You have some sentence fragments. They work for me, but there are people out there who are highly annoyed by sentence fragments; you won't want to risk having the person reading your application be one of them.
A few other thoughts ...
I was clearly born in the wrong time period.
I am being picky here, but "time period" sounds too broad to me. Go ahead and nail it down. Say "decade" instead. It rolls off the tongue easier and has the feel that you are going for.
Keep it consistent. You use "40s" here, but "sixties" later.
so that I could make it just in time for the musical revolution that was the sixties
"Make it just in time for the" is pretty wordy and slows down the pace of the piece. Try plugging something else in here. ... so that I could participate in the musical revolution, so I could relish the musical revolution, so I could be a musical revolutionary ...
I am an old school rocker. I have all the symptoms. A contemptuous outlook on the course of modern rock, a sense of elitist arrogance in my own music taste, and of course, the ability to make sophisticated and profound comments on what sometimes sound like absolute crap.
Personally, I would combine these so that you don't have a fragment or two particularly short sentences right next to each other. I am not quite sure what you are saying in the last part of this sentence. I think that you are implying that you are commenting on the more modern music, but there isn't continuity ... it goes from dissing the new, praising the old, to dissing the new again. AND, I would use "musical" instead of "music" and "sounds" instead of "sound."
the two great Jimmys, Hendrix and Page
This is problematic in my mind because of the different spellings. You can't really take two words that are spelled differently and make them into a plural (in print at least). It is akin to calling a Kari and a Carrie the two Karis or the two Carries. True, Hendrix did spell his name "Jimmy" at one time, but not while he was famous and it is not how he is known. It isn't horrible, but I am nitpicking here.
, and the sense of freedom and possibility that came with it.
This is a fragment.
It has nice energy. If you clean it up a little bit, it will make a strong statement.