GSS, I harmonize it this way: Where your main chords in G major would be G, C, D, am and em, in G Mixolydian you use G, C, F (or dm), am and em. In G major you have access to the bm chord, but you obviously can't use it in Mixolydian because of the f/f# clash. You could try b-dim but somebody has decreed that diminished chords are Not-Folk-Music. Leeneia's description of the scale is technically correct but hard to sing that way, unless you're really rock solid on your intervals. I think of it more like having an upper leading tone to the sixth, rather than the accustomed lower leading tone to the octave in the major scale. At least that's the way it is usually used in melodies. Harmonizing the important G's, as Leeneia put it, with C's works sometimes, sometimes G's are better... you have to let your ear tell you what the song wants, I guess. Going with the C really emphasizes that "floating" feeling at the end of phrases. Cheers -Glenn
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