"Yeah, I got a lot of grief for that," the frontman said with a laugh recently when reminded of the performance in April. Yet neither the grief nor the Coachella crowd's reaction deterred him. Last week, Julian Casablancas + The Voidz (as they are officially billed) released , a bracing debut album full of soured political invective inspired by what he referred to as "all the insanity going on in America": for him, that's corporate greed, police-state overreach and destruction of the environment.

Melodic but often brutally textured - and with knotty structures that stretch one song, , to nearly 11 minutes - the music sets aside the tidy songcraft that made The Strokes poster boys of the garage-rock revival that swept New York in the early 2000s. And Casablancas isn't the only one moving on from those days.

The week before, his old friend Karen Orzolek - better known as Karen O of the Yeah Yeah Yeahs - put out , a disarming solo project that exchanges her band's frantic throb for barebones acoustic arrangements. Written and recorded in 2006 and 2007, isn't angry like ; its delicate melodies are as flush with romantic possibility as the album's title suggests. But it similarly unsettles an established persona.

"I think maybe we both have more licence to do these projects because we've been through it all before," says Orzolek. "We've been around the block a few times, and with the good fortune to have had success with what we've done. That frees us up to present something you might not expect."

For Casablancas, the shift comes none too soon; indeed, he calls the album he has been striving to make since right after the Strokes' hit 2001 debut, . The records he actually made were marred by compromises, he says: with his bandmates on The Strokes' next few records, and with his own commercial aspirations on , his 2009 solo set.

"I really regret not following my heart for that," he says at home in New York. "In my head, I was like, 'Do I want to do a weirder thing?' But I thought it would've been swept under the rug, so I went the opposite way."

- an electro-pop jaunt - was swept under the rug anyway: it sold fewer copies than any Strokes album, including last year's , which was roundly criticised as a careless fulfilment of the band's contract with RCA Records.

So Casablancas, 36, was determined to stick to his guns for his first effort with The Voidz, whose members include players he'd originally recruited for solo shows. The aggressive sound, he says, reflects his love of punk bands such as Black Flag and his more recent examination of "modern classical music and weird jazz". And the lyrics channel his sense of outrage that began growing during George W. Bush's presidency, which Casablancas calls "a wake-up zone".

"The rhetoric of America - 'All men are created equal' - that was a big deal that kind of spoke to the promise of this place," the frontman says. "But it's been so hijacked. Now everyone's just trying to get ahead, and it feels like it's getting a little point-of-no-return-y."

Jake Bercovici, who plays bass and keyboards, says the band's music is intended to be challenging, even ugly, but "hopefully, it comes across as considered grime".

That description seems equally to suit Casablancas' approach at Cult Records, the label Casablancas founded as a way of ensuring creative control over . Five years later, the company's roster has grown - it's issuing both and - but it still operates like a scrappy indie, says Lysee Webb, who works with Casablancas at the label.

"One thing we've paid careful mind to is the kind of grass-roots campaigns that are so easily overlooked now," Webb says, pointing to a network of street teams tasked with distributing stickers and flyers - old-school record-industry artefacts rarely seen in the iTunes era. There's also the label's limited-edition cigarette lighter, which houses a USB flash drive loaded with MP3s of the album's 12 songs.

"Sometimes Julian will say something and we'll think it's just a random thought," says Warren Fu, another Cult staffer. "But then he'll really want us to follow up on it."

Orzolek says she was drawn to Casablancas' company in part because of that from-the-ground-up spirit. As with the Strokes, the Yeah Yeah Yeahs' latest album, 2013's , completed the band's deal with a major label; Orzolek has also dabbled in music for theatre and film, garnering an Oscar nomination earlier this year for from Spike Jonze's movie . Cult, the part-time Angeleno says, feels like a welcome respite from the big time - and an appropriate home for a record as raw and as surprising as .

"When you start out making music, your attitude is so naive," she says. "You're reaching out, but to what you have no idea."

That changes once people take notice, she says: expectations can cloud one's vision. "At this point in our careers, it's nice to know you can return to that exploratory space."