I used to back up a fiddle player that loved playing modally. He would jump back and forth betweem major and parrallel minor chords so often that I thought it safest to avoid thirds altogether. Now I'm being told that I'm wasn't playing chords.

So it has to be three different notes. Perhaps I could lower the top note by a whole step--E B D--no third. Is it a chord. For what it's worth, I'll hang with the Groves Definition, and not cite my qualifications.