Breaking down a Jazz etude for for first time, would like some help with function.
The final chord in measure 3 is a clear deviation from major key I've found and I'd like to understand why. First off, despite the claim of Bb7, there is not an A flat in the rising 5th motif. Is it implied due to the chord before? Is it just lazy writing? Second, this is a II chord instead of a ii. I've noticed that starting the Ab major scale on Bb brings in the mixolydian scale, and the smoothness of this motif definitely sounds like its being utilized, that being said this is probably supposed to be a V/V thing right? Why is this leading to iii and not the V then? The iii definitely feels like much actually has in fact been resolved, and in fact ends the phrase.
Conceptually I'm not really sure what I should be taking away from this, but feel like this is quite instructive. Can I treat this as some sort of deceptive cadence where instead of V/V to iv its V/V to iii?
Also, measure two, the vii not being diminished is catching me off guard. Is this just a technique that simply makes the vii smoother, similar to how we use harmonic minor to smooth out the V and vii in minor?