Do jazz musicians ever use the tune's melody when improvising?
The short answer is: yes and no.
Some do, and most don't.
The early jazz musicians did, and the early first-hand oral account of the birth of jazz tell us that jazz was indeed created in this way: One musician would play the melody "straight" while another musician improvised and embellished it. (Often a clarinetist.)
Over time, jazz musicians began isolating the chords to a song, improvising their own melodies over them without referring to the original melody at all. This is one of the big innovations of jazz, and Louis Armstrong was a pioneer of this approach.
The chord progressions can be learned independently of the melodies. You can start practicing this way by simply improvising over I/vi/ii/V in all 12 keys. Don't even associate these chords with any tunes, just improvise over them.
On the other hand, many jazz musicians go too far in this direction, and never think of the melody at all when they're improvising. The goal is to have it both ways. Jazz greats like Sonny Rollins and even Miles Davis often construct their solos around a tune's melody, even when it's not immediately apparent.
Try both approaches, and find the balance that's right for you.
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