[Smt-talk] prolongation

Eytan Agmon agmonz at 012.net.il
Sun Jul 17 08:15:17 PDT 2011



(1)    I believe that Schenker would also not regard (say) the “global” prolonged tonic as belonging to the same level as the I-V-I by which it is prolonged.

(2)    A chord progression Y-X-Y assumes that X and Y occupy the same “tonal space” (=diatonic system).

(3)    There exists a logical interdependence between the vertical and horizontal dimensions, in particular, between progressions involving triads and seventh chords and what I call (Musikometrika 3, 1991) “efficient” voice leading.


Therefore, as far as I can see, the Y-X-Y model “lets Y grow” in much the same sense as Schenker’s. (Melodic prolongation is analogous, yet distinct from harmonic prolongation.)


Eytan Agmon

Bar-Ilan University 


From: Nicolas Meeùs [mailto:nicolas.meeus at paris-sorbonne.fr] 
Sent: Sunday, July 17, 2011 5:40 PM
To: Eytan Agmon
Cc: 'SMT Talk'
Subject: Re: [Smt-talk] prolongation


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

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.]


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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