Augmented triads are quite rare in practice, but I’ve included them for completeness.
I’ve not created any proficiency tests for augmented triads since you’re unlikely to need them in almost any song. They are easy to create “on the fly” if necessary by simply forming a major triad and raising the ˆ5 a semitone.
Something truly weird happens on the fretboard when you do however:
Notice anything?
All three “inversions” of the augmented triads have the exact same shape! How weird is that?
It happens because the augmented triad is the only one where the interval between each note in the chord is identical. A diminished chord has an M3 (four semitones) between each pair of notes: root to M3, M3 to A5, A5 to root.
Don’t make the mistake of thinking diminished triads are also symmetrical like this. Although a diminished triad is two “stacked m3 intervals”, the interval from the P5 up to the next root is a P4, not an m3.