[Smt-talk] Criteria for Old and New

[Nicolas Meeùs]

Ildar,

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:

    ...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.
    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

which I'd literally translate as follows:

    ...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.
    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].

('Vulgaire', in 18th-century French, means "common".)
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^#7 I IV^9 IV^6 _5 V^7 I etc., while the fundamental bass 
reads I V^7 I VI^7 II^7 V^7 I with the Arabic numeral 7 denoting the 
dominant chords in Rameau's sense. IV^9 is for Rameau a VI^7 with a 
"supposed" third, and IV^6 _5 of course is an inverted II^7 .

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:

    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)
    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.

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".

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.

Yours,

Nicolas Meeùs
Université Paris-Sorbonne





Le 10/03/2013 17:48, Ildar Khannanov a écrit :
> Dear Dimitar and Paul,
> 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.
> 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).
> 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.
> Best,
> Ildar Khannanov
> Peabody Conservatory
> solfeggio7 at yahoo.co <mailto:solfeggio7 at yahoo.com>
>
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