The so-called "German Sixth" Chord
Here's another sonority unique to Western music - but not limited strictly to art music proper - that comes down to us with a useless nationalistic appelation: The so-called German Sixth chord. This chord - or rather these chords - are known to us with a jazz background as Substitute Secondary Dominants, or simply as "Sub-Fives". Because the jazz theory explanation for these chords is so much more convienient and descriptive than even Dr. Cho's traditional-based rationale for them, this is the terminology that I will employ.
The theoretical derivation of these chords is based on the fact that they share an enharmonic tritone with the regular secondary dominant that targets the same chord. I have presented this in the first measure of the example above where you can see that the V7/V and the SubV7/V share enharmonically the tritone between C and F-sharp/G-flat.
In their employment in traditional music, the Substitute Secondary Dominants are not notated as dominant seventh chords, however: The minor seventh of that chord is notated as an Augmented Sixth in the first version, which I have presented in the second measure of the example, and the fifth is also notated as a Doubly Augmented Fourth in the second version, which is presented in the third measure. These enharmonic modifications of the sub-fives have to do with their respective traditional resolutions.
On the middle staff I have given these respective traditional resolutions where the first version of the now Enharmonic Substitute Secondary Dominant resolves directly to it's target, in this case the V chord. Note that a parallel perfect fifth results from this resolution, and that there is no transformation: The chord tones maintain their respective functions with the enharmonic minor seventh just doubling the root of the target chord, presumably momentarily before it moves down to become the seventh again. In early employments of this chord, composers tended to hide this parallelism by delaying the resolution of the fifth with a flat-6 to 5 suspension. Later composers who favored this chord, such as Chopin, had no qualms about allowing for the parallel fifth to occur directly. In fact, there are so many parallel fifths in Chopin's music that they really do constitute an aspect of his style, which is quite "jazzy" with respect to the voice leading.
The second two measures of the middle staff present the traditional resolution of the second version of the enharmonic sub-five that has the notated doubly augmented fifth. This chord progresses to a I(6/4) sonority - which admittedly does not exist independently, but rather is only a suspended version of the V chord - before finally resolving to the V7. Note here that the final dominant seventh has a doubled root, but no fifth. Obviously this is going to be problematic if harmonic canon writing is the goal. Not only that, but the resolution figure already has a constant root, so in the virtual five voice method for writing harmonic canons, this resolution will create parallel octaves with the constant root bass.
Now, if a triadic texture is being composed in the upper stratum, no such problem would arise so long as the texture is momentarily changed to four real parts. The upper stratum simply recieves a diminished triad and the bass creates the SubV by arranging itself a major third below the lowest note in that diminished triad. In this sense, substitute secondary dominants are really more appropriate for the essentially triadic transformational environment: The upper triad then has a proper clockwise transformation and the bass maintains it's constant root motion with no problems with parallelisms. I suppose I should mention at this point that accompanied harmonic canons can obviously be composed with a triadic upper stratum and a repeating root progression pattern over a constant root bass, but they would not be double canons, which has been my particular interest to this point. I suppose I should compose one of those to demonstrate some of these sonorities in that context.
In order to employ substitute secondary dominants in a virtual five voice texture over a constant root bass - as I have been doing thus far in my examples since the Secondary Dominants and Harmonic Canons post - the regular clockwise transformation that strong decending root motions normally get would have to be employed. This creates problems if the target chord is of the major gender because an augmented second would result if the resolution were made directly. In order to maintain the glass-smooth voice leading I prefer, the target chord must either be of the minor gender, or it must be changed to the minor gender momentarily. I have demonstrated this on the bottom staff of the example. This resolution sounds very unusual: The minor seventh or enharmonic augmented sixth resolves outward as per usual, but the tritone does not "do it's thing". This, combined with the unexpected minor gender of the target in this particular resolution, can only be described as a peculiar effect. Nothing could better explain why I use these chords sparingly: They are simply highly problematic in their various methods of employment.
The theoretical derivation of these chords is based on the fact that they share an enharmonic tritone with the regular secondary dominant that targets the same chord. I have presented this in the first measure of the example above where you can see that the V7/V and the SubV7/V share enharmonically the tritone between C and F-sharp/G-flat.
In their employment in traditional music, the Substitute Secondary Dominants are not notated as dominant seventh chords, however: The minor seventh of that chord is notated as an Augmented Sixth in the first version, which I have presented in the second measure of the example, and the fifth is also notated as a Doubly Augmented Fourth in the second version, which is presented in the third measure. These enharmonic modifications of the sub-fives have to do with their respective traditional resolutions.
On the middle staff I have given these respective traditional resolutions where the first version of the now Enharmonic Substitute Secondary Dominant resolves directly to it's target, in this case the V chord. Note that a parallel perfect fifth results from this resolution, and that there is no transformation: The chord tones maintain their respective functions with the enharmonic minor seventh just doubling the root of the target chord, presumably momentarily before it moves down to become the seventh again. In early employments of this chord, composers tended to hide this parallelism by delaying the resolution of the fifth with a flat-6 to 5 suspension. Later composers who favored this chord, such as Chopin, had no qualms about allowing for the parallel fifth to occur directly. In fact, there are so many parallel fifths in Chopin's music that they really do constitute an aspect of his style, which is quite "jazzy" with respect to the voice leading.
The second two measures of the middle staff present the traditional resolution of the second version of the enharmonic sub-five that has the notated doubly augmented fifth. This chord progresses to a I(6/4) sonority - which admittedly does not exist independently, but rather is only a suspended version of the V chord - before finally resolving to the V7. Note here that the final dominant seventh has a doubled root, but no fifth. Obviously this is going to be problematic if harmonic canon writing is the goal. Not only that, but the resolution figure already has a constant root, so in the virtual five voice method for writing harmonic canons, this resolution will create parallel octaves with the constant root bass.
Now, if a triadic texture is being composed in the upper stratum, no such problem would arise so long as the texture is momentarily changed to four real parts. The upper stratum simply recieves a diminished triad and the bass creates the SubV by arranging itself a major third below the lowest note in that diminished triad. In this sense, substitute secondary dominants are really more appropriate for the essentially triadic transformational environment: The upper triad then has a proper clockwise transformation and the bass maintains it's constant root motion with no problems with parallelisms. I suppose I should mention at this point that accompanied harmonic canons can obviously be composed with a triadic upper stratum and a repeating root progression pattern over a constant root bass, but they would not be double canons, which has been my particular interest to this point. I suppose I should compose one of those to demonstrate some of these sonorities in that context.
In order to employ substitute secondary dominants in a virtual five voice texture over a constant root bass - as I have been doing thus far in my examples since the Secondary Dominants and Harmonic Canons post - the regular clockwise transformation that strong decending root motions normally get would have to be employed. This creates problems if the target chord is of the major gender because an augmented second would result if the resolution were made directly. In order to maintain the glass-smooth voice leading I prefer, the target chord must either be of the minor gender, or it must be changed to the minor gender momentarily. I have demonstrated this on the bottom staff of the example. This resolution sounds very unusual: The minor seventh or enharmonic augmented sixth resolves outward as per usual, but the tritone does not "do it's thing". This, combined with the unexpected minor gender of the target in this particular resolution, can only be described as a peculiar effect. Nothing could better explain why I use these chords sparingly: They are simply highly problematic in their various methods of employment.
posted by Hucbald at 11:44 AM
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