[Smt-talk] BELGIAN +6

[Dmitri Tymoczko]

Hi Ildar,

> Your hearing of the three national chords as derived from the V/V seems very intriguing to me. Indeed, is there not an Fa# in each of them? My position, nevertheless, of considering them a part of subdominant function is based upon the fact that these adjacencies (Fa# to Sol, Re# to Mi) are the parts of different keys, not the given Do major. They belong to different geometries and different physics. There is the geometry of tonic (TSDT) and other neighboring spaces with their own tension-resolution patterns. For being a Dominant function, the chord must have a leading tone in a given key, and that is what exactly missing in German, French and Italian chords. So, I should say that French, German and Italian chords in the given key serve the role of Subdominant because the original chords from which they are derived are IV and ii, and because all three do not have the Leading Tone in the given key. The fact that the altered chords have tendencies to leave a given geometry does not change their function in the original space of TSDT. And the V/V is not their only tendency, if to be precise.

My difficulty with this is the notion of "derived from" which strikes me as ambiguous.  The German 6/5 can be "derived" in multiple ways:

	Way 1: take viio6/5/V and lower the bass by semitone.
	Way 2: take iv6/5 and raise the root by semitone.

You seem to think that Way 2 is the right one, but I can't follow you in that.  To me, they're both equally true, which means that "derived from" can't help us determine function.

The other difficulty I have is the idea that semitonal alteration doesn't change chord function.  This I just don't believe.  For example, IV is a subdominant, but #ivo is a viio/V chord, an applied dominant.  Your argument seems to work just as well for applied dominants as for augmented sixths -- for you, viio/V should be a subdominant, not a "dominant of the dominant" chord.  I can't follow you here -- if the term "function" is to be useful for me, then there has to be a difference between subdominant and dominant of the dominant.

>  You observed the placement of the German chord in variations. Strange choice! I completely agree with you that we have to observe the placement of a chord in order to analyze its structural meaning. However, it seems more logical to me to find the most common placement of the German chord, in preparation of the terminal dominant or a cadence. I make my final definition of it s Subdominant because it is placed in the 6th metric measure of the metric period. Or, like in Mozart concerti and sonatas, right before the Cadenza, resolving into the dominant in the main key.

Just to be clear: my claim was that composers regularly use augmented sixths in passages where, in earlier versions of the same music, they had V/V (or vice versa), whereas you don't find the same intersubstitution of IV (or ii) and the augmented sixths.  In all honesty, this seems pretty decisive to me -- about as strong an argument as you're ever going to get in music theory.  It strongly suggests that composers conceive V/V and the augmented sixth as "basically the same" or "analogous" whereas they didn't feel that way about the augmented sixths and IV or ii.

My intuition is that V/V before V is about as common as augmented sixths are in the same spots -- and that the applied dominants appear in basically the same places, including before the I6/4 that leads to a cadenza.  (David Lewin used to emphasize to me that V/V was one of Beethoven's favorite chords.)  I'd need to look at statistics to back this up, but offhand that seems right.

>  There has been an objection earlier, that the three named chords cannot be the Subdominant because they do not have Fa, but Fa# instead. But, by the same logic, they cannot be the chords of the V/V because instead of Re the German chord has Re#.

Except that dominant chords have ^b2 all the time -- in late Beethoven, Schubert, Chopin, etc.  The only issue here is that the augmented sixths appeared first as V/V chords in minor, where the ^b6 is given by the key signature.  To me, that's not at all mysterious.  The obvious thought is that V/V in minor has voice leading awkwardnesses, with ^#6 moving down to ^5, contravening standard minor-mode practice.  Sometimes you even have ^b6->^#6->^5, which is quite awkward.  So composers just started retaining the key signature's ^b6 in the applied dominant V/V, producing the augmented sixth.

Best wishes,
DT

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)
http://dmitri.tymoczko.com