While the first episode in a minor rondo frequently goes to the relative major (III), later ones sometimes go to the parallel major. And the return is convincing because it's part of the form and returns to the home key along with the refrain, which is pretty much the definition of what a rondo form does.
What does Picardy Third mean in music?
: the major third as introduced into the final chord of a musical composition written in a minor key.
Why was the Picardy Third invented?
As a harmonic device the Picardy Third was first introduced in the Renaissance Era, which is between years 1400-1600. It was often thought at this time that the Major key and major chords were more “correct”, stable, and consonant than minor chords, so audiences and musicians expected the music to end that way.
How do you use Picardy 3?
A Picardy Third (or Tierce de Picardie) is where a major chord is written as the final chord of a piece that has mostly been in the minor key. This is achieved very simply by raising the minor 3rd of the expected minor chord by a semitone to create a major 3rd.