Los Angeles

You'd think the members of SuperHeavy—Mick Jagger, Damian Marley, Dave Stewart, Joss Stone and A.R. Rahman—would have enough experience in the recording studio to make cutting a new album a breeze.

"I think we realized on the first day that this is the oddest situation we've ever been in," Mr. Stewart said at his Hollywood office.

"I said to Dave, 'What are we doing here with no songs?'" Mr. Jagger recalled by phone. "'What happens if this doesn't happen?' On the videos, we look like children having a great time. But it was high pressure."

"It was all done on the spot," Mr. Rahman said at his West Hollywood home. "Dave said to me, 'You need to write a song.' OK, give me a few days. 'No. Right now.'"

Now that SuperHeavy's self-titled album is out, the remaining issue is whether listeners can accept pancultural, pangenerational music from a group of musicians with imposing histories. There's Mr. Jagger with the Rolling Stones, of course, and Mr. Stewart with the Eurythmics. The Chennai, India-born Mr. Rahman is a two-time Academy Award-winning composer for his work on "Slumdog Millionaire"; Mr. Marley, the youngest son of Bob Marley, is a successful reggae artist; and Ms. Stone, though only 24 years old, just issued her fifth studio album, "LP1," produced by Mr. Stewart.

"It's hard, when you come from a history where you've created something epic, to be allowed to do anything else," said Mr. Stewart, who recently released a solo disc, "The Blackbird Diaries." "The Eurythmics stopped 21 years ago. Twenty-one years is a long time."

It's even more difficult for Mr. Jagger, who's currently preparing an expanded reissue of the Stones' album "Some Girls." The SuperHeavy acoustic ballad "Never Gonna Change" brings to mind several Stones classics, such as "Angie" and "Wild Horses," and for a few minutes the new band's concept is lost to the memories of one of rock's greatest groups.

But "Never Gonna Change" is the only song on "SuperHeavy" to feature one voice. "Energy," on the other hand, features Messrs. Jagger and Marley employing the Jamaican spitfire rapping technique known as toasting, with Ms. Stone joining in on a sung chorus; Mr. Stewart wails on guitar and Mr. Jagger contributes a bluesy harmonica solo, while drive is provided by Mr. Marley's rhythm section—featuring Courtney Diedrick on drums and Shiah Coore on bass—and Mr. Rahman on synths. In "Satyameva Jayathe," which bears the sweeping grandeur of Mr. Rahman's cinema pop, Mr. Marley toasts while Messrs. Jagger and Rahman take turns singing the verses.

"SuperHeavy" succeeds as a synthesis of seemingly dissimilar streams of rock and pop. As the album unfolds, the instinct to identify influences surrenders to an acceptance of the concept. With Mr. Marley as the dominant voice, the overarching feel of the music is joy—not merely because the fusion works, but because it works so well.

"It's still music with a groove," Mr. Jagger said. "But I didn't feel like we were copping something else."

The journey to birth for SuperHeavy began at Mr. Stewart's home in Jamaica. "Below me is Saint Ann's Bay and Lime Hall is above me," he said, referring to cities in Saint Ann's parish where Bob Marley, Burning Spear and other reggae giants were born.

"Everyone plays their sound systems really loud—there's a clash of sound. One day, some guy was toasting in a high voice and another was singing what sounded like an Islamic morning prayer. I wondered whether you could make some Jamaican music with an Indian bluesy thing or an Asian-Indian thing."

Mr. Stewart contacted Mr. Jagger, with whom he worked on the soundtrack to the 2004 remake of the film "Alfie."

"I thought it was a really interesting mixture," Mr. Jagger recalled. "It's going to work. But how?"

Mr. Stewart invited the musicians to Henson Recording Studios here and told everyone that informality would rule. "We're not going to be sitting in a writing room. It would be dull," he announced. "We could jam anything on the spot."

In the first five days, according to Mr. Stewart, they wrote 17 songs, with the vocalists taking responsibility for developing melodies. Musicians began to pair off to write together. At one point, Mr. Stewart and Ms. Stone recorded a track while Mr. Diedrick, unaware the red light was on, was tuning his drum kit. Mr. Stewart cleaned the track and released the song on Ms. Stone's "LP1."

In the end, the musicians surrendered to the on-the-fly recording process, perhaps against their customary way of working. Mr. Marley likes a bit more control, Mr. Stewart said, and Mr. Rahman conceded he didn't attempt to drive the process. At first, Mr. Jagger was a tad wary of working with musicians he didn't know.

"It was all give and take," Mr. Jagger said. "You rely on your critical faculties because you're not aware of their capabilities."

"At first, we didn't know what the hell we were doing," Mr. Stewart said. "But by the end of the first day we were really pleased."

Mr. Fusilli is the Journal's rock and pop music critic. Email him at [email protected] or follow him on Twitter: @wsjrock.