The guy I play with (a) plays moothie a lot better than you do, Dick, and (b) plays a Marine Band only rarely and a chromatic almost never, in both cases for music where intonation is a whole nother ballgame. I am talking about playing traditional music on 24-hole diatonics, for the most part, and as Rick Epping implies, they are best tuned
to provide pure thirds.

Making the thirds just in a harmonica or other free-reed gives you much stronger chords - a harmonica is a quiet instrument and you need all the extra power you can get (not just in Western music: a Chinese mouth organ is much louder, but listen to their tuning). Same goes for a harpsichord in an orchestra for that matter.