yes and no. Jazz is usually based on sophisticated harmonies. Most folk has basic harmonies but subtle. The folk so-called modes opened the door for modal harmony which prior to the folk revival was not much found in jazz. Folk can be re-harmonized (much to the chagrin of those who consider themselves purists) and has been in many cases as it has changed to fit popular tastes. The melodies, however, can be quite unique and beautiful and in and of themselves be rather sophisticated at times. Greensleeves is an example (if you want to call it folk). It was originally constructed as an Aolian mode but the Dorian came from Ralph Vaughan Williams adaptation using the natural sixth rather than the flatted sixth of the Aolian scale. The Water Is Wide is another case where the melody is quite flowing and there have been re-harmonizations of the tune, notably the arrangement from the Twenties for the baritone, John Charles Thomas. This is the arrangement that Pete Seeger has used. John Jacob Niles has written songs that are beautifully constructed melodically which you might call "folk-styled" songs.

Usually, the melody is a vehicle for the story but there are examples where the melodies can stand on their own aside from the lyric.

Today's jazz tends toward a minimalist harmonic approach influenced by the playing and writing of Miles Davis. This may be closer to what we think of as modal folk. The difference is that in jazz the chord constructions are extended to include alterations that may be dissonant to some untrained ears.

I think that if you are really into chord sophistication and chord changes with improvisation built on them, folk music does not have the harmonic range unless it has been souped up by arrangers or composers.

I think, however, it would be foolish to assume that folk melodies are uninteresting and devoid of a certain kind of musical sophistication that stems from the way they are ornamented and changed from verse to verse by traditional exponents in folk-style singing and playing. The music can be fascinating and appealing in a different way with subtle complexities that appear to be disarmingly simple.

I am finding as the definition of folk music changes and broadens that jazz influences the improvisation and interpretation in this idiom.

Frank Hamilton