For 18 months, Mick Jagger has been working on a secret album with Dave Stewart, Joss Stone, Damian Marley and AR Rahman. Super Heavy is the fitting name of this heavyweight musical collective, who plan to release their debut "fusion" album in September.

"It's a bit odd," Jagger told Rolling Stone. "A different kind of record than what people would expect." It's certainly a motley crew: one Stones frontman, one Eurythmics founder, one English soul singer, plus Bob Marley's youngest son and India's most famous film composer. But Jagger promised that Super Heavy's music is "not all weird and strange". Fans, he said, "will find most of it accessible".

Accessible – but full of harmonica. Super Heavy has four vocalists, so Jagger does "other things" besides singing, including playing guitar and a producing lots of "high energy" mouth organ. The music is informed by all of the band's contributors, ranging "from reggae to ballads to Indian songs in Urdu".

Super Heavy was Stewart's idea, inspired by the sounds washing into his home in St Ann's Bay, Jamaica. "I'd hear three sound systems all playing different things," he said. "I always love that, along with Indian orchestras. I said to Mick, 'How could we make a fusion?'" They started brainstorming and making phone calls and, six months later, Stewart, Jagger, Stone, Marley and Rahman converged in a Los Angeles studio. "We didn't know what the hell we were doing," Stewart said. "We were just jamming and making a noise. It was like when a band first starts up in your garage. Sometimes Damien would kick it off and then Joss would sing something on top of it. We might have a 22-minute jam and it would become a six-minute song."

Although Super Heavy have no plans to tour, Stewart said not to "rule out the possibility". It may depend on Jagger's other gigging plans, about which he remains evasive. "I don't have any announcement to make at the moment," he said. "I'm just, uh, y'know ... just doing this right now."

The Rolling Stones haven't toured since 2007, but next year sees the 50th anniversary of the band's first ever gig, which took place at the Marquee Club in London on 12 July 1962. Keith Richards said last week he wouldn't rule out hitting the road again to mark the occasion.

"Something's blowing in the wind," he said. "The idea's there. We kind of know we should do it but nobody's put their finger on the moment yet. This is what we have to ask each other: do we want to go out in a blaze of glory? We can, if Mick and Charlie [Watts] feel like I do – that we can still turn people on. We don't have to prove nothing any more. I just love playing, and I miss the crowd."