"By the same token the C major scale is a mode of the E phrygian scale"
NO, this isnt correct thinking IMO, the C major scale contains modes...
C IONIAN
D DORIAN
E PHRYGIAN
F LYDIAN
G MIXO
A AOLEAN
B LOCRIAN
C major scale CONTAINS these modes, C major scale ISNT these modes...
each mode has a different sound, they also happen to share the same notes, but each degree does not have the same harmonic function...
because of this, it is wrong to think of them as being the same thing...
if you are playing over a D dorian vamp, you are playing JUST THAT, nothing else... if you play notes from the E phrygian mode, you will not hear phrygian, you will hear Dorian, because the chord progression is pointing that way... (you will hear D dorian starting on its 2nd)
this is why its not correct to think of all of them as the same thing, just because they contain the same notes doesNOT mean they are the same... they have diff formulas, and diff harmonized properties...
the chord defines the mode... if their is no chord, the way you phrase, and the note that is the TONIC becomes the root of that MODE within that SCALE...