For a while, from the mid ’70s through the early ’80s, the future of jazz seemed to rest with David Murray, not Wynton Marsalis (who at that point was little more than a freakish prodigy). Murray, who is about to visit Boston for the first time in years, was in his early 20s, and he had it all: he was a tenor-saxophonist with a big, brawny tone and a mile-wide vibrato whose stylistic pedigree extended back to the likes of Ben Webster and Paul Gonsalves and forward to the sonic extremes of Albert Ayler, Archie Shepp, and late Coltrane. In pieces like "Flowers for Albert" and "Bechet’s Bounce," he paid tribute to the jazz tradition while pushing at its boundaries, weaving improvisations that were well-schooled in fundamentals but could at any moment veer off into wild, free-range excursions. He commanded the full range of his horn, from deep R&B honks to altissimo shrieks, and he was only slightly less agile on his second instrument, the bass clarinet.

In short order, Murray, a California native transplanted to New York City, was fronting trios, quartets, then a big band and an octet. Collaborating with the cornettist Butch Morris in the big band and especially the octet, he honed his writing skills, creating multi-voiced vehicles for collective improvisation that in their bold formal design and headlong exuberance echoed Charles Mingus’s blues-and-roots drenched prayer meetings. In the meantime, he had formed the World Saxophone Quartet with Mingus alumnus Hamiet Bluiett, Julius Hemphill, and Oliver Lake, and that outfit rapidly proceeded from avant-garde experiment to world-wide attraction, as steeped in uptown showmanship as in down-home grooves and heady musical complexity.

But that was all in a galaxy long ago and far away. Although Murray continued to crank out albums at a ferocious rate in the ’80s and ’90s, his local appearances became a rarity. Never a regular on the Regattabar/Scullers circuit, he’d show up for the occasional quartet date at John Clifford’s Green Street Grill in Central Square. There were mutterings about pernicious management. For whatever reason, and despite honorific treatment at international venues like the Montreal Jazz Festival, he wasn’t a dominant US concert attraction.

Now come the ’00s and it turns out Murray has been busy indeed. In the mid ’90s, he began a relationship with the Montreal-based Justin Time label that’s recently seen him both expanding his reach and sharpening his focus. Albums with Guadeloupe’s Gwo-Ka drum masters (most recently on 2002’s Yonn-Dé) dig into the French-African-Caribbean jazz connection. Octet Plays Trane (2000) returned to that ensemble with a fresh perspective on the work of the master. Speaking in Tongues (1999) goes back to spirituals and church music. And the brand new Now Is Another Time, with a large ensemble of mostly Cuban musicians, is one of the best-realized combinations of Afro-Cuban dance forms and jazz big-band writing to come along in years. What’s more, Murray’s solo improvisations have been revived by his new surroundings.

So where has he been? Paris. When I catch up with him for a brief phone conversation, it turns out that nearly seven years ago he hooked up with the French concert organizer Valérie Malot and "we started making babies and stuff." The couple now run their own booking agency, 3D Family, with a strong emphasis on Caribbean and international artists. Gwo-Ka drummer and vocalist Klod Kiavué is Malot’s brother-in-law, and her grandfather is Cuban. "I’m trying to deal with different people in different parts of the world," Murray explains, "trying to bring jazz to what they do, trying to bring what they do to jazz."

As we talk, Murray and Malot are in the midst of entertaining a group of musicians from producer/composer Kip Hanrahan’s "Conjure" project — poet Ishmael Reed (on whose poetry the music is based), Meters guitarist Leo Nocentelli, Taj Mahal. "To me, jazz needs a lift," Murray continues, sounding relaxed and far removed from jazz’s culture wars, "and in my small, tiny tiny way, with my small record company, I’m trying to do that. I’ve made enough records in jazz to have some say, and I’m still making jazz records. I’m not running away from jazz, but I’m not scared of other things, either." As for his US connection, "I come to New York every month. You’d be surprised how much I’m in the States. My ties are very close. I’m not an expatriate."

David Murray and the Gwo-Ka Masters play the Copley Theatre, 225 Clarendon Street, this Sunday, April 13, at 7:30 p.m. as part of the Equinox Jazz Festival. Also as part of Equinox, Anthony Brown’s Asian American Orchestra plays Tuckerman Hall, 10 Tuckerman Street in Worcester, this Friday, April 11. For tickets and information, call (617) 308-7332 or visit www.jcmcsite.com.