[Smt-talk] Chords of the augmented sixth-diminished third

[Ninov, Dimitar N]

Dear Stephen,

Thank you very much for your input. 

Here is where we differ: I do not automatically assign a secondary dominant function to all structures that contain a raised forth scale degree. A harmonic function is a result of two factors: structure and context. To give an illustration of how I distinguish between altered subdominants and secondary dominants in context, I will pick up a diminished seventh chord. The chords of the augmented sixth work in the same manner, so what is said about the diminished chord will hold true for them too. Also, when I use the term "subdominant" generally, it encompasses both IV and II.

When a diminished seventh chord built on #2 in major, for example, resolves into a tonic structure (I, I6 and even I 6/4 which has an outer tonic structure if not a function) it behaves in a manner which is quite different than the manner it exhibits when resolving to V. A different behavior means a different function.

In the former case, regardless of the spelling, the tone d# points upward and resolves upward thus revealing the actual root of the chord as the raised second scale degree. In other words, when this chord resolves into the tonic, it is a raised or altered supertonic that stems from ii7. Waltyer Piston calls this a raised supertonic, jazmmen call it #iio7, other people call it "a common tone diminished seventh chord", and still others call it "an altered subdominant on the second scale degree". Please, note that this resolution is not deceptive, in other words, this is not a misspelled viio7 of V which resolves deceptively into the tonic; neither is it viio7/iii which resolves deceptively. In the context: I-V4/3-#iio7-I6, or I-ii7-#iio7 - I6 its goal is the tonic; in fact we would experience some sort of mild "deception" if the tonic did not come! This is why I call it an altered subdominant. Even if it resolves into I6/4 cadential (the dissonant chord itself resolves into the cadential in the same manner as it resolves into the tonic). Since the resolution of #iio7 into the tonic does not tonicize a secondary triad but emphasizes the main tonic instead, it is not a secondary dominant. I also explain this chord as ii7 (#3, #1) a two seventh chord with a raised root and third, to show the connection with its diatonic counterpart.

In the latter case, when resolving directly into V, the same chord reveals a different tendency: regardless of the spelling, the tone Eb points downward and resolves downward. Thus a tonicization of V (a secondary tonic), takes place, and of course, the function is secondary dominant, or viio7 of V.

Now you say there is no such thing as #IV chord. Please, allow me to disagree. This would mean that the "common tone diminished seventh chord" only exists in major, but this assumption is unsupported. It is true that in minor we do not have a raised second scale degree. However, if you play the tonic in a minor key, then play a diminished seventh chord on the same bass and resolve back into the tonic, you would experience a #ivo7 (in this case inverted as #ivo4/3) which depends on the tonic and corresponds directly with it. When it resolves into i, i6 and i6/4 it neither resolves deceptively, nor tonicizes a secondary tonic to be called a secondary dominant.

All of the above, transferred to the chords of the augmented sixth/diminished third will holds true: when they resolve into a tonic structure (I, I6, I6/4) they are altered subdominants; and when they resolve directly into V, they tonicize the latter via leading tone and are thus functioning as altered dominants. 

But this is not all: he above considerations allow us to tonicize secondary triads not only via secondary dominants but also via secondary subdominants which are altered. For instance, in C major we  may tonicize the ii chord via two different "Ger.+6" chords: one which contains the leading tone to ii, and one which does not, but contains the tonic note of ii. In the former case we will have the Eb7 chord acting as viio6/5 (b3) of ii (or vii+6/5 of ii); and in the latter case we will use the Bb7 chord which will function as iv+6/5 of ii. The iv7 chord in d-minor is Gm7; just raise the root and resolve, but not into V; into the tonic (d) instead. The chord is very well explained as iv7 (#1) - a minorsubdominant with a raised root, which shows its direct connection with iv7. This practice will allow us to analyze things with greater ease and context sensitive, instead of automatically prescribe a dominant function to most similar cases.

By the way, Walter Piston goes to the extreme by saying that the augmented sixth chords are subdlominant in nature, even if they resolve into V, which I do not support either. It depends on the context.

Generally, the key may be expanded in such a manner as to include various relatively and really altered chords that depend on the main tonic and do not necessarily act as secondary functions.

Thank you for your patience.

Best regards,

Dimitar

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
________________________________________
From: Stephen Jablonsky [jablonsky at optimum.net]
Sent: Sunday, February 05, 2012 5:11 PM
To: Ninov, Dimitar N
Cc: smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Chords of the augmented sixth-diminished third

Dimitar,

You were doing great until you got to paragraph 5. Roman numerals are not used to describe pitch classes. They are used to describe harmonic function and thus the Ger+6 should be notated as vii#6/5 of V. Augmented sixth chords are altered dominants, not subdominants, because they have leading tones and all chords that have leading tones are dominant in function, at least where I come from. BTW, there is no such thing as the #IV chord unless you are in Lydian and that is another kettle of avgolemono entirely.


On Feb 5, 2012, at 4:36 PM, Ninov, Dimitar N wrote:

Dear Colleagues,

I have always been wondering why some theorists would use geographic names instead of Roman numerals to express a harmonic function that could be determined by a simple analysis. Geographic names are not universally employed (outside of the English speaking world), and, according to my observations and teaching practice, students who only use geographic names for these typical altered chords gradually loose the ability to analyze a variety of altered chords which do not fit the "mold" of "Italian", "German" and "French". Furthermore, they loose the ability to visually recognize those three common chords when they are in different bass positions.

About the so-called "Russian augmented sixth" - I think Rimsky Korskakov is right when he lists it as a counterpart of the "Ger+6" in minor. However, he never referred to any geographic names himself.

Of course, this prospective discussion could go for pages on end. Here I only wanted to generalize my main points on the so-called "augmented sixth chords as follows:

1. It is true that they have been derived through linear motion. But many chords have been derived linearly (even the seventh chord as a structure) and today we take them for granted - after having decided to use them deliberately as vertical sonorities with a concrete function.
2. The so called "augmented sixth chords" are not augmented chords by structure. In this sense, the term "augmented sixth chord" formally implies an augmented triad in first inversion - something which has nothing to do with the intended meaning. Therefore, "chords of the augmented sixth" seems a more precise name to avoid the imperfection of language.
3. They have a root, for a rootless structure does not have an intense and concrete harmonic function as they do.
4. When they appear in a position that displays a diminished third instead of an augmented sixth, the +6 number does not make sense. For example, the so-called "Ger.+6" in root position does not exhibit an augmented sixth but a diminished third. Yet many theorists simply ignore this fact and keep writing the misleading Ger.+6. When I ask my students where the augmented sixth is, they cannot find it, because it is not there. If, for some musicians, +6 and dim. 3 are the same thing, then we should also equalize the major seventh with a minor second, for example, and consider all possible secondal sonorities as different types of "major seventh chords".
5. Depending on the context, they are either altered subdominants, or altered dominants. Therefore, Roman numerals such as IV, II, V, and VII will do an excellent job - especially if they are used in a  general manner, without much clutter (for instance, #ivo7 (b3) is a visually clumsy and unappealing substitute for "Ger.+6" in minor, but IV 6+/5 or IV6/5 alt. are nice alternatives). Note that I use capital Roman letters only; the size of the chords could be revealed by the key signature plus any additional alterations.

I would appreciate any thoughts in this regard.

Dimitar

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