This is a collection of notes that sound cool. It was used often enough to be given a name. If you abandon all tertian harmony and think of it as a collection of notes it makes it much simpler. They’re a bunch of notes that have interesting voice leading
Why are they called augmented 6th chords?
When you see any raised tone, you expect it to resolve upward. When you see a lowered tone, you expect it to resolve down. When you resolve the two tendancy tones in an augmented 6th chord they both resolve to sol of the key that leads to the dominant. It fuctions as the pre-dominant leading to the dominant.
If you invert an A6 you get a d3. The augmented 6th chord doesn’t have inversions because it can’t be a chord.
They all have a b6 and #4. They also all have 1.
The Italian augmented 6th chord (It+6) is spelled le, do, fi. OR, b6, 1, #4. These are 6th chords because of the interval of an augmented 6th between the b6 and #4. They have no inversion. When doubling in an Italian augmented 6th chord, you double scale degree 1.
The German Augmented 6th chord (Ger+6) has the same notes as the Italian but adds b3 (me). It is spelled b6, 1, b3, #4; or le, do, me, fi.
The French augmented 6th chord (Fr+6) has the same notes as the Italian, but adds re, or scale degree 2. It is spelled b6, 1, 2, #4. Le, Do, Re, Fi.
Major: I - vi - It+6 - V - I Minor: i - VI - It+6 - i6/4 - V - i
you can avoid PP5 by inserting a i6/4 between the +6 chord and V
Using an augmented 6th chord can give you a chromatic bassline, like do la le so do in the major example.
Augmented 6th chords are used for voice leading purposes.
You don’t mark these in leadsheet because they are not triadic.
By taking the chord out of the secondary function, it means what note we are highlighting, not what key it is coming from.