Tenors, Anyone? Meet Sax Player Joe Henderson : Jazz: Long acknowledged as a saxophonist’s saxophonist, the musician wins ‘sudden’ fame. He will be at Catalina Bar & Grill Tuesday through Sunday.

The late Dexter Gordon was fond of telling audiences that playing “Body and Soul” was a moment of truth for every tenor saxophonist. And in the 53 years since Coleman Hawkins turned that sad Johnny Green dirge into his own concerto, tenors have felt challenged to take hold of the tune and project--if not define--the full measure of their personalities.

Joe Henderson is no different.

Some tenors can bowl you over with just their big sound. But what is compelling about Henderson is the elegance of his tone and craftsmanship. With him, as with few players anywhere, you can almost see the improvisation take shape from his horn the way a sculpture emerges from a glass-blower’s pipe. The 55-year-old Henderson has long been acknowledged as an improviser’s improviser, a saxophonist’s saxophonist.

“What’s amazing about all the times I’ve played with him is that Joe never has a bad night, never has a bad minute,” pianist Renee Rosnes told Down Beat magazine.

The mainstream, in the meantime, has tended to shrug its collective shoulders and say, “Joe who?”

Then came 1992, the year Joe Henderson finally became a star.

The coming-out party started in February with the release of “Lush Life: The Music of Billy Strayhorn” (Verve). On that album, Henderson, who appears Tuesday through Sunday at Catalina Bar & Grill in Hollywood, performed lucid, authoritative and moving renditions of pieces by Duke Ellington’s great collaborator in solo, duo and quintet settings with trumpeter Wynton Marsalis, bassist Christian McBride, pianist Stephen Scott and drummer Gregory Hutchinson.

With such formidable talent at hand and Strayhorn’s intricate, passionate music perfectly suited for Henderson’s style, critical praise was practically a given.

But what stunned everyone--even the record’s producers and especially Henderson himself--was “Lush Life’s” commercial success. It topped the Billboard jazz charts for seven consecutive weeks and won the critics’ and readers’ polls in Down Beat magazine for “Album of the Year.” In a rare sweep, Henderson himself won top honors from both critics and readers in Down Beat as both Jazz Musician of the Year and Tenor Saxophonist of the Year.

A second album, “The Standard Joe” (Red), was released later in the year featuring him with bassist Rufus Reid and drummer Al Foster on which he performs several standards--including two renditions of “Body and Soul.” Between club dates and concerts worldwide, he worked on another album for Verve, similar in concept to the Strayhorn tribute, featuring music associated with Miles Davis.

Among all the nice things that have happened to Henderson this year, perhaps the most meaningful took place April 20, four days before his 55th birthday, when his hometown of Lima, Ohio, gave him the key to the city.

Did he, in his wildest dreams, expect “Lush Life” to do this well?

“Not really,” he says, his penchant for droll understatement as prevalent in conversation as in his playing. “I mean, what I usually do is come into a studio and maybe, hopefully, come out with the best effort I can record at the time. I assume everybody in the studio has the same thing in mind.

“But in terms of audience acceptance . . . I mean this has been overwhelming. I mean . . . I thought it was a pretty good album, if I can have an opinion of my own stuff, which I guess I shouldn’t. . . . But to have the audience think the same thing. Well, that’s not the way things usually go down.”

A trim, gray-haired grandfather of four, Henderson exudes an engaging combination of youthful energy and measured eminence in conversation.

He loves words. He says Herman Hesse, Norman Mailer, Truman Capote and the Bible are as influential in his playing as Coltrane, Sonny Rollins, Charlie Parker, Don Byas, Bud Powell, Stan Getz and Ben Webster. For someone like Henderson, whose approach to improvisation is strongly dependent on narrative strategy, such informed interest in language shouldn’t be surprising.

“I love good writing, wherever I find it,” he says. “And yeah, it’s a lot like what I do except that a writer can go back and erase something and start over. With me, once something’s out there, it’s there. And I can’t get it back.”

So what, in a changing, shifting art form like jazz, is the constant by which the excellence of a performance is judged?

“Integrity,” Henderson says. “However you do it, whenever you do it, you want it to be good.”

Now, he finally has the success to match his gifts. Is he at all frustrated that it took so long?

“Oh, you know, I suppose it would have been nice if it happened sooner,” he says. “I would have had more toys, a couple more cars. . . . Maybe a couple of houses instead of the one I have now. But the house I have now is in the Twin Peaks area of San Francisco where the view is always spectacular. And I’ve got four grandchildren and a life I enjoy. All that didn’t just happen, like, right away, OK? I got it from staying with what I was doing, regardless of the rewards.”