[quote name='Hector' timestamp='1474934754' post='3141689']
Your way of looking at it doesn't personally work for me, I certainly wouldn't call E7 diatonic to C major but agree it has a function in a C major context. I find that distinction useful.
Still, if your way doesn't work for me I assume my way doesn't work for others, so I'm glad there's multiple takes on it in this thread. There's room for different ways of thinking about music theory for sure!
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Sometimes there is room: sometimes Harmony is pretty well-established. Secondary Dominants are diatonic, i.e. "of the key". They don't modulate and only add one note to the key (in the case of the E7, a G#) and their upper structures are therefore diatonic (so this E7 would extend to E7b9b13). It's not my way of thinking about - it's the way Parker, Ellington, Coltrane, Bach and Mozart looked at it and it's what's taught anywhere Harmony is studied.
However, taking Dominant Motion further, Extended Dominants (think the bridge to Jordu) are non-diatonic and their upper structures are much more varied.
But then, I'm studying George Russell at the moment; which puts a lot of this stuff out of the window.... ;-)