If I take the augmented sixth chord Ab-C-F#, why is its dominant G? This augmented chord is in the F minor scale, isn't it? But isn't G the dominant in C? Maybe I missed something on how to understand the build up of augmented chords?
There's a really simple reason why this sounds good and thus is found in music theory.
D7 (which is the V to
G maj) is spelled
D F♯ A C, and
A♭7 (the chord you've cited) is spelled
A♭ C E♭ G♭. In both cases, we've spelled the chords using the 1st, 3rd, 5th, and 7th scale tones. The crucial fact here is that
A♭7 share the exact same notes as their third and seventh. For both
A♭7, the 3rd and 7th are
F♯ / G♭.
Why does sharing the 3rd and 7th make
| A♭7 | G maj | sound as good
| D7 | G maj |? Besides the root, the 3rd and 7th are the most important tones for defining the quality of a chord. The presence of a flat vs. natural third and a flat vs. natural seventh distinguish major chords from minor chords from melodic minor chords from dominant seventh chords.* The 3rd and 7th are of crucial importance, and so any two chords which share the same 3rd and 7th are in a way interchangeable.
In fact, in jazz, taking a V–I progression like
| D7 | G maj | and substituting in
| A♭7 | G maj | is called a tritone substitution and is probably the most common chord substitution in the entire genre. This is called a tritone substitution because we're replacing
D7 with a chord that is exactly a tritone (six half steps) away.
A♭7 is in the key of
D♭ maj, which is similarly a tritone away from the
G maj tonal center.
In classical music, the traditional approach is for this chord (augmented sixth) to resolve to a dominant chord, not a major chord as I've shown above. So the classical music progression would be:
| A♭7 | G7 | C Maj | or
| D7 | D♭7 | G♭ Maj |. Additionally, classical musicians wouldn't call the first chord a dominant seventh chord--they would recognize the function it was serving and use that function to distinguish it as an 'augmented sixth' chord. This gives:
| A♭ aug 6 | G7 | C Maj | or
| D aug 6 | D♭7 | G♭ Maj |. Jazz theory doesn't draw this distinction and calls the first chord a dominant 7th chord.
*See below for distinctions based on the 3rd and 7th:
- major chord: natural 3rd, natural 7th
- minor chord: flat 3rd, flat 7th
- melodic minor chord: flat 3rd, natural 7th
- dominant 7th chord: natural 3rd, flat 7th
An augmented-sixth chord typically precedes a dominant. These augmented-sixth chords are so named because of the augmented-sixth interval between two of its pitches (in this case, between A♭ and F♯). These two pitches then move in contrary motion by semitone to reach scale-degree 5 of the key. Thus A♭ moves down a half step to G and F♯ moves up a half step to G. Since G is scale-degree 5 of C, we're looking at an augmented-sixth chord in C. This is why G is "the dominant" of your
A♭–C–F♯ augmented-sixth chord.
A♭–C–F♯ is not in the F-minor scale, since there is no F♯ in F minor.
You can also build an augmented-sixth chord backwards, by starting on the dominant. If we're in C, our scale-degree 5 is G. Now go up a half step from G and put that pitch (A♭; this is scale-degree ♭6) in the bass, then go down a half step from G and put that pitch (F♯; this is scale-degree ♯4) in an upper voice. Voila, there's your augmented-sixth interval, from which you can fill in your augmented-sixth chord.
Now, there are three types of augmented-sixth chords. All of them have that augmented-sixth interval between scale-degrees ♭6 and ♯4. They also all have scale-degree 1.
- If you just have those three pitches, we call it an Italian augmented-sixth chord.
- If you have those three pitches but add in scale-degree 2 (D in the key of C), we call it a French augmented-sixth chord.
- If you have those three pitches but add in scale-degree ♭3 (E♭ in the key of C), we call it a German augmented-sixth chord.
As so often when attempting to explain tonal harmony - a clue is 'hunt the tritone'. C and F# (however we spell them) are a tritone that want to resolve to B and G. This tritone interval occurs in D7 (which we all know resolves to G). But it's in the Aug6 chord as well.
The next stage is to realise that a tritone is symmetrical. It can resolve two ways. C and F# (Gb) can resolve to a Db chord - think of them as the engine of Ab7. (And that Aug6 chord looks a lot like Ab7, doesn't it!) You've nearly discovered 'tritone substitution'.