The mixolydian intervals are TTSTTST. If I start on D, then I generate: D, E, F#, G, A, B, C, D. C is already a whole tone below D. The Key-signature for a melody in this scale would show one sharp. Saying that this melody is "in the key of" G might or might not be accurate depending on what was meant. To say that a melody built on an A-dorian scale could be "in the key of" E or F might be accurate in some contexts, though I can't imagine any such context. That is, I can't imagine trying to communicate any information about such a melody alone that I would think was best communicated by saying that the melody was "in the key of" E or F. If the melody were embedded in a larger work, I might designate the larger work as being in the key of E or F. Whether a work in F with an embedded melody in D-mixolydian or A-dorian could be made to sound good is a separate question. In a 12-equal system, where F#=Gb, I suppose one could pull it off if one were clever enough.

T.