In some common jazz theory approach (that I don't support) it would be: C Ionian, E Phrygian, D Dorian, G Mixolydian.
I still think it is better to call the whole thing "Cmajor"
I agree with Aldevis about this, the idea of a mode per chord can be very misleading, it simplifies things in some respects but skirts around the main issue of learning harmonic functions to enable good strong melodic phrase construction.
CM7: My understanding;I can play a C major scale or the chord up to the 9th. My question, what notes can I start on?
Which note you start on is up to you. This is one thing that is wrong with the mode concept, as it sort of implies you start on the root.
To start with, a good guideline of thumb is that chord notes fall on a strong beat (1, 2, 3 and 4 in 4/4, and the notes in between the chord notes fall on a weaker beat, (e.g. 1
and 2
and). The in between chord notes can fall on strong beats, but usually need to be dealt with accordingly (e.g. as suspensions which resolve) so you can see, you really need to know the chord tones and their tendencies as opposed to just playing a mode/scale.
Scales do come to it, but the best approach is what Aldevis mentioned. Here is an example:
Typical progression: Am7 Dm7 G7 C.
All those chords are directly related to the key of C. (We call this a key centre), so the easiest scale to think is C major for all of those chords, (not D dorian for D, G mixolydian for G)
On every basic level, you can make up your impro melody from just this one scale, but for a better result you need to know the chord tones for each chord so you can do what I said above re: strong and weak beats.