My sax players

The sax is really the core instrument of jazz, and when it supplants the clarinet as the reed instrument the music develops in a different way. 

Two giants stand at the head. First, Coleman Hawkins. A deep, throaty sound and endlessly confident arpeggios, locked into the beat. He not only inaugurates the sax, but also can hold his own in the bebop era.  

Secondly, Lester Young, who invents coolness itself. (only a slight exaggeration). His lines float over the beat in an uncanny way.  He also has a way of improvising that is telling a story, as he liked to say, rather than using arpeggios and scales.  Lester paves the way for Bird, the greatest jazz musician of all time.  Bird makes time feel almost infinitely elastic, in the way that Cortázar wrote about in his short novel about him.  

Two swing era alto saxes, Johnny Hodges and Benny Carter, are also favorites of mine. 

Rollins and Coltrane define the post bop sax.  Rollins develops motifs, whereas Coltrane offers sheets of sound, and develops a different kind of rhythmic approach beyond the swung eighth note feel.  

Coltrane and Ornette define avant-garde jazz.  Bird, Coltrane, Ornette, are major jazz composers like Monk or Ellington/Strayhorn.  

Yet there is also a wealth of players in hard bop and cool jazz. Lee Konitz is probably one of the best, but there are many others. Paul Desmond? Mulligan?