One thing that is often overlooked is that the "chords" that we generally play, whether on guitar, melodeon, or whatever, often don't really harmonize with the melody--they are accompaniments--that is, independent rhythmic/melodic phrases that are really one or another species of counterpoint--

This is important to understand because if you sit down and write chord triads on the melody, you'll often come up with chords that don't really work on your instrument.