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<font face="Calibri">Ildar,<br>
<br>
French is a tricky language, and Rameau's even more. Your
quotation of Rameau does not say exactly what you understand. The
text you quote, which is p. 159 of Génération harmonique, concerns
the "supposition", the addition of notes belonging to the
"arithmetic proportion" (let's say, belonging to the inverted
harmonic series) under a consonant chord. This, he stresses,
cannot be done under the tonic ("un son principal"), but well
under a dominant, i.e., for him, any chord progressing by
ascending 4th. He writes: <br>
</font>
<blockquote>
<p>...de sorte que, pour exposer le fait plus clairement, on peut,
dans certains cas, ajouter une Tierce, ou une Quinte, au-dessous
d'une Dominante, et de son Harmonie.<br>
Les cas où cette addition peut se faire, n'ont d'autre principe
que le gout du chant d'une Basse, qui n'est plus la
fondamentale, et qu'on appelle vulgairement Continue<br>
</p>
</blockquote>
which I'd literally translate as follows:<br>
<blockquote>...so that, to state the fact more clearly, one may, in
certain cases, add a third or a fifth below a dominant and its
harmony.<br>
The cases were this addition can be done have no other principle
than the taste for a singing bass, which is no more the
fundamental [bass], and which is commonly called a thorough
[bass].<br>
</blockquote>
('Vulgaire', in 18th-century French, means "common".)<br>
There is question, in this sentence, neither of a "bass line of
non-harmonic nature", nor of something that would have been
misunderstood before Rameau, but merely of a concrete difference
between a real, singing bass, and the abstract fundamental bass.
Rameau's example XXIII that follows illustrates that by giving the
two basses one above the other for the same chords. The continuo
bass reads, in Roman numerals, I I<sup>#7</sup> I IV<sup>9</sup> IV<sup>6</sup><sub>5</sub>
V<sup>7</sup> I etc., while the fundamental bass reads I V<sup>7</sup>
I VI<sup>7</sup> II<sup>7</sup> V<sup>7</sup> I with the Arabic
numeral 7 denoting the dominant chords in Rameau's sense. IV<sup>9</sup>
is for Rameau a VI<sup>7</sup> with a "supposed" third, and IV<sup>6</sup><sub>5</sub>
of course is an inverted II<sup>7</sup>.<br>
<br>
This distinction between a singing bass and the fundamental bass,
oddly enough, surfaces at various points in Schenker's writings.
There is the passage from Counterpoint that you quote, where
Schenker writes:<br>
<blockquote>der Klang wird auskomponiert und als solcher auch durch
die horizontale Linie erwiesen. [...] Denn nun hatte, wie die
obere, ebenso auch die tiefere Stimme ihre eigenen Durchgänge, die
sich — wohlgemerkt zwischen den harmonischen Tönen desselben
Klanges — von Haus aus eben nur als wahre Durchgangstöne
erwiesen. (Kp I, xxiv-xxv)<br>
the chord is elaborated and as such also represented through the
horizontal line. [...] Now the lower voice, like the higher one,
has its own passing notes which – located between the harmonic
tones of the same chord – manifest themselves from the start as
true passing notes.<br>
</blockquote>
Also when he states (Das Meisterwerk I, p. 188 of the German
edition; I have neither the original German nor the translation at
hand just now) that in free composition, the 'Aussensatz' consists
in the counterpoint between two elaborated voices, the upper one and
an inner one above the implicit bass line ruling the fundamentals
and the degrees. The implicit bass line of course is Rameau's
fundamental bass and the elaborated inner one above it is Rameau's
"singing bass".<br>
<br>
That non-chord tones are "foreign to the harmony" is a tradition in
French theory. See for instance Rousseau's Dictionnaire, vol. 2, p.
203 sq, art. "Supposition". In the 19th century, the opposition
between "natural" dissonant chords and the other dissonances was
based on the same principle: while "natural" dissonances (e.g. the
dominant 7th) are found in the harmonic series, the other
dissonances result from voice leading. This is, among others, Fétis'
doctrine, and it is still very much adhered to in the Paris
Conservatoire even today.<br>
<br>
Yours,<br>
<br>
Nicolas Meeùs<br>
Université Paris-Sorbonne<br>
<br>
<br>
<br>
<br>
<br>
<div class="moz-cite-prefix">Le 10/03/2013 17:48, Ildar Khannanov a
écrit :<br>
</div>
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<div>Dear Dimitar and Paul,</div>
<div> </div>
<div>I may add that there are errors in Schenker's
theory in its speculative aspect as well. For example,
the treatment of non-chord tones as something that does
not belong to "so-called ""harmony"" (CP, p.xxiv). So,
for him, these are true non-harmonic tones--the proof of
existence of "pure theory of voice leading" (CP, p. 10).
However, all of them have harmonic origin.
For example, the anticipation note did not come from
outer space: it is a part of harmony of the following
chord. Suspension is the part of the previous harmony.
There is no Passing 6/4 chord: it is a passing Dominant
6/4. Students who learn Schenkerian theory before
harmony always write the supertonic triad in its place.
They follow the logic of Schenkerian theory, in which
the main criterion is adjacency. Yet, the I to ii
connection does not make sense at all functionally. That
is why this passing chord is exactly the Dominant 6/4.</div>
<div> </div>
<div>Before Rameau, in figured bass notation, these
non-chord tones were often treated as chord-tones
("9/4/2" chord, for example). The theorisists of this
tradition simply did not understand the logic of
harmony. Rameau qualifies them as those "who have the
taste for some bass line of non-harmonic nature, which
is also VULGARILY called continuo" (Generation
harmonique, p. 160).</div>
<div> </div>
<div>Everything in harmony can fit into Rameau's theory.
After all, he represents the Age of Reason. The Light of
Reason penetrates every place, every white spot on the
map and every remote dark place. In comparison with
that, the post-WWI environment, in which Schenker grew
up, is the Dark Age. The former produced the voice of
reason, the latter--the scream.</div>
<div> </div>
<div>Best,</div>
<div> </div>
<div>Ildar Khannanov</div>
<div>Peabody Conservatory</div>
<div><a moz-do-not-send="true"
href="mailto:solfeggio7@yahoo.com">solfeggio7@yahoo.co</a>
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