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guidot
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why are songs in mixolydian mode notated in major mode?

I am learning a "Hard days night" by the beatles which is in G mixolydian mode or C major. In the score I have of this song the writer notated the song in G major and used accidentals on the notes that are not part of the G major scale. Why couldn't they have just used C major as the home key as all the notes pertain to that key? Is this because the song keeps going back to that G chord? If this is the reason it seems silly because you could have a C major song with these chords in a bridge and then it would be notated in C major.

user35708