The augmented sixth chord exists to reach the dominant with more force than an ordinary pre-dominant can manage.
Build it on the flattened sixth. In C major that puts A♭ in the bass with F♯ above — the augmented sixth it’s named for. Those two notes sit a semitone either side of G. Resolve them outward and they converge on the dominant in contrary motion, and that convergence is the whole effect: two voices squeezing toward the same note from opposite directions.
Three versions, differing only in what fills the middle:
- Italian — A♭ C F♯, with the C doubled
- French — A♭ C D F♯
- German — A♭ C E♭ F♯
There is no known reason for the geographical names.
The German is the richest and the most awkward. A♭ to E♭ is a perfect fifth, and taking that straight to G–D gives you parallel fifths walking into the dominant. The standard fix is a cadential six-four first — G in the bass, C and E above — letting the dominant proper arrive a beat later. What you hear is unchanged; the voice leading survives inspection.
The other reason to know the chord is that it’s enharmonically a dominant seventh. G7 is G B D F. Respell that F as E♯ and it becomes a German sixth in B minor, measured from G as the flattened sixth. A plain dominant seventh in C major can therefore pivot into a cadence in B minor without a single pitch moving. Nothing changes but the spelling.
That’s the part worth carrying around. The chord sounds like tension. Its real use is ambiguity — one sonority sitting in two keys at once, and a way out of either.