[Smt-talk] prolongation

[Nicolas Meeùs]

In so far as Schenkerian prolongation can be represented by letters, I'd 
answer something like this:

If the prolongation of a chord *Y* produces a chord *x* (not all 
prolongations produce new chords), then, in specific cases, the result 
may be of the form *y–x–y*. It would however be mistaken to believe that 
the resulting *y*'s are the same thing as the original *Y*: they do not 
belong to the same level.

Going on with alphabetic labels, the model representing this situation 
might be formulated as follows:
_*y – x – y*_
*Y*

In what sense does Schenkerian prolongation "let Y grow"? I don't 
suppose it necessary to repeat here Schenker's organic metaphors. From a 
more technical point of view, Schenker views the initial chord as 
delimiting a "tonal space", intervals between disjunct degrees, open to 
be filled by conjunct voice leading. This particularly is the case of 
triads, the degrees of which remain disjunct in any inversion. The 
conjunct movements therefore necessarily involve notes foreign to the 
initial chord. This process of filling the tonal space by conjunct 
movements is the main process of prolongation: in lets the prolonged 
chord extend on a considerable span of time. [Calling this extension a 
"growth" is part of the organic metaphor, which one may or may not like; 
yet, even "extension" already is a metaphor: any description of music 
has to be metaphoric in a way or another.]
     Schenker himself gives the example of the first two bars of 
Chopin's Prelude op. 28 n. 6; one could easily extend the example to the 
first four bars: they form a four-bar prolongation of the chord of b 
minor, by arpeggiation, neighbor notes and passing notes, without any 
intervening new chord being created. One could similarly quote the first 
four bars of Chopin's Nocturne op. 27 n. 2, prolonging a Db major chord.
     In the first four bars of Bach's C major Prelude of WTC I, the 
chord of C major is prolonged by neighbour notes exclusively. Here, 
however, these filling notes meet to produce new chords, new tonal 
spaces, which might have been further prolonged if Bach had wanted to 
produce a longer work. Here, *Y* (C major) grows, is prolonged, into 
*y–z–x–y*; each of these is turn is shortly prolonged by arpeggios.

This brings us back to Dmitri's initial opposition between the 
descriptive usage of Roman numerals and the "intentional" idea of 
prolongation. In the case of Bach's Prelude, *y–z–x–y *could be replaced 
by I–ii–V–I. But that would say nothing of the origin of these four 
chords, of the reasons why they follow each other in that sense, etc. 
[In this particular case, the description by the voice leading does not 
say much either about the grammaticality of the phrase and, in 
particular, does not say why Bach could not have written I–V–ii–I; but 
that is another discussion.]

Yours,

Nicolas Meeùs
Université Paris-Sorbonne



Le 17/07/2011 10:22, Eytan Agmon a écrit :
>
> Nicolas wrote:
>
> “As to Y–X–Y as a ‘model of prolongation’, I can only repeat that this 
> would form an excessively superficial view of the process. There is 
> only one ‘Y’, that which is prolonged; the prolongation does not 
> consist in splitting Y in two in order to insert X between the two 
> parts, but in letting Y grow. ‘X’, if any, fully belongs to Y, of 
> which it is an organic outgrowth. Schenker's thought is not an easy 
> one; it certainly never is ‘naïve’.”
>
> Suppose that the “Y-X-Y model” includes a relationship between Y and 
> Y-X-Y. Then certainly Nicolas’s first objection is overcome (“there is 
> only one ‘Y’, that which is prolonged”). As to his second objection, I 
> think we need to have a clearer sense of what it means to “let Y grow” 
> (or “let X grow organically out of Y”) before we can judge the “Y-X-Y 
> model” in this sense as a “superficial” or “naïve” interpretation of 
> Schenkerian Prolongation.
>
> Eytan Agmon
>
> Bar-Ilan University
>
>
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