[Smt-talk] Criteria for Old and New

Mon Mar 11 10:35:13 PDT 2013

Dear Nicolas,

thank you for this clarification. I enjoy reading Rameau in the original. It dawned at me that he had a stronger point than Schenker imagined. By the way, Rameau does not seem to use the adjectives "real"  and "abstract." Apparently, it is your evaluation, from Schenkerian standpoint. In Rameau's terms, basso fondamentale is REAL, and singing bass is common, but not true.

Yes, I know, that Fetis and some other French teachers avoided Rameau's terminology. There must have been some political reasons for that.  Well, at the same time, Fetis aknowledged the profound contribution of Rameau to theory of tonality, including his own theory. 

It is common (and I would say, vulgar) to treat non-chord tones as non-harmonic tones. This, however, does not eliminate my question: are there true non-HARMONIC tones? What is the reason to treat them as non-HARMONIC? Perhaps, this is my fantasy, but the question remains open, because, if to reverse Schenker's argument, one can say that even the smallest "embellishment" note in classical style bears tonal-harmonic function (either T, or S, or D).

In addition, to your response to Dimitar, I do not think that T-S-D-T is an elaboration of tonic. There is no such thing as "tonic" before T-S-D-T plays out. It is clearly seen in modulation: we have not modulated until the full functional circle T-S-D-T in a new key has sounded. The T-S-D-T is the mainframe component of harmonic progression. It can be reduced only on paper, in ABSTRACT graphic analysis, but not in real living music.

Best,

Ildar Khannanov
Peabody Institute
Solfeggio7 at yahoo.com 

P.S. Looks like I will have a change to ask you some of these questions in person soon.

--- On Mon, 3/11/13, Nicolas Meeùs <nicolas.meeus at scarlet.be> wrote:

From: Nicolas Meeùs <nicolas.meeus at scarlet.be>
Subject: Re: [Smt-talk] Criteria for Old and New
To: 
Cc: "smt-talk at lists.societymusictheory.org" <smt-talk at lists.societymusictheory.org>
Date: Monday, March 11, 2013, 9:26 AM

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 IV9 IV65 V7 I etc., while the fundamental bass reads I V7 I VI7 II7 V7 I with the Arabic numeral 7 denoting the dominant chords in Rameau's sense. IV9 is for Rameau a VI7 with a "supposed" third, and IV65 of course is an inverted II7.

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 
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