Greg's physics is relevant to the original question - if you're in a resonant room, the echo will spell out the chords as you go. For John's Jig, you'll get something rather close to the chords I suggested being dictated to you from the ceiling. Play a chord that accentuates tones you aren't hearing in the tune, and the effect can be of some unrelated tune being played at the same time with the sound drifting in from outside.

I sometimes play in a very echoey pub. There's a show-off accordionist who often plays there - at the speed of his chord changes, the effect of his duet with himself via the ceiling is like something out of Charles Ives.