Thank you for explaining this, rather than "just saying I'm wrong". :) I was kind of getting that idea, but it still doesn't hold water with what I was saying that an Augmented 6 chord is not a dominant 7th chord. With what you wrote a Italian 6 chord is just a Ab7 (A#6). Without a 5th?? That's pretty much the interval that tells you if your playing an augmented chord or not. If you look at this, it actually all folds down into being just a simple major chord with a #6. I'll take the german 6th (which isn't how you described it, no 5th?? ;)) without the inversion.

Ab, C, Eb, F# - Ab#6 (yes..enharmonically (Gb) dominant 7th)

If you took out the 5th.

F#, Ab, C - F#dim(add2)

But my point is...

The Augmented 6 chord is an augmented triad with a 6th added to it.

Ab, C, E, F - Abaug6

The augmented triad is the key to understanding what I am saying. It's 100% accurate and is the modern way.

Ab, C, Eb - major
Ab, C, E - augmented

Maybe back before they had dominant 7th's, they used this way of describing the sound as a augmented sixth. But now the structure of chords is based on simple triads, then what comes after that is an extension. It looks to me that the french, german, and italian used the interval #6 as being augmented. How would they discribe a minor, or diminished chord? Let alone a augmented chord. Would it be an Ab augmented augmented 6 chord???? HAHAHA Simply, breaking the modern structure into a more primative state. The modern way is much much simpler.

First you take the root..Say its C.

Then figure out if it's major, minor, diminished, or augmented.

Say it's C augmented. Which would be the notes C, E, G#.

Say you wanted to add A to that for harmony purpose.

Now you have a Caug6 chord. C, E, G#, A.

The other way leaves you with no answer to whether it's a major, minor, augmented, or diminished chord. Which makes it more of an interval than a chord. Do they still use this chordal structure???

Maybe, I'm misunderstanding the use for this idea but to me it only complicates things and really causes alot of problems. Like I said before, I have no use for it.