King Crimson’s music has always had a transporting power, with an orchestral sweep driven by intense polyrhythms and great sheets of swirling sound. But just where the group, who play the Orpheum Theatre this Saturday, have carried listeners since they formed in London 34 years ago has depended on who’s had the tightest grip on their reins.

Back when lyricist Pete Sinfield was exerting his influence, pastoral albums with stories of dragons and mythic kings like Lizard and In the Wake of Poseidon (both Island) resulted. In the mid ’70s, when founder and guitarist Robert Fripp took firm control of the music, expansive and driving discs like the improvisatory Red and Larks Tongues in Aspic (also both Island), with its epic blend of beat poetry and jabbing sonics, arrived. And in the mid ’80s, when after a long break the band re-formed around Fripp, singer/guitarist Adrian Belew, drum legend Bill Bruford, and the versatile bassist Tony Levin, the King Crimson sound was defined by six-string interplay as delicate and detailed as a spider’s web crossed with Belew’s classic-pop-song sensibility.

Hearing the sheer thump and roar of the band’s new The Power To Believe (Sanctuary), you might assume that current drummer Pat Mastelotto is in control. The weave of polyrhythmic guitars and bass — the latter courtesy of former Fripp student Trey Gunn, who lays down a deep bottom with the hybrid Warr Guitar — is still in place, triggering all sorts of emotional rocket trips. But there’s a pounding foundation to it all that seems likely to be the work of the former Mister Mister drummer, albeit amped up on the buzz of sitting in the center of Crimson’s firestorm of instrumental interplay.

Nonetheless, when I caught up to Belew via phone from his Nashville studio, where King Crimson were rehearsing for their tour, he explained that it’s Fripp who insisted on rocking out. "I think Pat’s role in the band has caused King Crimson to be more of a heavy rock band than we used to be," he concedes, "but this album is really the result of Robert’s vision. When we began writing this material two and a half years ago, it was obvious that Robert had a real sense of where it was heading, and I told him I would do everything I could to support his vision." Thus there are vast, pitch-shifting plates of sound, places where the guitars scream like mating panthers, dizzying key and time changes, and plenty of sonic storm clouds roiling within the dense thickets of The Power To Believe’s 11 tracks.

As usual, Belew contributed lyrics and melodies. Often his vocal performances are as effects-laden as the guitars, and that adds to the album’s ironic streak. The title implies a kind of faith and humanity, and yet the lyrics reverberate with dark images. Even the cheeky, cheery "Happy with What You Have To Be Happy With" gives the impression that its message is more "Be happy with what you’ve been left." And "Facts of Life" remarks directly on the worsening conflicts in the Middle East and other dire circumstances tied to religious beliefs. ("It seems to me the greatest of all ironies that anyone would fight in the name of God," Belew says.) The disc’s cover is a stinging portrait of a baby being born into what appears to be a gas-masks-required fascist state.

But the development of King Crimson’s complex, grim, and powerful — albeit sonically uplifting — music is always something of a roll of the dice. Every time the members reconvene after a break, they come with a slightly altered sensibility. Other projects continuously steep them in new ideas and influences. Fripp had been performing solo, using sampling gear to layer a dense weave of colors and rhythms beneath gentle melodic improvisations. Gunn had played in a fusion power trio with the Texas guitarist Eric Johnson. And Belew had been neck-deep in writing songs, creating the kind of solo guitar and piano soundscapes found in his splendid 1995 The Guitar As Orchestra (Adrian Belew Presents), and exploring acrylic painting. He also played at Johnny D’s this fall with his on-and-off pop group the Bears, a band he thinks of "as my own private Beatles." He’s got another solo disc in the works too, and it’ll probably be weighty, since he’s recording with bassist Les Claypool and Tool drummer Danny Carrey.

"All of these things help keep me feeling challenged when King Crimson gets back together," he concludes. "We don’t make the kind of music you just sit around and play, so we have to relearn everything that we’ve created — and relearn how to create new music — each time."

King Crimson play Boston’s Orpheum Theatre this Saturday, March 8, at 7:30 p.m. Call (617) 931-2000.