Can an augmented sixth lead straight to tonic?

1. What does an Augmented 6th chord resolve to?
2. What does an augmented 6th invert to?
3. What is the purpose of augmented sixth chords?

What does an Augmented 6th chord resolve to?

This chord resolves to V. The notes of the augmented 6th interval resolve outward by half step to make an octave on the 5th scale degree; one tonic note moves to the leading tone, and one to the 2nd scale degree, making a V triad with the root doubled.

What does an augmented 6th invert to?

Being augmented, it is considered a dissonant interval. Its inversion is the diminished third, and its enharmonic equivalent is the minor seventh. In septimal meantone temperament, it is specifically equivalent to the harmonic seventh (a just interval of 7:4).

What is the purpose of augmented sixth chords?

Augmented sixth chords also help as an intermediate step between ♭VI and V in both minor and borrowed major keys. Moving from ♭VI - Ger⁺⁶ - V avoids parallel octaves from ♭6 - 5 in the doubled roots. They can serve as both tonicization and pivot chords in modulation.