alt-J follow up their debut album An Awesome Wave with This Is All Yours. The debut sold over a million copies worldwide and was the 2012 Mercury Prize winner, and the band found themselves at the outset of making a follow up in a new position of recording an album that was actually anticipated, and having gone from a four piece to a trio.

This Is All Yours opening song, "Intro" start's with Joe's voice, a pointillist, percussive "la-la-la-la", Philip Glass-like in its hypnotic simplicity, before Gus joins in with an answering counterpoint. This is not, as its title might imply, a brief throwaway before the album proper begins. Its middle section, introduced by Thom's thundering snare pattern, suddenly asserts itself before the song returns to its becalmed opening theme, only to be once again overwhelmed, by a brutal burst of martial drumming and battle cries. But these four minutes 39 seconds do so much more than open This Is All Yours.

"There was an element of mourning for the conditions we made the first album in," Gus admits. "Before we started making the new record, I was personally quite freaked out by the thought of getting together in some sort of anonymous rehearsal room. I can't imagine us being able to write an album in that setting. There was a real innocence to how we did things in the beginning, it was very much a case of us just having fun and enjoying each other's company. And I was worried that, with the new album, it was going to be a case of, "Ok, book this place for six weeks, we have to get it done'." The solution the band arrived at was a combination between a rented space in Hackney where they could write and then a studio space in Brixton where they would record with the producer Charlie Andrew, who had helped bring An Awesome Wave to life, "It was sort of like a cross between somebody's flat and a photographer's studio," Gus continues, "and we really relaxed there; we could pretty much treat the place as our own. You didn't feel like you were clocking in, walking past someone sat a desk. We could start work at midnight if we wanted to."

Where (and when) they wrote and recorded new songs was one thing; how they did so quite another matter. As mentioned earlier, four became three, when Gwil Sainsbury decided to leave the band. It was a disarming event for the band and one they found challenging to adjust to: "Even if you start from the base of being 100% committed to the thing you're making," says Thom, "the tiniest little things start to build this quite different momentum. There is interest from outside, then the internet gets involved, and before you know it "" and I think this is what happened with Gwil "" you're in a dressing room full of people you've never met before, who don't care about what you care about. If you're not aware of that, then you're in danger, and I think that happens to a lot of bands."

All four remain friends, and it's clear that Gus, Joe and Thom miss having Gwil by their side. "This is the core of our beings," says Thom. "It's what we are. So it was pretty hard at the time, but I feel proud of him for his decision now. He has his own vision. I think he just decided that he didn't want to waste his life on the things that weren't important to him. All the stuff he was required to do, even the touring, he never liked it. The teenager in me thought, "Why would you do that? You've left this amazing band.' I was angry with him at first. But then, when I spoke to him, he sounded the happiest I've ever heard him."

It has to be said, Thom and his bandmates seem in a pretty good place, too. Joe may say, referring to the making of the album: "We were definitely more aware that it was going to be listened to, and that did feel strange." But when you listen to new tracks such as "Every Other Freckle" or "Choice Kingdom," which are somehow disciplined and anarchic, taut and limber, at the same time, it's clear that that awareness didn't hamper the band's writing. This Is All Yours is emphatically, even defiantly, alt-J. When An Awesome Wave came out, the seemingly contradictory duality the band's music contained baffled some, who heard only the complexity and missed the beauty. The band, Joe says, were conscious of this, too "" and, he admits, have sometimes struggled with the issue themselves. "We work incredibly hard to craft our sound, but at the same time we are running on gut. It's hard to work out which is instinct and which nurture." "But both are all right," interrupts Gus. "I sometimes feel pressure to go one way or the other," Joe continues. "But actually, that's right: both are good."

Perhaps this perception developed because the band met as university students. "I wonder about that," says Joe. "And sometimes you can start thinking in that way, too; that people expect to see you as being identical to the music you make. It's strangely persuasive," he adds, "the myth of the artist. To the point where you sometimes feel you're meant to live up to those expectations "" as though you're reading Nuts magazine, but you're hiding it inside the New Statesman." Gus: "That's always happening to me." The band's use of a Miley Cyrus sample on the song, "Hunger of the Pine," further subverted this "myth". The American singer had been using An Awesome Wave's "Fitzpleasure" to soundtrack an interlude on her world tour (she is a big fan of the band), and Thom approached Miley to do a remix of her song 4X4. His work on this coincided with the writing of "Hunger of the Pine" and, when the idea occurred to him to sample Miley's "I'm a female rebel" vocal line, he didn't hesitate. "The main reason it's there is because it sounds good," he says. "That's the boring answer, but it's the honest one, too. I'm not saying we're not happy that it's her, because we are. Ok, if you look at alt-j and Miley Cyrus on paper, it just doesn't make any sense at all. But it made complete sese at the same time; that's why we left it there." Thom's view that Miley is fundamentally misunderstood as an artist was only strengthened by seeing her perform at the o2 arena earlier this year. "I have a lot of respect for her, and for those who respect what she does. It winds me up when people get in a right lather about her, though I can see why they might do. Look, she's winning, she's in control."

Control is an apt word to apply to This Is All Yours, too. The multiple and diverse elements the band work with on the album might, in the hands of other musicians, so easily have resulted in something unwieldy or overblown. All three band members admit that the temptation to constantly add new layers, or yank a song in a radically different direction, was a constant one. That said, you couldn't listen to the structural abandon of "Bloodflood II" its mournful piano intro giving way to sonorous brass, distorted vocals, interjecting static, euphoric falsetto backing vocals, huge, leaden-legged percussion, soaring strings and swelling crescendos "" or the madrigalian sections of "Every Other Freckle" and conclude that the musicians responsible for them were holding themselves back in the studio. "We like to try to tantalize listeners," laughs Joe, "giving them the right amount of something, just before they start craving it. You sort of want to drive people crazy, but not overuse the idea. That's the only form of self-censorship. You want to give them the idea but not ram it into their earholes." "We do add a lot of layers in the latter stages of recording a song," adds Gus, "and we certainly don't worry about how we're going to play it live "" we probably should, actually. We tend to just go for it. Our attitude is much more, "Let's worry about this later.'"

Three of the song titles reference the Japanese city of Nara, whose huge public park is filled with deer, which roam at will. "I see that as a metaphor for having the freedom to do what you want," says Gus. "And that's a freedom I really think we have," says Joe. "Kind of like Grand Theft Auto, where you have this city to run around in, as opposed to Super Mario, where you can only move forwards or backwards or jump up. I think we can have access to this whole big world by toggling round this space, but also walking around punching anyone you want to punch." Beside him, Gus is fighting to hold back laughter. "I'm laughing appreciatively, not mockingly," he insists.

Lyrically, the album balances the cryptic with the sensuous (the erotically charged "Warm Foothills," whose central character, Joe teases, "could be Iris Murdoch, but probably isn't", is a prime example of the latter). "On the first record," Joe explains, "most of the lyrics and the narratives had a meaning. But on this one, there are moments where I sing words, but I'm not aware what those words are, if that makes sense. When we actually sat down to do the lyrics, I had to really listen to what I was singing on the tape. You know, "Ok, I'm saying pharaoh here, and then I think I'm saying bone'. Sometimes, they don't make any sense; I suspect that people are going to come up with some fairly interesting interpretations of those moments."

In other words, over to us. Which is, Joe says, the point of the album title. "That's sort of what it means. Once the record is out, it's yours. You own it."