[Smt-talk] prolongation

[Nicolas Meeùs]

Le 17/07/2011 17:15, Eytan Agmon a écrit :
>
> (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.
>
Indeed. And this is why I consider that the two tonics in I–V–I are not 
the same as the prolonged tonic (and that, as Ildar told us, the second 
I is not the same as the first).
>
> (2)A chord progression Y-X-Y assumes that X and Y occupy the same 
> “tonal space” (=diatonic system).
>
For Schenker, the "tonal space" certainly is not the diatonic system. 
The concept is described mainly in /Erläuterungen/ (/Der Tonwille/ IX 
and X, /Das Meisterwerk /I and II). Schenker writes:
/Die Tonräume des Klanges misst die Urlinie aus und bringt den Klang so 
erst zum Ausdruck, zum Bewustsein/. /Die Urlinie ist ersters Durchgang, 
als solcher erste Melodie und zugleich Diatonie. Andere Taunräume als 
1-3, 3-5, 5-8 gibt est nicht, eienen anderen Ursprung des Durchganges, 
der Melodie gibt es nicht.
/In Ian Bent's translation: "The Urlinie measures out the tonal spaces 
within the chord, and thereby articulates the chord for the first time, 
bringing it to consciousness . The Urlinie is the first passing-tone 
progression [/erster Durchgang/]. As such it constitutes the first 
melody, and at the same time provides the diatonic content [/Diatonie/]. 
There are no other tonal spaces than those of 1–3, 3–5, and 5–8. There 
is no other origin for passing-tone progressions, or for melody."/
/Remarks about the translation (none of these are extremely important, I 
would hate to seem pedant about this; but they are slightly irritating):
– One possible translation of /Ausmessen/ is "to pace": it is by pacing 
the tonal spaces that the Urlinie takes their measure, and the pacing 
may be more important than the measure. [Note that the Urlinie, in this 
particular text, is an ascending line. It is changed in a descending one 
in fig. 4 of /Free Composition/, where Schenker nevertheless stresses 
its articulation on ^8 ^5 (^3) ^1 and its relation to the chord from 
which it emanates. The "diatony" (which is not exactly the diatonic 
system) results from the pacing of the space.
– Schenker really writes "...thereby brings the chord for the first time 
to expression, to consciousness". Ian Bent translation of /Ausdruck/ in 
"articulate" might refer to an expression in words, but this remains 
unclear.
– "The Urlinie ... _is_ the first melody and at the same time _is_ the 
/Diatonie/"; Schenker does not seem to refer to _providing_ a diatonic 
_content_/./

Tonal spaces are at first empty spaces. Any filling is dissonant, while 
the spaces themselve must be consonant [let's leave aside the problem of 
7th chords]: /
     Der este Urlinie-Durchgang is dissonierend (Sekund, Quart, Sept). 
Die Dissonanz wird in eine Konsonanz verwandelt, weil im Gegensatz zu 
jener nur diese allein mit ihren Tonräumen (siehe oben) wieder zu neuen 
Durchgängen, zu neu sich zweigender Melodie führen kann. Dies geschieht 
nun durch Prologationen in immer neuen Stimmführungsschichten/, etc.
     Ian Bent translates: "The first passing-tone progression comprised 
by the Urlinie generates dissonance (second, fourth, seventh). 
Dissonance is transformed into a consonance because only consonance, 
with its tonal spaces (as shown earlier) can, by contrast with 
dissonance, promote new passing-tone progressions and freshly burgeoning 
melodies. This comes about through prolongations in ever-renewing layers 
of voice-leading..."
     Remarks about the translation:
– Schenker does not say that the Urlinie _generates_ dissonance, but 
that it _is dissonant_.
– The new tonal spaces do not _promote_, they _lead to_ new passing-tone 
progressions.
– /sich zweigender/ belongs to Schenker's sophisticated German; it means 
"developing into new branches".

X does not occupy the same tonal space as Y: insofar as it is made 
consonant (by other parts of the voice leading), it creates a _new_ 
tonal space, probably within the same diatony. I suspect however that 
Schenker is not strict about keeping to the diatony: passing notes may 
include a b7 or a #4...
     The chord (/Klang/) has no conscious existence before it is 
expressed in prolongation. This confirms the idea of the chord initially 
being but an abstraction, a concept (/Harmonienbegriff/), as already 
stated in /Harmonielehre/.

> (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.)
>
We are speaking of descriptions. The Y–X–Y model appears merely to 
describe a 'pendular' situation, what Sadaï names the "a–b–a pattern". 
Schenker's description as prolongation appears to add strong precisions 
about how X relates to Y through voice leading (and certainly not by 
mere juxtaposition). Isn't the efficient voice leading merely a 
consequence of the structure of chords as piling 3ds, with the result 
that any note in between the borders of the tonal spaces is adjacent to 
at least one (and often both) of these borders?
     In addition, not all prolongations result in embedded chords.

Nicolas Meeùs
Université Paris-Sorbonne

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