[Smt-talk] Soudominante versus Sous-dominante (was: Subdominant versus Predominant)

[Ninov, Dimitar N]

Dear Thomas,

That is very interesting, especially because you mention the so-called "pseudo-soudominante" - Gb in C. It turns out that this bV or #IV may work very well in a final cadence; recently I harmonized "Lightly Row" in F major, and the final cadential progression of the simple binary form happened to be a sequence: Bb9-Eb9#11-Ab9-Dbmaj7-Gbmaj7-Cb7#11-F. In other words, sequentially we have IV-bVII-bIII-bVI-bII-bV (#IV)-I. Of course, some of these are secondary dominants, others are local tonics, and the final tonic is F. The bV is a strange animal; its spelling suggests bV but its contact with the tonic sounds plagal and suggest #IV. I explain this chord as derived under the influence of the Locrian mode.

Best regards,

Dimitar

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
________________________________________
From: Thomas Noll [noll at cs.tu-berlin.de]
Sent: Saturday, February 25, 2012 6:14 PM
To: Nicolas Meeùs
Cc: Ninov, Dimitar N; smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Soudominante versus Sous-dominante (was: Subdominant versus Predominant)

Dear Nicolas, dear Colleagues,
With the two meanings of subdominant (scale step below the dominant vs. fith below the tonic) you thematize another interesting distinction, which perhaps deserves to be given its own subject in the discussion. [NB: Is it possible that Rameau in "Nouveau système de musique théorique" not only adopts but also slightly changes Dandrieu's term "soudominant" towards "sous-dominant" just in order to leave a trace of the shift in the meaning, which he undertakes?]

In accomplishment to the historical and geographical subtleties in the currency of both concepts it is insightful to look at these alternatives from a mode-theoretical point of view. On the one hand the distinction yields different derviations of the same scale degree. On the other hand, - and that is the focus of my posting - one may ask for the circumstances under which this remarkable incidence holds. My hairsplitting question is: When do Soudominante and  Sous-dominante refer to the same scale degree?

For example in the chromatic mode
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C' the divider of the mode is G and its predecessor (the pseudo-"soudominante") is Gb. The "sous-dominante", however, the scale degree a fifth below the finalis C) is still the F.
[NB: David Clampitt and I have shown in our paper on modes that for standard modes (generalized Ionian) the origin of the folding coincides with the divider predecessor.
http://www.mtosmt.org/issues/mto.11.17.1/mto.11.17.1.clampitt_and_noll.html
In this example Gb is origin and divider predecessor]

What distinguishes the diatonic case from the chromatic one is the fact, that in the diatonic case the diazeuxis, i.e. the difference intervall between fifth and fourth (generator and co-generator) coincides with the major second (the larger step interval of the mode). This is (technicalities aside) equivalent to Eytan Agmon's (1989) definition of "diatonic" in his JMT paper:  "A Mathematical Model of the Diatonic System".

In other words, Agmon's generalization of the term "diatonic" circumscribes the conditions under which the terms Soudominante and Sous-dominante are competing definitions for the same scale degree.

Sincerely
Thomas Noll