I'm no expert, but I think the F is a transition chord, from the key of G back to E, in the same way that the D is a transition chord from the key of E to G.
D (maj) is not in the key of E; I think it would have been D dim (or Dm7b5?) to be in the key of E. But it is D because it helps the transition of the key change, as does the F (not F dim) to go back to key of E.
Of course, theory is only an observation of music, not a rule.
|