Jonathan Rado sounds pretty tired when I reach him in Brooklyn. Foxygen played the Music Hall of Williamsburg on North 6th Street the night before; after the gig they went on to DJ at another venue in the neighbourhood. "Billy, who runs a club called Baby's All Right asked if we wanted to play," Rado croaks. "I had a look at the scene there and I really didn't have a cool vinyl set with me. So I just played Guns and Roses. Which is what people wanna hear, right?!"

"I played 'Welcome To The Jungle', like sped up really fast, then 'Lawyers, Guns and Money' by Warren Zevon, also 'Sweet Child of Mine' sped up again so Axl Rose sounded way crazier, followed by Gram Parsons." He's being bashful; Foxygen know their vinyl - to the point where Rado's girlfriend has banned him from visiting record stores for spending too much money.

Given the band's notoriously raucous live performances, a post-show DJ set sounds like a sensible come down activity. Rado, his bandmate Sam France and their touring musicians have been on the road since the summer, playing material from new double album ...And Star Power, released earlier this month.

The album's curious title has, Rado tells me, been in the can for some time - since the making of the third Foxygen album We Are the 21st Century Ambassadors of Peace & Magic in 2012, with producer Richard Swift. "Sam came up with the name whilst we were recording - he was just like 'I think the album's gonna be called ...And Star Power and I was like 'Yeah, of course'. We knew it was going to be a double album from the beginning, it would be part of the concept - an ode to double albums and the excess of them and the fun that you can have within them. It's a story album, but it's not like Tommy or something!"

...And Star Power is a strong offering, clocking in at around 82 minutes with 24 songs between one and seven minutes long. The raw bluesy psych-rock DNA that ran through the band's first three albums is more apparent this time around; Foxygen's chaotic style of playing, use of distorted random samples, a cursory approach to takes and editing, and blistering number of reference points and influences has resulted in a swirling, unpredictable and striking record. The production style is raw and unmoderated, a result of the band's intense recording period.

"We recorded mostly all the instruments with the exception of a few tracks in my garage; in a studio I built," Rado explains. "There are really intense liner notes for the album that say stuff like the trumpet was recorded in a kitchen, but most of it was recorded in the garage. We recorded all the instrumental stuff in like a night; we'd start maybe at 6pm and finish at 6am. It was all pretty spontaneous. But we were doing that for like five months, after that we just couldn't be in there anymore. No windows, it was crazy. So we decided to go to the Beverley Hills Hotel - an extravagant LA place to finish the album. I think the cabin fever thing worked - making records in a windowless room is pretty awesome, but five months is a long time to be in there."

The album's rough edges are as intentional as they are accidental. Rado is up front about the wilder end of the Foxygen sound, helped in part on ...All Star Power by an incredible versatile backline. "Sam and I play all the instruments on the album for the most part. I think it comes from the fact that neither one of us is an amazing drummer or whatever. The rhythm is always going to be a little bit shoddy. That's an important part of it - that bluesy bar room feel. Even with Krautrock, with Can, there's a human element to it. I feel like there's a certain point where music lost that, or at least popular music did."

We move on to talking about popular music and the band's influences. Traces of Led Zeppelin, Black Sabbath, The Faces, Pink Floyd, The Stooges, The Doors and probably even Guns N' Roses are scattered throughout Foxygen's music, but there were plenty of other artists who held significance for both Rado and France while growing up in California.

"There's not much of a music scene in Westlake; it's the suburbs. It's where actors go to retire. There's a lot of old sitcom actors you see out eating at restaurants which is kind of bizarre. The lack of a music scene and a frustration at that was possibly an inspiration in itself. I played in a lot of bands. Blink-182 are one of the reasons I started playing guitar. I really liked when I was eight years old, how they looked when they held their guitars, you know down to their knees. But then I started playing and my tastes changed. Me and Sam discovered the Flaming Lips and Beck and stuff like that, which took us from basic classic rock like Jimi Hendrix to The Doors into areas of music that we'd never heard before, that blew our minds."

On the subject of The Doors, at the keyboard, Rado produces the most incredible organ lines and piano work - a defining characteristic of Foxygen's output. Is there a little of the Strange Days-era psychedelia in Rado's music? "My favourite Doors era was probably LA Woman; fat drunk Jim with a beard or like the Soft Parade era. We were talking about this the other day, that the Doors are cheesy in your mind but when you actually start thinking about their albums, you're like 'Wow they are so good!' Ray Manzarek was an amazing organist. From maybe 11 to 14, I only listened to the Doors. It's in my brain."

Our conversation moves on to the question of comparisons. Foxygen are in the frustrating position of making incredible music that draws - subconsciously or otherwise - on some of the 20th century's most popular, successful and venerated bands; the sort that rock critics, music writers and journalists love to write about. "When we write the songs, maybe subconsciously they sort of morph in to sounds that can be compared to others whether it's a bassline from Booker T, or a guitar line from Steve Cropper or a drum fill from Hal Blaine," Rado counters. "It's nice to be compared to those things. It's always going to be in there but it can also lead to lazy journalism - I've read reviews which are based on us 'sounding like this'."

The band are in the UK this week as part of a busy tour schedule which takes in a stack of European countries before heading back to the US.

"London's always the first stop on our tours and I'm always so jet-lagged!" Rado says. "I'm always like we're going to do so much stuff and then I fall asleep at 3pm and wake up in the middle of the night. Hopefully, I can go to see Big Ben. I don't know! I have no idea, we'll probably have no time to do anything but I wanna do a vacation where I can go to all the places we play on tour, but actually get out there to see it all."

Foxygen play Village Underground on Friday 31 October. ...And Star Power is out now, on Jagjagwar.