Hello @frogman
The three greatest tenor players have been Trane, Rollins and Henderson. Probably in that order. Bottom line is, who has gotten copied the most by other tenor players? Those three are the top three.
I think Wayne Shorter should be 3rd, between Rollins and Henderson. If your only going by how often they are/were copied and their virtuosity then, yes to the big 3 you mentioned.
However it could be argued that Shorter was the most prolific tenor sax composer of all of them. Wayne Shorter can best be described as "a life of reinvention".
From 1957 through 1967, Coltrane had a 10 year run that could never be approached by any tenor player since then (it never has). Rollins has longevity going for him as well as being arguably the best improvisor on the tenor bar none, including Coltrane.
Henderson had a great run and belongs up there. I just started listening and appreciating Henderson over the last few years. His first 4 recording sessions for Blue Note are arguably the best first 4 recording sessions as a leader among all of the players we are discussing.
What I have learned about listening and studying jazz in the last 25 years is that the majority of "pure straight ahead" jazz listeners who limit there repertoire of albums to the golden era of jazz - 1935 - 1965, do not like change. Some even abhor it.
A great example of a tenor that we have not mentioned yet, a man who’s recording output pretty much stayed true to the "jazz purists", is Stan Getz. Getz won the Down Beat tenor poll more then any of the players we mentioned. Getz’ tone is beautiful and easily recognizable, and he always played like that in the pocket and very enjoyable style.
Getz never tried to "branch out" and experiment (unless you count the bossa nova recordings in which he still played the same beautiful tone in a "new thing" setting).
Rollins, on the other hand, was constantly "on the move". He experimented with Emboucher, breathing, different tenor manufacturers, rhythm, melody, harmony, chords and space. I think Sonny’s detractors are put off by his tone, which he played on purpose. He wanted a "large sound" but there are many examples of him mellowing his tone on certain songs.
Sonny was also the "strongest tenor player" of all of them. After he quit using dope he started a strict workout regiment with dumb bells (he brought them everywhere and would use them in between live sets and during breaks recording. He set up a pull up station in his apartment in NYC.
Pianist Paul Bley, who played on Sonny’s great studio session with Coleman Hawkins, Sonny Meets Hawk, and toured with him during that period, said that he could not "keep up" with Sonny. And he was not the only musician who had trouble with Sonny’s staying power on extended improvised medleys sometimes lasting an hour or more. Bassists, drummers, and many other pianists of the time are all quoted in Sonny’s new biography on Sonny’s strength and physique.