Louis Armstrong said it clearly: “. . . there’s people all over the world, they like to hear that lead. Ain’t no sense playing a hundred notes if one will do, Joe Oliver always used to say, ‘Think about that lead.'”
What many people cherish in the music they call jazz is improvisation. I understand this: much of the pleasure in hearing a jazz musician at work or at play is observing the new beautiful structures (s)he builds on familiar melody, chords, and rhythms. Consider Lester Young playing I GOT RHYTHM. As I write now, someone is creating something lovely and surprising on familiar themes. Experienced listeners can discern the original structure as they admire the variations on the theme.
But melody still has so much to say to us, to give us, and while melodic embellishment with a swinging harmonic and rhythmic underpinning may not be the only way to present creative improvised music, it can still be deeply satisfying.
Two examples, from mid-1946: Bunk Johnson, trumpet; Don Ewell, piano; Alphonse Steele, improvising on melodies that were “pretty” and well-established even then. KATHLEEN was written in 1875; DOLL in 1911:
I don’t espouse this as the only rewarding way to play, but it still sounds very good to me.
May your happiness increase!