[Smt-talk] Subdominant versus Predominant

[Ninov, Dimitar N]

Dear Jean-Michel,

Actually, Rameau did think of S as "laquelle est par conséquent au même
    intervalle de la tonique en descendant, qu'est la dominante en
    montant [...]. 

This is a clear idea of "fifth below the tonic, is it not?" In addition, Reber (as cited by Ildar) points that "sous-dominante is the scale step a p.5 below tonic, as a reflection of the dominante". Furthermore, the term sous-dominant (a chord which is below the dominant) has been interpreted in German theory as a "low dominant" (a chord which functions as a dominant below the tonic) implying the fact that S is a reflection D on the other side of the tonic. The process is simple: the French pointed where this chord stands on the scale, and the German interpreted its distance from the tonic in the light of harmonic functionality.

It was Rousseau who thoguth Rameau has confused himself: "Je puis me tromper dans l'acception des deux motsprécédents, n'ayant pas sous les yeux, en écrivant cet article, les
    écrits de Monsieur Rameau. Peut-être entend-il simplement, par sous-dominante, la note qui est un degré au-dessous de la dominante."
    [...].

But I am afraid that neither Nicholas nor you understand that the main point of our discussion is not whether the French think that S is a chord below D or the Germans think it is a chord below T. The discussion is about the fact that the function of any chord in a key is determined by its distance from the center of gravity (T) which is the only paradigm in the diatonic system. In this regard, how does the chord which is one degree below D refer to the tonal center? The chord which is below D refers to the tonic as a mirror reflection of D on the other side of the center. Of course, it does not posses the instability of D because of its structure, which reveals the presence of the tonic note and the absence of the leading tone. 

PD and "a chord which is below D" are not the same; PD implies function, and "sous-dominante" implies location. PD implies that the sole function of S is to stand before the dominant, which it is not; it also corresponds perfectly with the tonic. Sous-dominate means that in the scale controlled by the tonic, this is a chord on the fourth scale degree - one degree below D (as you point out), for better orientation.

It is good that you brought the focus of the fourth scale degree. The 4th scale degree in reference to what? In reference to the tonal center, from which we count the degrees. What is, roughly said, the characteristic of the S function? In reference to the tonic, it is an unstable chord whose instability is higher than that of the mediants, and lower than that of the dominants. Also, in a diatonic setting it counterbalances the tendency of the dominant to feel as a potential tonic, in the same way as the dominant counterbalances the tendency of the subdominant to assume the power from the tonic and become a tonic itself. This amazing interaction can be observed in the following simple experiment: without any tuning into a key, play the triads on G, F and C in any order. The triad on C will naturally emerge as a central chord
among those three chords. Why? Because, in the competition for local stability, the triads which surround C at an equal interval from both sides, neutralize themselves and become pro-active towards the C chord which attracts them as a center of gravity. 

Best regards,

Dimitar

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
________________________________________
From: Jean-Michel Boulay [jeanmboulay at googlemail.com]
Sent: Sunday, February 26, 2012 10:57 AM
To: Ninov, Dimitar N; smt-talk at lists.societymusictheory.org
Subject: RE: [Smt-talk] Subdominant versus Predominant

Dear Dimitar,

I quote from your last message: "No disagreement here either - the S chord
is a reflection of D as referred to the tonal center; it lies a perfect
fifth in the opposite direction from the tonic - a mirror inversion of the
position of D with T as an axis. Remember: T as an axis."

I hope you do not think that French theorists of the 19th century (and of a
major part of the 20th also, by the way) actually think that way. In French
theory, the word "sous-d9ominante" does not mean "dominant from below", but
only "4th degree", i.e. "the degree below the dominant". In the same way, in
French, the 6th degree of the scale is called "sus-dominante", i.e. "the
degree above the dominant", and the second degree is the "sus-tonique", i.e.
"the degree above the tonic". So, there is no idea of a "fifth below the
tonic" implied.

Best regards,

Jean-Michel Boulay
Bolzano, Italy



-----Message d'origine-----
De : smt-talk-bounces at lists.societymusictheory.org
[mailto:smt-talk-bounces at lists.societymusictheory.org] De la part de Ninov,
Dimitar N
Envoyé : dimanche 26 février 2012 17:00
À : smt-talk at lists.societymusictheory.org
Objet : [Smt-talk] Subdominant versus Predominant

Dear Nicholas,

Thank you for this quotations. They only reflect what I have been saying up
to now, namely: "By associating the fourth degree to the two preceding ones
(the first and the fifth), the tonal effect is complete." Also, "...they [T,
S,, and D] form the "bonnes notes" of the key". That is not Schenkerian, is
it? Schenker does not need the 4th scale degree to complete the tonal effect
and he does not think that T, S and D form the "bonnes notes" of the key -
he builds a house on two columns instead of three.

Another quotation from your letter: "And it is by no means true that Reber
explains it as "a reflection of the dominante". No disagreement here either
- the S chord is a reflection of D as referred to the tonal center; it lies
a perfect fifth in the opposite direction from the tonic - a mirror
inversion of the position of D with T as an axis. Remember: T as an axis.

I do not have to prove that all the chords in a key relate to the tonic.
This is an axiom, not a theorem. Otherwise, the tonic would not posses the
power of gravity, and there will be no key. PD is an invented sub-category
which implies a "dominant paradigm" which does not exist at a pure diatonic
level. The only paradigm in a key is the tonic. Only when the dominant is
tonicized does it create a temporary paradigm, as it happens with any
tonicized major and minor triads. But many theorists claim that, even if the
dominant is tonicized, they steel hear it as D, not as a local T. There is
some truth in this.

Best regards,

Dimitar

Reber, in this treatise of 287 pages, writes the word "sous-dominante"
only four or five times in all:
-- p. 5, when he describes the names of the degrees of the scale. It may be
noted that he names the sixth degree "sus-dominante ou sous-sensible", i.e.
referring it either to the dominant or to the "sensible", certainly not to
the tonic. The name "submediant" is unknown in French (or was until
recently).
-- p. 12, where he says (a) that the tonique, the dominante and the
sous-dominante are good notes to be doubled in harmony, and (b) that they
form the "bonnes notes" of the key.
-- p. 19, where he writes: "By associating the fourth degree to the two
preceeding ones (the first and the fifth), the tonal effect is complete, as
the set of the chords of these three degrees include all the notes of the
scale, as can be verified by disposing these chords as follows:" (a figure
shows the chords a fifth apart and labels them respectively "domin.",
"tonique." and "sous-dom.")
-- p. 41, where he describes the plagal cadence. "It consists in the chord
of the 4th degree (sous-dominante) either in fundamental position or
inverted, followed by the chord of the tonic;".
After that, the subdominant is not mentioned anymore. And it is by no means
true that Reber explains it as "a reflection of the dominante".

It is striking that, in more than half these few cases, the word is
associated with the expression "4th degree"; it may be reminded here that
Fétis never uses the word "sous-dominante" and always speaks of "the 4th
degree". I take this to be characteristic of 19th-century French treatises,
where the subdominant is hardly considered. There is at most a vague
reminiscence of the arrangement of the three chords forming just intonation,
and that's it.
     As to the French teachers of harmony being "proud of Rameau", they
explicitly claimed to the contrary. Catel's treatise was chosen against the
Ramists; Fétis derides Boely's "Les véritables causes de l'ignorance" as
being written in the defense of Rameau; Berton (1814) and Dourlen (1838)
nominally criticize the errors of Rameau. I can agree that the French
teachers of harmony were more Ramist than they were conscious of; but they
certainly were no "proud" Ramists.

Cordialement,

Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr





Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
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