The family of augmented sixth chords, like the diminished 7th and Neapolitan chords, originate in the minor mode. Augmented sixth chords are chromatic variants of the subdominant. That is, subdominants with roots raised a half step. Although augmented sixth chords are derived from subdominants, they are not really chords that can completely function like their counterparts. For example, raising the root of a subdominant in minor produces a chord with a diminished fifth and diminished third. Furthermore, because the notes necessary to form the chord don't occur within the key, augmented sixth chords are considered chromatic. Since this chord's structure is unlike any other diatonic tonal chord, the properties we attribute to diatonic chords, such as the property of stability for root position chords, do not apply to augmented sixth chords. This is an important point, because it hints at the contrapuntal origin of augmented sixth chords. In fact, one could go as far as to say that augmented sixth chords are of completely contrapuntal origins, i. e., linear chords.
Although augmented sixth chords do not share all the properties of their subdominant counterparts they do share one very important function: they are dominant preparations. More precisely, augmented sixth chords are leading tone or chromatic preparations of V. However, since the interval of the augmented 6th (unlike the tritone), does not determine any particular key, the chord of resolution does not sound like a tonic. If anything, the augmented sixth strengthens the dominant function of the chord of resolution. Two factors contribute to the strengthening of dominant function: first, the dominant is approached in all voices by step, so no fifth motion takes place between the chords; second, in the usual voice leading, the dominant scale degree is in the outer voices approached by contrary motion.
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Although augmented sixth chords are in general derived from the subdominant, they are in particular derived from a specific subdominant function, the Phrygian cadence. A half cadence in the minor mode approached by IV6 produces a Phrygian cadence. The Phrygian cadence takes its name from the bass motion producing the cadence. Scale degree 6 moves by half step down to scale degree 5. The bass voice, however, is not the only fixed voice leading characteristic of this cadence. Scale degree 5 is also in the soprano voice approached by scale degree 4, while the inner voices both contain scale degree 1 moving to scale degrees 7 and 2. Example 1 illustrates the Phrygian cadence.
Sometimes composers added a chromatic passing tone between scale degrees 4 and 5. Of course, the practice was derived from preceding the dominant by its own dominant, since the secondary dominant of V contains scale degree #4 as well. It is simply a matter of applying the same technique in a similar voice leading situation. As Example 2 illustrates, the chromatic passing tone occurs on the weak portion of the beat.
Eventually, composers no longer introduced the chromatic passing tone on the weak portion of the beat. That is, they substituted scale degree #4 for scale degree 4. The chord that resulted from this substitution contained the interval of the augmented sixth between scale degree #4, usually occurring in the soprano, and scale degree 6, the lowered sixth scale degree from the natural minor usually occurring in the bass. Therefore, although we speak of augmented sixths chords as "chords," they are really the product of linear motion.
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The Italian Sixth is the simplest of the augmented sixth chords. In the discussion above, we started with a phrygian cadence, added a chromatic passing tone, and then removed the preparation for the passing tone and rhythmically displaced the chromatic note. This procedure produces the Italian Sixth chord. See Example 3.
This form of augmented sixth contains only three different notes. Like the doubling in the phrygian cadence, you double scale degree 1 or the fifth of the chord (third above the bass) in four voice textures. The remaining augmented sixth chords can be thought of as voice leading alternatives of the Italian Sixth. For example, although the alternative name for augmented sixth chords, leading tone chords, implies that each voice moves by half step to a note of the dominant, one of the doubled notes moves to its note of resolution by whole step. We can generate another type of augmented sixth chord by altering the whole step motion.
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Adding a seventh to an Italian Sixth chord produces a German 6/5. See Example 4. The new note, scale degree 3, moves to the same note of resolution, scale degree 2 or the fifth of the V chord, as its counterpart, the doubled fifth of the Italian Sixth. However in the German 6/5, the new note moves to its note of resolution by half step rather than whole step. Consequently, the German 6/5 is truly a "leading tone" chord.
The German 6/5 produces a voice leading problem; the new note creates parallel fifths between the bass and tenor. To eliminate the fifths, the German 6/5 moves to the cadential 6/4 rather than directly to V. In minor, the German 6/5 will share two common tones with the cadential 6/4. See Example 5.
In major the German 6/5 will share one common tone with the cadential 6/4, and one note will move chromatically. See Example 6.
Composers often have the German 6/5 move directly to V without an intervening cadential 6/4. The parallel 5ths are either masked by figuration or placed in the inner voices where they are not heard as prominently.
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When the German 6/5 moves to the cadential 6/4 in major, one note (the seventh of the 6/5 or fifth above the bass) moves chromatically (to the sixth above the bass in the cadential 6/4). In order to more clearly notate the voice leading, the seventh of the German 6/5 is spelled enharmonically. In Example 7, the Eb is spelled as D#, since the voice leading moves up. The interval produced by the D# above the bass is a doubly augmented fourth, hence the name of the chord. However, the change is purely notational, because the progression functions and sounds the same as its counterpart.
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Another voice leading possibility eliminates the doubled 3rd above the bass of the Italian Sixth and eliminates the parallel 5ths caused by the German 6/5. Rather than doubling the 3rd above the bass or adding a seventh to an Italian Sixth chord, one can substitute an augmented 4th above the bass. The new note, scale degree 2, will be a common tone with the chord of resolution, V. This chord is commonly called the French 4/3 or French Sixth. The French Sixth, like the diminished seventh chord, contains two tritones. A more informal way of thinking about this chord's derivation is to say that it is a V of V with a flattened fifth (in fact, the designation French 4/3 appears to suggest an altered II origin for the chord). Unlike the diminished seventh, which links its tritones by the interval of the minor 3rd, the French 4/3 links its tritones by the interval of the diminished 3rd. This method of linking, in part, accounts for the chords distinctive sound. The French 4/3 can move to either V (see Example 8) or to the cadential 6/4 (see Example 9).
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In Examples 3 through 9 each augmented sixth chord was approached by the IV, since this is the most common preparation for augmented sixth chords. Augmented sixth chords are derived from the subdominant, so introducing them via IV creates very smooth voice leading. In Examples 3 through 9, a chromatic voice exchange from IV prepares the augmented sixth chord (see example 10). The voice exchange was then filled in by a passing chord.
An augmented sixth can also be approached by an altered II chord or V of V (see Example 11).
The Submediant, VI, is the simplest preparation for an augmented sixth chord. Just add #4 to VI (bVIb in major) to generate the German 4/3 (see Example 12).
A very common bass progression is to descend to the dominant by way of scale degree 6; that is, 1-6-5. Scale degree 6 can be harmonized with either IV6 or VI. Since, as Example 12 illustrates, VI is very closely related to an augmented sixth chord in structure, an augmented sixth chord can be substituted for VI in the bass progression with scale degrees 1-6-5 (see Example 13).
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The German 6/5 is equivalent to a dominant 7th in sound. That is, by simply playing a dominant 7th or German 6/5 at the keyboard with no notational reference and without resolving either chord, the chords sound identical. The resolution determines the identity of the chord, and the resolution determines whether the chord is spelled as a dominant 7th or a German 6/5. The note determining the functional identity of the chord is the seventh of the dominant 7th and the "root" of the German 6/5 (the note that usually appears in the soprano and forms the interval of the augmented sixth with the bass).
Enharmonically, the note is the same in each chord. For example, in C major the German 6/5 is Ab-C-Eb-F#. The F# moves up to G in the resolution. If, however, we respell the F# as Gb, we generate a dominant 7th, Ab-C-Eb-Gb, that moves to a Db chord. How would a Db chord function within the context of C major? Answering this question highlights another interesting use of the Dominant 7th/German 6/5 duality; a German 6/5 that resolves as a dominant 7th becomes V of the Neapolitan. The German 6/5 must be the German 6/5 of the dominant of the key for this to work. One extended use of augmented sixth chords is to introduce an augmented sixth chord that moves to a chord other than the dominant. Since the German 6/5 has a dual nature, it is an excellent agent of modulation.
Composers often took advantage of the Dominant 7th/German 6/5 duality. One of the best examples I know is the opening of the second movement of Beethoven's Piano Sonata Op. 53, the Waldstein. Example 14 contains the first nine measures of the movement. Play the excerpt.
Although the chord in measure 1 is spelled as a German 6/5, if you are not looking at the score, it sounds like a dominant 7th. I think the way the chord unfolds in pitch space heightens the aural perception of the chord as a dominant 7th. When the dominant 7th/German 6/5 resolves in measure 2, we realize that the chord was a German 6/5, because the "7th" resolves up instead of down indicating that the interval between the outer voices was an augmented sixth not a minor seventh. Especially worth noting is that it is the tonic chord that is transformed into the German 6/5. On a first hearing, one might believe that Beethoven was up to his old tricks by beginning a piece with V of IV (assuming, of course, one knew that key was F major). The chord's resolution, however, quickly leads us into new territory, which leads to a new question: what function does this progression serve?
The chord of resolution in measure 2 is heard as a dominant, which in this case, implies the key of a minor. As stated above, the German 6/5 is a good agent of modulation, so perhaps it is functioning in that capacity in this piece. The events of measure 3, however, quickly dispel that notion. The apparent dominant of a minor is itself made minor and leads to a diminished chord over the same bass note that resolves to a B major chord in first inversion. Of course, the B major chord could be heard as a back-relating dominant of the dominant of a minor, or the beginning of a circle of fifths progression. The point is, the goal of the progression is at this point unclear. In measure 5, the B major chord is made diminished, in the same manner the dominant of a minor was made minor, through chromatic alteration. With the entrance of the diminished chord at the beginning of measure 5, we have the first chord that relates directly to the key of F major, VII6 of V. The second chord in measure 5 reveals a close relationship between VII of V and the Italian Sixth chord. By lowering the bass of VII6 of V a half step, the chord becomes an Italian Sixth chord. Unlike the German 6/5 that opens the passage, the Italian Sixth lead to the dominant of F major. The remainder of the passage prolongs the movement to the tonic with the progression VI-II6-V7-I. Although we now know a little more about the mechanics of the progression, we still do not know the what function the German 6/5 performed.
Essentially, the passage connects the tonic, which becomes the German 6/5, to the dominant in measure 6. The dominant is then prolonged in measures 7 and 8, and then leads to the tonic in measure 9. The key to this puzzle lies in how the bass line connects scale degree 1 to scale 5. See Example 15.
There is a problem with this type of descending bass line in major: how do you make scale degree 7 go down instead of back up to the tonic? Of course, the simplest solution is to transform it into some other scale degree. As part of the dominant of a minor, E is no longer the leading tone of F major, so it can go up or down. Therefore, in one sense, the German 6/5 preceding the E major triad helps to transform the pitch E from a leading tone into a scale degree that can move more freely. The effect of this passage is marvelous, because it is simultaneously spontaneous and teleological. The passage gives one the impression of wandering in an exploratory fashion, and yet we are brought safely back to our home base.
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