Re: A bit of Theory, 6 and 9 chords
A simple, boneheaded way to look at this is that the 9 is higher than the b7, but the 6 is lower than the b7.
Sounds utterly obvious and overly simplistic, but it's true when you look at how chords are formed: The answer really is that simple.
In building a 6th chord note by note from the root upward, the b7 is not "along the way" to the highest added interval in the chord (the 6). In other words, you're done forming the chord before you reach the b7 (1-3-5-6-done). But in a 9th chord, the b7 *is* "along the way" to the highest added interval in the chord (the 9). Moving up the intervals, you get to the b7 before the chord has been fully formed (1-3-5-not done yet so add b7-9-done). As you can see, it has a lot to do with what octaves you are using for the added notes, not just what notes they are. A 2nd chord does not contain all the same notes as a 9th chord, just as a 6th chord does not contain all the same notes as a 13th chord.
Bottom line that needs to be understood: The underlying "rule" to follow is
not that the b7 goes into all them fancy chords with the extra numbers. The rule is that
IF the fancy number tacked on the chord is higher than 7, THEN the b7 goes in.
Additionally, common ear sense regarding why you don't put a b7 into a 6th chord: It would be horrible sounding (for most purposes) for a chord to feature two adjacent notes within the same octave.
My favorite add9 is without the third. Just a really cool sound. The first one I learned was your basic cowboy A chord with the B string left open; I still use that one a lot in barre form.
One possible wrinkle I see in calling it a 2 chord is that in conversation it could (under certain circumstances) be confused with a diatonic ii chord.
With the 2 played, and no 3 in the chord, it is called a suspended chord. An add9 chord is a standard triad, with a high 2, but no b7. In other words, a 9th chord formed without stopping at the b7 along the way.