The question is, Theolonius Monk was famous for playing far-out chord accompaniments to melodies--he himself characterized them as "the wrong chords". What I wanted to know was, how were these wrong chords derived?

The answer, or at least part of the answer, is that they were quartals, which are chords, or, more precisely note groups, that are substituted for chords, that are based on fourths--another part of it seems to be that the melody was harmonized with intermittent seconds, particularly at the beginning and end of phrases--