There's something to clarify before David Lee Roth gets down to business, talking about his life with and return to Van Halen, arguably the most important American hard rock band ever. Namely: why did I have to watch a video of him putting his sheepdog though its paces before I was allowed to speak to him?

It's hard to tell why – because Roth's answers are circumlocutory, filled with metaphor and grandly entertaining – but my guess is it's to illustrate how his life has returned to its beginnings. "My background is in Indiana," he says. "My grandparents came from Europe in 1917 and made their living working in a general store, and selling beer by the pail for four cents in the 20s in Newcastle, Indiana, which today is still bib overalls, livestock and the great outdoors. Just down the street is Indiana University where my pop went to school – he later became a doctor. But while he was just starting college when I was born we lived in a little house at the edge of a farmer's property and I grew up chasing muskrats and collaring dogs." Training a sheepdog, then, is coming "full circle".

Full circle in another sense, too, for next week's release of the new Van Halen album, A Different Kind of Truth, marks the first recordings Roth has made with the band since departing amid a cloud of bitterness in 1985, when he was replaced by his arch-enemy Sammy Hagar (as far back as the 70s, Hagar was calling Roth a "faggot", Roth responding by saying Hagar had "a social problem").

Though Indiana-born, Roth was hardly your typical farmboy. His Uncle Manny ran the New York bohemian hangout Cafe Wha? until 1988, putting on the likes of Bob Dylan and Lenny Bruce, and Roth would hang out there as kid visiting in the early 1960s. He was never much of a student, bouncing around schools – for disciplinary reasons; he's evidently ferociously bright, even if he often chooses not to show the world – until he moved to Pasadena, California, as a teenager, where he enrolled at Pasadena City College and met the man with whom his life would become entwined, a young guitarist called Eddie Van Halen.

For seven years – from the 1978 release of their debut album, until Roth's departure as frontman in 1985 – Van Halen were a living, breathing cartoon of the rock'n'roll lifestyle. They were mocked for the supposed excess of demanding a jar of M&Ms in their dressing room at each show, with all the brown ones removed (though the reason for that was to check the promoter's attention to detail: if he couldn't get such a simple task right, what else might he have missed?). They celebrated sex and drugs and drink. Then they celebrated them some more. If Sunset Strip in the 1960s had been the party, Van Halen, a decade later, were the after-party. And the world lapped it up: the Roth-era Van Halen sold 35m albums, despite their sometimes variable quality. There were masterpieces – their debut, a shock as seismic as punk, and Roth's final album with the group, 1984 (the one that gave us Jump and the marvellously goofy Hot For Teacher with its apocalyptic drum intro) – and there was the tossed-off, 31-minute long Diver Down, from 1982, heavy on covers and instrumentals.

"Van Halen was an island unto ourselves," Roth says. "If you stop at that island – we recommend you do, but abandon all hope – do not back up! It was like Port Royal in the 1700s. It didn't belong to anybody, which was why it was great."

But was it ever hard work appearing to be having that much fun all the time? "I was a surgical tech right out of high school, I sold clothes; I shovelled shit at a horse stable for years. I've been rich and I've been poor," he says. "Rich is better. Totally better." He laughs, a great wheezy crackle. "The job we have is a privilege. The Van Halens [Eddie and his brother Alex, the drummer] and I have had steady jobs since we were 12 years old. Mine was working before and after school at a horse stable. For them it was paper routes. Mr Van Halen was classic European: you're making your money for the rent. I was lucky I didn't have to do that … Even at your worst moments, there's a whole lot of Shakespeare going on. How can you not appreciate it? At your lonesomest, most catastrophic, it's still pretty cinematic. I think the smiles were genuine. Don't mistake them for simplistic grins – there's a lot of pirate smiling." Piratical sounds about right, for Van Halen were adept at picking fights, too. When they headlined the 1983 US festival in California, in front of 375,000 people, and millions more watching on MTV – for a reported $1.5m fee – a bombed-out-of-his-mind Roth took on the Clash, who were also appearing: "I wanna take this time to say that this is real whiskey here … the only people who put iced tea in Jack Daniel's bottles is the Clash, baby!" That came moments after addressing a member of the crowd at whom Roth had taken umbrage: "Hey, man, don't be squirting water at me! I'm gonna fuck your girlfriend, pal!"

David performing in Florida in 1983 Photograph: Neal Preston/CORBIS

From the very beginning, Van Halen sounded unique. Their first album, with its clean, popcentric sound, changed the face of hard rock: there was no use of the devil's interval, the chord progression that traditionally signals metallic doom. Instead, as Roth says: "We're the band that sold a Ricky Ricardo rhumba in Jamie's Cryin'. Dance the Night Away is Santana, because we used to play all those weddings and those dances at the backyard parties."

The combination of chart-baiting pop and tough rock guitar spawned a legion of imitators in the LA hair metal scene – Mötley Crüe, Poison, Cinderella, Warrant and the like – who tried to set up camp on Van Halen Island. "I don't know who coined the phrase imitation is the sincerest form of flattery," Roth observes. "I think David Mamet coined the phrase imitation is the sincerest form of stealing. Probably a litigating attorney coined it first. OK, if imitation is the sincerest form of flattery then there are a whole lot of dogs out there … At worst I feel like I'm driving past a traffic accident and I'm relieved no one was killed."

Van Halen were there first, though, and they were the best. They sounded like the future (it's no coincidence that Eddie Van Halen's alien guitar caterwauling was used in a scene in Back to the Future, to convince George McFly he was being visited by a being from another dimension). Eruption, the famous guitar solo from the first Van Halen album – and the Back to the Future wake-up call – showed a new generation of players how to bring the flash: you didn't need 10 minutes for your solo to make the point – 100 seconds would do.

If you look closely, Roth says, it's easy to see where Van Halen took their inspirations from. "I can point for you and go: right there we're imitating Eric Clapton; right there I'm imitating vocally David Bowie; right there is Bruce Springsteen" – he puts on a gruff voice, aping the Boss – "'Diamond Dave, you're a big man!'" – and he guffaws – "but this is how you create a signature sound. If you're lucky to have it, there's no way around it. I actively imitated everything from the Nicholas Brothers tap dancing to Mick Jagger going 'Oooh yeah!' But because of whatever it never sounds like anything to you but David Lee. And when Edward plays you might never have heard the material before but you instantly recognise it as fast as, say, Jimi's guitar."

Crucially, though, Roth says they were never just a metal band, even though they revolutionised the genre. "Metal is a bit specific," Roth says. "The neighbourhoods we grew up, learning, acquiring musical knowledge, were very separate neighbourhoods, unlike, for example, New York City where Mr Chin lives next to Mr Steinberg who owes rent to Mr Patel and they all speak Serbo-Croatian. It's just the school system. Here [in California], the Venice Beach surf neighbourhood is very different than San Bernadino Hell's Angels. Below south of the harbour freeway: 'Que pasa? What are you looking at?' And that all works into Van Halen. You can hear it - it's loudly diverse but you can't feel the seams. It's like if you go to a car show and you Stevie Wonder it: you can't feel where the Chevy turned into a Mercedes door frame which turned into – that's a De Soto grill! –" and suddenly he's no longer the blind man at the car show, he's an aggrieved Mexican kid wondering why the blind man's hands are all over his girl – "'That's my girlfriend loco! What are you doing?'" He guffaws. "All those different neighbourhoods add up into the sound, and to say it's one kind of sound – no! It's so much of a hybrid that you have to give it its own name." He concludes his spiel, bafflingly, with the tale of Yip Harburg. "He was a millionaire industrialist who lost everything in the stock market crash of 1929 and when his kids and his wife said: 'You can earn it back honey," he said: 'No, I've always dreamed of being a lyric writer on Broadway.' And he did. He started from absolutely nothing, with no background, and he wrote Brother Can You Spare a Dime, arguably the most famous American song of the Depression, and he wrote the lyrics and the melody for Over the Rainbow. How's Yip doing so far? I confine the theatre of my fame to what would Yip think?"

Those different neighbourhoods, plus the steals from Springsteen and Bowie and Yip Harburg, were what made the band unique. Even on the demos they recorded with Gene Simmons of Kiss in 1976, they already sound like a band who are only themselves, sui generis. "It's not magic," Roth says by way of explanation. "It's science. And the beautful thing about science is it's true whether you believe it or not." And then we're off. "For example, the busing programme in America started in 1966 and my sister and I were sent off to schools an hour and a half away that were 95% black and Spanish speaking. Today I only listen to R&B – only listen to R&B – from any time period, doesn't matter, doesn't matter at all, whether it's big band swing all the way up to anything that's on Beatport. The Van Halens went to Ridgemont High. Ever see the movie? That was their high school – 98% Jeff Spiccoli and home of the monster riff and every ending to every song should sound like world war nine or just the end of the world. Who does endings better than Van Halen live? I'll send you a ticket. I'm ready to argue this. Unarguably the best endings ever, right? They sound like the end of everything. Biblical. And the guitar solo? It is a religious icon, certainly on a par with some of our more popular professional sports, which I maintain are religions. Put the football down – I'm ready to argue." He laughs. "That's how we do the solo." And laughs again. "And you'll know when the solo's coming because there's a scream. There are moments. Combine the two and what you have is hard rock from the 70s. We enjoyed our fame in the 80s but we had nothing musically to do with it. And you can interpret that four different ways, depending on how I just said it."

David finally reunited with Van Halen.

After Roth left Van Halen, he embarked on a solo career that started brightly before fading away, but he found another lease of life, even before he first reunited with Van Halen for a tour in 2007. "I'm a state-licensed EMT [emergency medical technician] in New York." It seems staggeringly unlikely, but an internet search reveals it to be true. "I probably have over 200 911 calls on my ticket in the last six years alone. I live a very different life away from music."

Even so, he has chosen once again to hitch himself to the Van Halen wagon. Is it possible he and Eddie Van Halen – for all the very public acrimony between them – need each other to create anything resembling their best work? For the first time, Roth pauses – there are 30 seconds before he speaks. Then, finally: "Clearly. Very astute. Clearly." Apart, they're footnotes; together, they're a novel. "We went to school together. Literally. We took theory and orchestration together. We both have almost identical backgrounds in how we learnt. We learnt at the back of the hand from eastern-European teachers. Unfriendly eastern-European teachers." And for a long time, they shared the same aims: "I always thought of it as part of a group. I never thought in terms of Rod Stewart, I thought in terms of the Rolling Stones or the Sex Pistols. I think Edward thought in the same vein."

And does knowing you need each other make the tensions between you all the worse? And we're off on one of those long, rambling, glorious answers. "Jesus, let's go back to the 1600s again. People didn't understand psychology, right? You showed them emotional content and made somebody cry and they thought it was demons. One of the best reviews you can get in my estimation is from the villagers if they killed all the actors and buried them at the cross so their ghosts couldn't haunt the village – because everyone left the play crying and laughing and they couldn't understand why. Today we give them an Oscar for that kind of emotional ride. Being human has caused so much of that. Let's really back into some theory here. What is art? Simple, I think – something that forces and compels you to think, and that can be a mint condition copy of Raging Bull or it can be the Kardashians. The same questions will be asked and you will be forced to confront yourself, and you will be forced to triangulate where you stand on everything from racist politics to haircuts. And are they really different? Do you follow? You're going to ask the same questions and that … shit … is … art. And it has caused you to question more than that goddam soup can Warhol sold us. Or tried to. Bring that one up. You follow? You are compelled into argument. Consequently, arguing about our band and our rock'n'roll - you can do that certainly for longer than actually listening to it." Then he laughs long and loud, and offers the perspective that comes with being 56, happy, and aware that there's more to life than telling the world that it might as well jump. "Van Halen music is whisky in a paper cup! Short doses and not every night, PLEASE!"

• A Different Kind of Truth is released on Interscope on Monday.