The most stable chord, traditional teaching tells us, is the root position triad – the one with the fundamental on the bottom.
A more elusive arrangement puts the third of the chord in the bass – nice for subverting the obvious hierarchy of the root.
That leaves the 64 chord, meaning a triad with the fifth in the bass. Traditional teaching tells us this chord requires special treatment. It can set up a cadence, it can connect two other chords. Mostly, though, it can’t just sit there, it has to go somewhere. It contains a powerful interval above the bass, a fourth — not exactly a dissonance, but an interval that requires motion.
I like to call it the America Chord. No triad is more powerful; no triad is more unstable. That combination of power and instability has no geopolitical analogue more telling than the good old USA.