The fact that supergroups generally offer up only the sound of clashing egos and painfully discordant sensibilities makes the band’s debut album all the more pleasantly surprising.

Formed earlier this year by Foo Fighter Dave Grohl, Queens of the Stone Age frontman Josh Homme and the former Led Zeppelin bass player and multi-instrumentalist John Paul Jones, the trio have succeeded in pooling their resources to create a record that stands tall on its own terms.

“We might not make it,” says Homme with pride. “But I’ll be damned if we didn’t reach for something.”

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Long term Led Zep fanatics and friends since the days when the former was the drummer in Nirvana, Grohl and Homme were the driving force behind the formation of the band.

Having worked with Jones on Foo Fighters’ In Your Honor album, Grohl decided to play matchmaker at his 40th birthday party, held last January at Medieval Times, a novelty children’s restaurant in Los Angeles. Deliberately seating Homme and Jones next to each other, he sat back and watched nature take its course.

“We met at Medieval Times, which is somewhere people have their 14th birthday parties, not their 40th,” laughs Jones.

“We were sitting there with paper crowns on our heads and drinking dragon soup – completely stupid! But once Josh had got over the sheer embarrassment of it all we got on really well.” Grohl’s ruse worked to perfection: within 48 hours the trio were jamming at Homme’s home studio, and the music immediately fell into place. According to Grohl: “I knew within two minutes. This is the best band I’ve ever been in…”

With Jones commuting from England, they began working on an album, recording intensively for two week periods then taking a couple of weeks off.

Homme sang and played guitar, Grohl clambered back behind his drum kit, and Jones played bass and “about eight different instruments – some of which I don’t even know what they’re called”, says Homme. They wrote everything together, recording live and adding overdubs quickly before moving on to the next song.

“We completely forgot about the ‘supergroup’ tag,” says Jones. “We just got on with it. The machines were turned on all the time, and we worked really hard and basically wrote and recorded the album at the same time.

“It was a very democratic effort: ‘What have you got? This could go here, maybe put this here…’ We were getting to know each other at the same time, so it was like a voyage of discovery.”

Given Jones’s past and the other members’ love of his former band, it’s little wonder that Them Crooked Vultures’ sonic imprint leans towards Led Zeppelin’s trademark sound, the songs built on great slabs of heavy, surging rhythm.

They ditched several acoustic numbers after deciding that “we needed to roll in like Hannibal and ruin your town,” says Homme, in an evocative summation of the music’s controlled ferocity. “You don’t often get the chance to be an immovable force. It’s like the Titanic’s going down and the band is still playing.”

There was no compromise on power, but they were all wary of being overly experimental. “It needed to be songs, and they need to be economical, even if there’s improvisation leading the way,” says Homme. “We wanted to put some hooks in there.”

Aside from a natural musical empathy, what really rescued the project from self-indulgence was the intense secrecy all three men invested in the process.

Partly this was due to contractual complications, but it was also about dodging the deadening weight of expectation. As three musicians whose individual reputations preceded them, it was imperative that no-one was breathing down their necks or pre-judging the results.

“It’s a complex little situation, and we knew really early on that it would be a tremendous shame if we let things from outside get in the way,” says Homme.

“We wanted to make it about music as much as possible and ignore the pedigree, not rest on our laurels. The best thing you can do is say nothing, so we didn’t allow it to exist for other people. Absolutely nobody, management or anybody, knew anything at all, and that in itself became contagious.”

The logistics involved in maintaining this veil of secrecy were mind-boggling. Engineer Alan Moulder was sworn to silence. Homme’s wife, Brody Dalle of alternative US group Spinnerette, mentioned in an interview that her husband was working on a new project and then quickly muttered, “I’m not at liberty to talk about it,” no doubt glancing nervously at the exits as she did so.

Grohl likened it to having a secret lover. The band members, says Jones, “couldn’t be seen in the same place at the same time. Really! Only two members were allowed out together, stuff like that. It was really hard but I genuinely think it was worth it, because people had no idea what to expect when it did come out, which was great.”

For Jones, the timing was fortuitous. Following the one-off Led Zeppelin reunion at London’s O2 Arena at the end of 2007, he and guitarist Jimmy Page had tried to keep the momentum flowing.

“When we realised that Robert [Plant] didn’t want to do any more Zeppelin stuff, Jimmy and I thought we’d find a singer and start another band,” he says. “We couldn’t really agree so the project foundered, and it was at the end of that that Dave approached me. It happened at the right time, and it was another reason I was happy to go along with the secrecy.

“When Jimmy and I were trying to start a new band that wasn’t Led Zeppelin we were constantly surrounded by speculation. In the end it was like, ‘Oh bloody hell, Shut up. Let us get on with it.’”

With the album finished and rumours beginning to circulate on the internet, Them Crooked Vultures finally broke cover in August, making their live debut at a small club in Chicago. “To play in front of an audience who didn’t know a note of our music was great,” says Jones.

“They’d go mad at the end of a song, and then they’d all have to shut up and listen to the rest of it, because they didn’t know what’s coming next.”

Since then things have taken a more conventional twist, with the release of the album last month and now a tour. “What a relief,” laughs Jones. “I can talk to my friends again.” The circumstances surrounding the making of the album were so unique and intense that it would be no surprise if the idea of making another didn’t appeal. Homme, however, is keen to repeat the experience at some future point. “I think we should probably do a couple of records, I hope that’s what happens,” he says. “We were just picking up recording steam when we stopped.” In which case, album number two could be downright dangerous.

Them Crooked Vultures is out now on Sony. They play the Corn Exchange, Edinburgh, tonight.