#1
A C major chord points to C as the root and the tonic center. What intervals and chords are ambigous and deny a root. An interval of FB cancels out the sense of F as key. I think this is why in the progression CFGC F isn't the tonic. The B in G major cancels F out.
What other intervals deny a note or chord as the tonic?
#2
Quote by Zombiechao
An interval of FB cancels out the sense of F as key.


It doesn't really though, because thats just the lydian mode, and if you played FB then FC it would make sense.
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#3
Quote by Zombiechao
A C major chord points to C as the root and the tonic center. What intervals and chords are ambigous and deny a root. An interval of FB cancels out the sense of F as key. I think this is why in the progression CFGC F isn't the tonic. The B in G major cancels F out.
What other intervals deny a note or chord as the tonic?


It's not really a matter of canceling anything out. Those chords are not in F simply because they are derived from the C Major scale.....not the F Major scale. C F & G are the primary chords in the Key of C Major.

So rather than looking for notes that "cancel or deny a root from being the key center", I would suggest you just learn the key signatures.
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#4
The progression C F G is in the key of C.


It's a simple I IV V progression.
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#5
The thing you want to keep aware of, in soling in a mode, is using a V7 it wants to pull back to a I Tonic. Simply put, if you are playing in E phrygian, and you throw in a G7, you now have created a situation where the progression wants to turn into C major. If you GO to that C major, you may find that its harder now to keep E as your tonal center

ii V7 and I in jazz tends to be a little forgiving, so you will notice that Dorian over this seems to maintain its shape pretty well as long as you go back to the Dm7 etc following the Cmaj7, say if you were doing something like, Dm7 G13 Cmaj7.