World's Greatest Tenors

Btw, Tia's band is all female. (beside the trumpeter) Yeah, the drummer also, really :)

Charles, agree on Dexter, and "Prez" would have been on my list if it had been four instead of three. I listed three only because the OP listed three. Since he didn't say "favorite" but "greatest", "greatest" seems to imply "most influential" since anything else is subjective. I think who the most influential have been is pretty well established and agreed upon by knowledgable fans and critics. I also like Acman3's choice of Wayne Shorter, besides being a great player was one of the very best jazz composers. So, for stature and influence:

Hawkins, Prez, Trane, Sonny, and I am tempted to add Joe Henderson

For listening pleasure:

The above and I would add Dexter, Getz, Zoot Sims, Charles Lloyd, Johnny Griffin, Hank Mobley

And for sheer virtuosity (ability to do anything on the instrument from a technical standpoint), IMO the greatest ever virtuoso on the instrument has to be Michael Brecker.

Hi Frogman,
Good points,
Virtuoso? wow, really tough to say. Certainly Coltrane and I'd have to put James Carter on this plane as well. Joe Henderson is an under appreciated but massive talent! You could make a very favorable comparison of his work vs Wayne Shorter(the better known). The more I think about it Sonny Stitt was a virtuoso if there ever was one, total mastery of the saxophone in any genre he chose. I could discuss this topic for days as I have such admiration for these extraordinary musicians.
Charles,

Frogman,
You always present a very reasoned perspective and commentary which I sincerely appreciate. On pure technical prowess I get your point about Brecker's status. The thing is though I approach music as such an art form that I judge the musicians on the overall package they have to offer and my emotional reaction to how they play. So the ones who pull me into their music the deepest (and keep me there as well) are more compelling and influential in my estimation.

On technique I've read the same about Jimmy Dorsey on alto sax (flawless they said) yet I'll take Charlie Parker in an instance for actually listening to and enjoying (no slouch when it comes to technique eithe). I'm most moved by the musician's ability to communicate and connect with emotion.
Charles,

Charles, all good points.

Michael Brecker had an ability to overcome the technical obstacles posed
by the instrument that put him in a league of his own. I know some will be
surprised by this comment, but not even Coltrane had such a flawless
facility and ability to play in any register, at any speed, with flawless
intonation and utter control; he was a freak of nature. His ability to play in
the the"altissimo" register of the instrument is a case in point.
This is an extremely difficult technique used more and more by modern
players, and involves playing above the natural range of the instrument by
manipulation of the harmonics created by the notes in the natural range.
This allows the player to play in the range of the alto and soprano (much
higher). He was able to do this in an effortless way and as if it were the
natural range of the horn and not just an "effect". Stylistic
considerations are a different matter and subjective. There is only so much
that I can take of his post-Coltane/with-a-little-funk-thrown-in style. Still
credit should be given where credit is due.

Brecker: v=m5l1OTkNGFk>http://m.youtube.com/watch?v=m5l1OTkNGFk

Coltrane: v=03juO5oS2gg>http://m.youtube.com/watch?v=03juO5oS2gg

I find it interesting that after listening to Brecker's version, Coltrane's seems
almost polite; slower, less fire. Until one feels the slow simmer in
Coltrane's; the incredible building of tension. Brecker can fly down the
highway because he has driven it many times before and was given
directions by Coltrane. Coltrane is driving down the road for the first time,
looking for the address and exploring. That's what made him the genius he
was, and his version is, ultimately, better music; IMO. Still, as far as
playing the instrument Brecker was like no one else; but, a little bit like a
great ss amp that does every thing "perfectly": amazing clarity, incredible
bass, staging, etc. and still.....something missing.

v=fJt3qeuPdns>http://m.youtube.com/watch?v=fJt3qeuPdns

Regards.