (in the late '80s, I think), Leonard  
> Meyer forcefully questioned this assumption.

*********************************************************
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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