For many who’ve followed his career since he first surfaced as a solo artist in the alternative ’90s, there’s the perception Sean Lennon has been less than busy in recent years. That lack of exposure might explain why it’s been a quiet start for the debut North American tour of GOASTT (aka the Ghost of a Saber Tooth Tiger), the duo he founded with Charlotte Kemp Muhl back in 2008.

“It’s been a progression,” Lennon reports, on the line before a show in Phoenix. “But things are going great right now—they’ve been getting better and better with each show. We’re getting more comfortable with playing. And the shows have been more and more packed, which is really nice, maybe because the record has been out a bit longer now.”

The album he speaks of is the sweeping and cinematic Midnight Sun, the third full-length for GOASTT, and the first, critics agree, to truly reveal the extent of the band’s songwriting powers. Kemp Muhl and Lennon cover a crazy amount of sonic ground on the psychedelic-tipped record, whether it’s “Golden Earring” mixing porno-sonic organs and break-of-dawn flutes with acid-laced guitar violence, or “Last Call” blending faux-Dixieland horns with prog-king keyboards and peyote-country guitars. That Midnight Sun has been hailed as a richly detailed artistic triumph is in many ways a recognition of the work that went into it. Just because Lennon has been out of the public eye doesn’t mean that he wasn’t busy.

“We’ve been working on this record for years,” the 38-year-old says. “A lot of those years were, I think, a time where we were very inspired and really charged up. We were in the studio, though—a place where we were sort of locked away. So maybe it didn’t seem like we were busy or inspired to other people, but we certainly were.”

It should be noted that whenever Lennon talks about GOASTT, he always uses the word we. This might be partly because, for reasons to do with his father having been in a somewhat successful band back in the day, he tends to get most of the attention when people write about the group. GOASTT is, however, very much a collaborative effort. Kemp Muhl—who enjoys an ongoing and successful career as a supermodel—is not only his bandmate, but also his long-time partner, the two having been together for the past eight years.

Midnight Sun has the couple taking a major step forward from their previous records, the psych-lite Jardin du Luxembourg and the stripped-down Acoustic Sessions. What you hear on the new album’s 12 meticulously assembled tracks is two people doing almost everything themselves, with the multitalented Lennon handling the bulk of the instruments. The New York–based prodigy can rip it up on guitar like Syd Barrett (check out the extended freak-out on “Last Call”), attack a kit like an amphetamined Keith Moon (see the frenzied “Too Deep”), and put together string arrangements that would impress George Martin. On the other side of things, Kemp Muhl—who also plays bass—brings an elegant Euro-cool vibe to the proceedings, her vocals on the lounge-tinged “Johannesburg” bringing to mind the iconic likes of Charlotte Gainsbourg and Chan Marshall.

“The only thing that defines GOASTT compared to other projects is that we do everything together,” Lennon says. “Every decision is shared. We are both the boss, and we write every song together. That defines everything for us—this is Charlotte’s and my creation. We see this project as a real extension of our relationship.”

Based on the lyrics on Midnight Sun, that relationship can be, at times, gloriously out-there. Understandably, Lennon is reluctant to decode the album’s songs, half of which seem like they might be pulled from experience (“Everywhere you go you’re in the microscope,” from “Animals”), and half of which suggest that someone has a pipeline to some really great weed. (“She doesn’t wanna watch Twin Peaks again with you/She already saw the director’s cut on Pay Per View,” from “Too Deep”).

“I think that music and lyrics are to be read into by the listener,” he offers. “That’s the fun part of it—to sit around and try and think what Hendrix was thinking when he wrote ‘Manic Depression’. I often wonder about it, and the fact that there are no right or wrong answers. That can only come from the mouth of the person who wrote it. Part of the appeal of making art comes from my experience as a listener and as a fan of other people’s work. So I think that it’s fun to create things that people will wonder about, or that will stimulate some kind of inner introspection.”

The lyrics are better viewed, then, as a byproduct of both band members having led interesting, artistically fulfilling lives. By the time she hit 15, Kemp Muhl was already out of her Republican, Catholic home in Atlanta and living alone in New York, jetting around the world to modelling assignments. Rather than attempting to cash in on his family name, Lennon started his musical career in the background, playing bass for Japanese underground trip-pop experimentalists Cibo Matto; early gigs found him sharing stages with the drug-damaged likes of the Butthole Surfers.

After releasing early solo albums on the Beastie Boys–owned Grand Royal label, Lennon carved out a successful career as a session musician, playing with artists such as the Strokes’ Albert Hammond Jr., the Flaming Lips, and Marianne Faithfull. As a member of the Plastic Ono Band, he’s also overseen and arranged records by his mother, Yoko Ono.

Lennon and Kemp Muhl run their own Chimera record label out of their Lower Manhattan home, a red-brick boho house where Wilco guitarist Nels Cline and Cibo Matto’s Yuka Honda live on the top floor. With Kemp Muhl still maintaining her modelling career, the couple have little downtime, which is also true of the creative crowd they run with.

“Everyone we know is so busy,” Lennon says. “We would love to be recording with other people, but a lot of time Charlotte and I are writing in the studio, so we don’t want to have other people sitting around waiting for us, when they really don’t have the time to do that. So while we do everything ourselves, that’s not necessarily how we’d like to do things. Theoretically, it would be nice to have a band all the time, but that’s something that we are still working towards.”

GOASTT, then, is a project that has yet to reach its full potential—which is kind of amazing when one considers what Lennon and Kemp Muhl have accomplished with the excellent Midnight Sun.

“Working together with your partner can be hard,” Lennon acknowledges. “It can actually be the hardest thing in the world. But I think that the results are what keep us pushing through at the hardest moments, because we really do love what we are doing together.”

GOASTT plays the Imperial on Friday (May 23).