What you're training
An augmented sixth chord is built on the flatted 6th scale degree and pulls outward to the dominant instead of falling a fifth like an ordinary dominant chord. The German sixth is the sneaky one — spelled Ab–C–Eb–F#, it's the exact same four notes, same piano keys, as an Ab dominant seventh chord (Ab–C–Eb–Gb). The chord alone can't tell you which one it is; only where it resolves gives it away. This drill trains that resolution-first listening, then moves on to the three flavors of augmented sixth themselves — Italian, French, and German — each one note richer than the last.
Two levels, one skill
Level 1 plays the ambiguous Ab7 shape, then its resolution — outward to G major means it was a German sixth; down a fifth to Db major means it was a plain dominant seventh. Level 2 moves to A minor resolving to E major and splits the augmented sixth family itself: Italian (F–A–D#, no fifth at all), French (F–A–B–D#, the gap split by a major 2nd), and German (F–A–C–D#, the gap filled by a minor 3rd — the fullest of the three, and the same shape as Level 1's ambiguous chord).
Go deeper
This drill is Trio 5 of the chromatic-harmony series — the augmented sixth's outward pull to the dominant, and the enharmonic trick that makes the German sixth sound identical to a dominant seventh. The theory: augmented sixth chords → covers how these chords are built and notated. For the real-world payoff, All 7 augmented sixths in a 57-piece corpus, each featured → lets you hear every one in context. Another single-semitone chromaticism — the Neapolitan → is the other lane of this series, if you want a pre-dominant that darkens by one half step instead of pulling outward.
Where it fits
Comfortable with chord quality and cadence resolution already? Augmented sixth chords are the most chromatic pre-dominant in this series — a great next step after the Neapolitan. The full drill ladder has everything else.