Here is an easy way to remember the differences between French, German, and Italian augmented sixth chords.

Let’s use E major for our example.

The augmented sixth

One thing all augmented sixth chords have is, well, an augmented sixth. I know; duh. All augmented sixth chords resolve to sol (5). In E that is B. Since this augmented sixth resolves to sol (5) – the upper pitch goes up a half step and the lower pitch goes down a half step. So, in E major, we have C natural resolving down to B, and A# resolving up to B.

Resolution

 In E major, what are the likely chords that might contain two Bs? Right, B major – V – would qualify.

Resolving to V

So would E major, but in second inversion (the B is in the “bass”).

Resolving to I 6/4

Augmented Sixth chords resolve to V or I 6/4.

All Augmented Sixth chords have a major third. In our E major example that would be E. (C E A#).

Augmented sixth with third

So, what is the difference between the three?

The fourth pitch.

An Italian sixth adds an E to double the third.

Italian augmented sixth chord

A German sixth adds a G.

German augmented sixth chord

A French sixth adds an F#.

French augmented sixth chord

Let’s see, German G, French F, and an E for Italian (pronounce it as an Italian would).

But that German sixth sounds just like a dominant seventh, (and the Italian sounds pretty damn close) so what’s the big deal? Context. What dominant seventh fits into E major? B7 (V7). No others without alteration. So it doesn’t function as V7, but instead approaches V as a plagal cadence would. And actually, that’s where they come from. (plagal cadences arose from counterpoint and counterpoint arose from guys getting drunk and singing around the fire in the cave).

A Jazz musician would say that the French sixth sounds like a 7b5 chord because, well, it is. But you aren’t going to find a French sixth used like ii-V7b5 anywhere. The thing is Haydn knew as much about Jazz as Wynton knows about writing for orchestra (cf. that bloody awful Swing Symphony).

My undergraduate theory teacher was mediocre on his best days, but this was one gem of his that stands out. Like a mushroom.

Next up, demented sixth chords…