Arctic Monkeys’ frontman Alex Turner is in a darkened room within a rehearsal space in Burbank, Calif. “Just before you called, I was disappearing into a screen,” he says, speaking slowly, choosing his thoughts.

“All the lads are back together to figure out how to play some of these tunes on the new record,” he says through his thick English accent. “I feel like this week, we’ve begun to break through some of it. You start to get a feeling like when you get back on the stage.”

Arctic Monkeys haven’t been on stage together in four years. The U.K. rockers delivered their most commercially successful album to date, AM, in 2013, peaking at No. 6 on the Billboard 200 and earning the band its first Hot 100 hit with “Do I Wanna Know?” (peaking at No. 70 in 2014). But soon after, the quartet -- which includes Matt Helders (drums), Jamie Cook (guitar) and Nick O'Malley (bass) -- surprisingly went on hiatus, as Turner turned his attention to side band with Miles Kane, The Last Shadow Puppets.

On May 11, Arctic Monkeys will reunite for its sixth album, Tranquility Base Hotel + Casino (Domino), in which Turner swaps his guitar for a Steinway and delivers a stream of obscure references to Neil Postman’s Information-Action Ratio and Charles Bukowski over cavernous compositions.

The piano was an unexpected gift for his 30th birthday from a friend: “It was quite a rush, really,” Turner recalls of its unveiling. “Prior to that point I didn’t really have many ideas, and in my memory, that was the point at which they started to come. I really do think sitting at the piano tricked me into writing a lot of this stuff.” He had gotten to a point with the guitar where he knew where everything was going to fall. “Sitting at the piano took me immediately to a different place,” he says. “There are chords that came out, my fingers were falling different places, and the sounds were giving me ideas. That I was the guy sitting at the piano also gave me ideas.”

Turner’s new instrumental playground resulted in Arctic Monkeys’ most ambitious album to date. AM was sonically different from 2011’s Suck It and See, and he was encouraged by that to take yet another turn. “With the commercial success of the last record,” he says with a pause -- briefly tripping over the words “commercial success,” as if it were a foreign phrase -- “I don’t think I felt the pressure of that hanging over the creative process. But there was a pressure, in that we step it up and do something different again -- try and fly high.”

Arctic Monkeys have been flying high since the arrival of the band’s racing 2005 debut album Whatever People Say I Am, That's What I'm Not, which became the fastest-selling debut album in U.K. chart history upon its release, and earned a Grammy nomination for best alternative music album. On each LP since, Turner established himself as an ingenious lyricist who can cinematically capture a specific moment in time.

All the while, he’s managed to fly relatively under the radar in the public eye, only adding to the allure of anything he’s released. Turner has no presence on social media outside of the band’s promotional- and informational-only posts -- “Technology is worth keeping an eye on,” he warns -- but says if he were to get on any of the apps, he'd likely just share Bukowski excerpts.

The upcoming album's opening track, “Star Treatment,” exposes the inner turmoil Turner felt following the band’s arrival: “I just wanted to be one of The Strokes, now look at the mess you made me make,” he sings. So, then, it comes as no surprise that following the success of AM that Turner found himself wanting to reroute his approach. The songs that follow are so full, and each word so carefully selected, that the messiness he sings of is hardly even a consideration. As a result, the writing on Tranquility is enlightened and evolved to the point of occasionally requiring a Google search for context.

Largely written on his own in the “Lunar Surface” -- his Los Angeles home studio named for the theory of the faked moon landing -- the lyrics have the cadence of poetry and invite annotation. While he’s not especially big on conspiracy theories, he does like “moon stuff” and says, “Once I started, it was hard to put the lid back on the science-fiction lexicon. There was a film [my friends and I] were watching called World On a Wire -- it’s a [Rainer Werner] Fassbinder film -- and that was definitely what pushed me over the edge into, ‘Let’s go and write about another world in order to comment on this one.’”

Tranquility chronicles many of Turner’s observations: technology and its control (“Batphone,” on which he sings about “getting sucked into a hole through a handheld device”), bougie taquerias (“Four Out Of Five”) and modern-day American politics (“Golden Trunks” reimagines the “leader of the free world” as a “wrestler wearing tight golden trunks”), though he avoids overtly sharing his opinion on anything.

“In the past I’ve struggled to find the poetry in [politics] and I think I’ve managed a way to find it this time, with some encouragement,” Turner says. “I’ve always thought that, writing anything that relates to politics, it’s a lot to do with the way you go about it. Being able to write about the power of allusion and suggestion is important to keep in mind.”

The most concise lyric comes courtesy of the ominous-sounding “She Looks Like Fun,” on which Turner recognizes: “There’s no limit to the length of the dickheads we can be.” Elsewhere, there’s the foreboding title track, the more experimental Beatles-inspired “The World’s First Ever Monster Truck Front Flip” and the gather-around-the-piano closing ballad “The Ultracheese.”

Turner recorded most of the vocals at home on his Tascam 388, a vintage 8-track, but the songs came alive once the band gathered at France’s La Frette, a studio built within a 19th century mansion that their longtime producer James Ford had wanted to record at. “It was the first time we were all together, and I think what the record got from that was this energy of the band that wasn’t there before,” Turner recalls.

While at La Frette, the group tried to channel the approach that Dion took on Born to Be With You and The Beach Boys on Pet Sounds: “I think over time you just learn that [the magic is made] with a lot of people in the room all at once and everything spilling over all the microphones,” Turner says. “We did a little bit of that on this album, but one day I’d like to go the whole way there.” Turner points to the outro on “Four Out of Five” as an example of Born to Be With You’s influence.

Once Tranquility was done and Turner had landed back on his Lunar Surface, he was quick to task himself with a new project: designing the album’s artwork. A visionary who has a hand in all aspects of his work, he knew he wanted it to mirror, in some way, the album’s title: “I liked the idea of naming [the album] after a place, because to me records that I’ve been in love with and continue to be in love with feel like they’re places that you can go for a while. I very much feel like if [Born to Be With You] were a place I would’ve moved there a long time ago.”

For the album’s name, he plucked the place mentioned on the would-be title track, the fictional Tranquility Base Hotel and Casino, on which he sings of “Jesus in the day spa filling out the information form,” because, “That [phrase] seemed like the right name for this family of music.” From there, he began to think about architectural models and started sketching ideas on a piece of graph paper.

“I liked this idea of a six-sided shape, because it was the sixth record,” he relates. “I drew a hexagon, I thought that was a kind of dumb idea, and then two months later I made this spinning thing on top of a Revox tape machine. In between that, there are a lot of things that aren’t the artwork and I made a real mess. But it all makes sense to me now. In the past I’ve definitely had record covers that don’t, to me, represent what’s on the wax, and I certainly don’t feel that way about this one. By the end of it, I think I’d forgotten there even was a record. I’d just gotten obsessed with cardboard.”

With both the album and its artwork done, Turner’s attention is now on Arctic Monkeys’ live return, with tour dates in Europe and North America, including headlining sets at Lollapalooza and Firefly. But, true to form, his tone remains neutral even when speaking about the nearing release date.

“I’m getting intermittently excited throughout these days,” he says, seemingly composed about what’s to come. But as for getting the band back together under a new umbrella of sound? “It feels like it’s been a long time coming.”

This article originally appeared in the April 21 issue of Billboard.