The offices of Jack White's record label, Third Man Records, landed like a spaceship on an unloved lot in downtown Nashville in 2009. The area is not a salubrious one: his neighbours are a methadone clinic, a halfway house and the Rescue Mission, the city's main homeless shelter. On a cloudless, airless morning in May, when it's already 30C by 9am, every corner has a sentry of hard-luck cases on crutches and men with teeth like a crossword puzzle. Third Man, meanwhile, is a squat and purposeful brick building. It is painted all in black, save for three steel roller shutters that each represent a juncture of White's life: one is yellow, a nod to the livery of the upholstery business he started when he was 21; the second is red, the signature colour of his blues-rock band, the White Stripes; the last is blue, the colour he has latterly adopted for his solo career.

Through the front door, you begin a journey down the neural pathways of White's brain. At his behest, Third Man staff dress exclusively in yellow, black and a dash of white: men wear sharp suits and skinny ties, with three thin lines scratched, as if by an animal's claw, through the centre; the women's dresses are prim and Mondrian-inspired, with a frisson added by low-denier hosiery. The soundtrack is supplied by vinyl rotating on vintage record players, a gumball machine dispenses yellow, black and white gobstoppers, and the room is surveilled by the beady eyes of esoteric taxidermy that includes a peacock in full plume and a splendid Himalayan wild goat grazing among the soft seating.

As you walk around, depending on your inclination, you will either admire Jack White a little bit more for the singularity of his vision or dismiss this as a gimmicky curiosity shop. Either reaction would not displease the space's 38-year-old curator. The output of Third Man Records is wilfully unconventional: White recently produced a new album with Neil Young – A Letter Home, acoustic versions of Young's favourite songs – but they recorded it in a 1947 Voice-o-Graph booth that imbues the tracks with a sandpaper crackle. He has overseen the production of a limited-edition vinyl that smells of peaches (The Ghost Who Walks, the 2010 debut album by his then-wife Karen Elson), a playable, $250 gold-plated disc (for Jay-Z's soundtrack to last year's film adaptation of The Great Gatsby) and a 12in LP that had to be smashed to play the 7in single in the centre (for another of White's bands, the Dead Weather).

These are conceptually straightforward, however, compared with White's plans for his second solo album, Lazaretto. Come 9 June, it will be available as a CD or digital version, naturally, but he will also release a limited-edition vinyl "ultra LP", which has hidden tracks, one song with alternate introductions (depending on where the needle is dropped) and a hand-etched hologram floating in the "dead wax" between the last grooves and the label. All of which suggests a man with a lot of wild ideas who is doing whatever the hell he wants.

After I've been snooping around for 40 minutes or so, White arrives in his black Tesla Model S electric sports car. He is turned out nattily: an aquamarine shirt is co-ordinated with leather Oxford shoes; his hair spills out of a black newsboy cap and he wears dazzling white socks, as he always does. His metal belt buckle features the Third Man logo – three blocky figures in front of a globe – and the Roman numerals "III", a number that has been a lucky omen for White since an epiphany he had as an upholsterer. He beckons me past the stuffed goat into an office, on the smoked-glass door of which are painted the words: "John A White III DDS. Family Dentistry 9am to 3pm."

Business is good? White nods his head, fires up a dainty cigarillo. "We have almost no consideration for profit and I think that's why we are highly profitable," he says. His dark eyes dart, he speaks in flurries, more Detroit, his hometown, than Nashville, his adopted one. "I just don't care. People always told me over the years: 'You have such a mind for business and marketing.' That's hilarious because I never ever think about it. I've never chased after hits and I've never chased after people's attention. Third Man Records stands for a lot of things and when you stand for things, people come to you."

The White Stripes were that rare critical-commercial crossover – their 2003 album, Elephant, led by the world-conquering Seven Nation Army, sold 4m copies – but White could never, I suggest, be accused of trying to please all of the people, all of the time. "I always feel a little alone in that sense," he replies, taking a drag. "I purposely put things up that will turn a lot of people off. The White Stripes was all about that: brother and sister dressed in red, white and black; the girl's in ponytails with a peppermint swirl on the bass drum, the guy's singing the blues… This was a turn-off for a lot of people. They said, 'This isn't the blues!'"

Of course Jack and Meg White, the band's drummer and silent partner, weren't brother and sister, they were ex-husband and wife; but anyone who thought that the band's novelty look or fictional back-story besmirched its authenticity, argues White, was missing the point. "So that was when I was like, 'That's exactly why me and you shouldn't share anything!' It was over between me and that viewer or that listener immediately and I was fine with that. Now you get down to the people who really care, who want to dig deeper."

White, as he acknowledges, has become adept at pre-empting public dissection of his new music. Some will inevitably complain that Lazaretto is not as good as a White Stripes record, and there's not much he can do about that. Others will say that it sounds exactly like the White Stripes or one of his – don't dare call them "side projects" – other bands: the Raconteurs or the Dead Weather.

"All I can do is attack the song, song by song, [it] doesn't matter if it's the Dead Weather, the Raconteurs or me, I'm attacking the song," he says. "Sometimes they sound really different and sometimes people will say, 'That sounds exactly like a White Stripes song with five people playing on it.' If anything that'd be a compliment to me. I'd be flattered. I don't know, it's going to be me on there no matter what."

White tries to make the creative process distinct for each incarnation. For Lazaretto, his innovation was to take his time. White Stripes albums were often written and recorded furiously: White Blood Cells, their 2001 breakthrough, was made in three days. The new record is the product of 18 months of tinkering. Sometimes White would complete the music and return to put down the lyrics months later.

"It was a bad idea to write like that," he concedes. He eventually got some inspiration when he found a stack of short stories and plays he'd written when he was 19. They were average, mostly, even embarrassing, but the odd phrase and character was salvageable. "I thought, 'What if you write a song with yourself?' Collaborate with your 19-year-old self on a song." He lets rip a honking laugh: "And don't give him any royalties."

White is braced for people picking through his lyrics on Lazaretto like cub reporters rifling through a celebrity's rubbish bins. With his first solo album, 2012's Blunderbuss, there was endless speculation about how personal White – hot from his divorce from British supermodel Elson – had got, with the singer forced to reaffirm that he would never be stupid enough to write open letters to loved ones, past or present. When the subject comes up this morning, it is the one moment when his voice rises in mild irritation.

White with his ex-wife Karen Elson. Photograph: Gareth Cattermole/Getty Images

"I write what I write, and some people might think one thing and other people something else," he says. "I know it's not about me, so I get a little bit upset that I have to waste so much time clearing that up with the listener or the press or whatever. It feels a little bit like this is a conversation from the 1960s, when people like Dylan broke those barriers down. I shouldn't have to have this conversation now."

White does eventually concede that some personal observations and bugbears have slipped on to the record. He doesn't own a mobile phone or engage with social media, and clearly has reservations about technology's relentless march. These sentiments find their way on to Entitlement, a rant about the younger generation's desire for instant gratification. White is doing his own bit to turn back the clock: at his gigs, he enforces a strict ban on the audience shooting pictures or video; at home, he only allows his children – Scarlett, eight, and Hank, six – to play with mechanical toys. "There's romance and beauty in that in a real physical way," he says, "and that's more important for them than to just quickly cop to video games and iPads."

He also admits the title track of the album captures something of his life right now. A lazaretto is a medical quarantine, traditionally occupied by contagious sea dogs returned from voyage. White is so busy these days that the idea of such a place has become almost exotic: "I fantasise about living in one-room apartments and being in a work camp somewhere, where there's absolutely nothing around me but a cot and a teapot and a sink." When was the last time White sat around and did nothing? "Maybe when I was a teenager," he decides. "When I was 21, I already had my own upholstery shop, I had a mortgage, I had a house. So I was 18 or 19 the last time I woke up and was like, 'Ahhh! I guess I'll play chess today.'"

Lazaretto is dedicated to three feminist pioneers: Florence Green from Norfolk, the last surviving veteran of the first world war until her death in 2012; the American anarchist and writer Voltairine de Cleyre; and "Amazing" Grace Hopper, a computer scientist and rear admiral in the US navy. How much should we read into that? White admits that he barely knows more than a paragraph's biography of each of them, but he jotted their names down at various points in the recording process. He says: "So, just another way to provoke thought, I guess."

Of course, it's never that straightforward with White. From the White Stripes to the Dead Weather, much of his work has been collaborations with women, and as a producer at Third Man he has worked with countless more. But this has not been enough for him to swerve charges of misogyny. The complaints were levelled most explicitly in a 2012 article in the Atlantic magazine, entitled "Jack White's Women Problem", which painted White as a dinosaur who was controlling towards women and guilty of patronising them in his songs, such as Freedom at 21 from Blunderbuss.

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"I really don't get that," says White, riled, "because you look at the R&B and hip-hop world and, for God's sake, they are talking about kicking pregnant women down the stairs and every other word is 'bitch'. I don't know where the hell people got that from me because I've done so much work in my life to promote female musicians and artists. I mean, I've worked with more women than you could ever imagine, eight to 80: Loretta Lynn, Wanda Jackson, Alicia Keys, Ruby Amanfu, Alison Mosshart, Meg White and on and on. I respect and I'm inspired by them so much."

A part of White's success has unmistakably been the mystique that surrounds him, not least through his own cultivation. When the White Stripes broke through at the turn of the millennium, details of his childhood emerged unsteadily and unreliably. White assiduously avoided clearing up the tittle-tattle, until eventually birth, marriage and divorce certificates were slightly churlishly unearthed by journalists. These confirmed that he was born John Anthony Gillis, the last of 10 children, the seventh son, to parents who worked for the Roman Catholic archdiocese of Detroit. He married Megan White in 1996, took her name, taught her how to drum, and they divorced in 2000. Sitting with him now, a giraffe's neck and head looming over us, it is clear that the man still enjoys a degree of artifice.

White, therefore, can't have enjoyed the past few months. When he and Elson divorced in 2011, the split was so amicable they celebrated with a party: "a positive swing bang humdinger," they called it on the invites. But the relationship soured and last summer Elson sought and received a restraining order against White. She wanted to restrict his access to their children and complained that White had refused on various occasions to attend family counselling. As an embarrassing aside, an email to their shared business manager was released in which White described Dan Auerbach, the singer-guitarist of the Black Keys, as an "asshole" who "ripped off" the White Stripes.

The details were sensational; not least that Jack White sends emails. But when the subject comes up, he is, surprisingly, not evasive. He has spent the morning with Scarlett and Hank, and he is reportedly back on good terms with Elson. Many of their problems, both parties apparently concede, came from overexcited lawyers. But today White does not stop there.

"I'm a very provocative person and very intimidating," he concedes. "So it's very hit-or-miss who can hang with me. I don't blame anyone who doesn't want to be around me – it's expected." He laughs wryly, "I'm incredibly complicated, incredibly full of energy, incredibly busy and I never stop thinking, I never stop creating. Sitting next to me in a room or laying next to me in a bed, it could be a lot of work. To be friends with me, have breakfast with me, have coffee, is a lot of work, too. It's like you're going to lunch with Larry David, Alan Partridge and Chris Rock all in one person – maybe with a little bit of Woody Allen mixed in there. And some people might not think it's funny!"

Meg and Jack White performing at Madison Square Garden in 2007. Photograph: Stephen Lovekin/WireImage

So White is not surprised when his endeavours – the White Stripes, or his marriages – don't last for ever? "I expect them not to, yeah," he replies. "So I try to make the best of everything as it's happening. The overwhelming goals of my life are to create community, create family, create scenarios where things get better and last a long time. Create them! But knowing in the back of my head that my personality is a tragic Greek figure that will possibly destroy it and perhaps that was my plan all along."

As for Elson's specific gripe about counselling, White admits that he has had therapy, but not for years, and he wouldn't seek treatment again. "Loss hurts, insults hurt, death hurts," he says. "You can't change that, you can only change your perspective on it. If you said to a therapist – and I haven't been to one in many years, because it just doesn't do anything for me anymore – but if you said to a therapist: 'My dad beat me every day and then murdered all my brothers and sisters in front of me, before turning the gun on himself. And it was in the newspaper the next day and I got fired from my job because of the scandal of it…' If you said something like that to a therapist, all they can ever say is, 'Wow, that's too bad. I guess we've got to figure out a way for that not to bother you any more.'

"So when you figure out that trick, that becomes how you attack anything bad. You figure out a way to look at it so it doesn't bother you so much anymore. My problem is that most of it is private, so I don't really want people to know about it, but you can't help people knowing about some things."

Last August, in response to Elson's legal accusations, White filed his own motion, citing an email from Elson that described him as "an amazing father". (He makes a point of only touring in blocks of two weeks so that he is never away too long from Scarlett and Hank.) Did it pain White that he had to go public?

"Pick your battles, you just do what makes sense at any given time," he says. "Some people go on talk shows and then cry in front of Oprah Winfrey or Barbara Walters and they tell you every goddamn last thing about their life. I don't know; I don't really need that kind of attention. I'm like, 'Shit, I'm not using my children to sell a couple more records or something like that.'"

White doesn't mention the Black Keys by name, but he's happy to sound off in general about where modern music is getting it wrong. Trent Reznor of Nine Inch Nails complained recently of artists trying to appeal to an obscure coterie of blog writers, and White agrees there may be something in that. But, to him, the main problem is musicians playing it safe. "You're learning how other people are dressing on the playground, and you are dressing like them because it's the easiest way to get through the week," he says. "You can't applaud that; I don't applaud that activity."

White only feels like he has a few kindred spirits: Bob Dylan, Jay-Z, Kanye West and specifically Neil Young, who shares his fascination with mechanical objects and a desire to keep experimenting. "We are both putting ourselves on stage and presenting ourselves to people," says White. "Now you can take the easy way out: you can go on in jeans and a T-shirt and say, 'Hey, look at me, I'm real.' Or you can go onstage in a three-piece suit and hat and say, 'I'm real… Or maybe I'm not! What's more interesting?' And everyone makes the jeans and T-shirt choice. I mean, 95% of people do."

There's no doubt that White is sincere, but he also clearly derives some satisfaction from being an outsider. Since he moved in, the area of Nashville around Third Man has become unexpectedly desirable. This had led to discussions in recent times between the city and business owners about moving out the homeless and replacing them with creative types, including – the horror! – a Soho House-style members' club. The plans would see White's property shoot up in value, but he is strongly opposed to them. "This is a solid neighbourhood, everyone looks out for each other," Ben Swank, Third Man's co-founder, had explained to me on my tour. "The work the Rescue Mission does is more important than what we're doing."

Pretence and authenticity are subjects that White spends a lot of time thinking about. They were at the heart of the White Stripes and those notions remain central to his life now. Third Man Records could be full of the latest recording equipment; instead it houses a darkroom for developing photographs and an antique lathe that once carved out James Brown records and now cuts vinyl straight from a live performance. White refuses to use computer programs such as Pro Tools to clean up his recordings, and Lazaretto was recorded by analogue means, in his home studio on a 16-track Neve mixing console, and the tape was edited with a razor blade.

But all that really matters to White is whether what's being created is worthwhile and will endure "like little time capsules". He has no idea if they will, but he's found a test he is happy with. I ask whose opinion he most valued on Lazaretto. "My kids," White replies. "I watch their eyes and their body movements when they listen to the songs. Because children don't lie. If they are not responding to something, it's probably not that good. But if a kid says, 'Can you play that song again?' You're like, 'Oh yeah!' Now I know we got somewhere because a kid would never say that unless they really felt it inside."