Exclusive: for a free download from The Mars Volta, scroll to the bottom of this article

The Mars Volta are simultaneously throwbacks and futurists to whom the three-minute song is an alien concept. In the past six years, the guitarist Omar Rodriguez-Lopez and the singer/lyricist Cedric Bixler-Zavala have unleashed five “concept” albums packed with long, freeform musical pieces with bizarre titles and cover art that would not have disgraced a Yes album. Their last album, The Bedlam in Goliath, a sprawling, dense, dark work that entered the American charts at No 3, was, despite some exquisite moments, too much to bear. But now comes Octahedron, lighter, acoustic, melodic... and almost traditional. Except for its dark lyrics, driven by the memories of childhood friends who disappeared at a lake near El Paso.

Omar and Cedric met in a rehearsal garage in the Texas border town 20 years ago, two kids with green mohawks. “My bandmates were ruthless,” Cedric recalls. “They forced me to listen to things I wasn’t into. The punkest thing is to be well versed in all sorts of music.” While others in the band were street urchins who stole their instruments, Omar and Cedric were sub­urban kids, first-generation middle-class. Raised in the barrios of Puerto Rico, Omar’s father became a doctor; Cedric’s was a university professor. From the beginning, they were inseparable, smart and driven. “Over the years, people have been unsettled by how close we are,” Omar says. ‘They shouldn’t be that close, they share clothes, they have lived together for 13 years” — “and,” adds Cedric, “they finish each other’s sentences.”

Omar’s hotel bedroom could belong to a hyperactive teenager — stills and video cameras, a drum machine, bottles of vitamins, an Asimov sci-fi classic, a brace of guitars, half-empty takeaway containers, charging mobile phones and a fully automatic plastic BB gun. Dark memories, still-forming ideas and arcane philosophies rat-a-tat from his mouth. While Omar, in his big framed glasses and floral shirt, is 33 and looks all of 16, Cedric, two years older and just as skinny, wears his past enthusiasms on his sleeves. Tattoos of the comedian Andy Kaufman, The Wicker Man, R2-D2, a Shogun Warrior, Joan Crawford and a giant spider cover his arms.

Growing up in El Paso gave them their edge. It’s a no man’s land, neither America nor Mexico, gritty, ugly, but beautiful, like a Sam Peckinpah movie. “On the surface, it looks like still water, but underneath is a lot of crazy shit,” Omar says. “Everybody in high school went over the border to Juarez, because that’s where you could drink underage. Which meant you could be arrested for a week, you could be murdered, raped — you could disappear. It is a free-for-all.”

Their original band, At the Drive-In, have attained near-legendary status: hardcore punk with a twist, driven by unpredictable rhythms, Cedric’s often surreal words and muscle-defying stage performances. “We were the only five guys in town who cared enough to quit their jobs, go tour, make no money, then come back to do it again,” Omar says. “Other people were happy to be hometown heroes. We wanted to play in other countries, experience the culture, even if it was playing to nobody.”

ATD imploded on the verge of breakthrough, partly due to boredom, partly to musical differences. Cedric and Omar flirted with a dub band, De Facto, before forming the Mars Volta with the sound manipulator Jeremy Ward. The name comes from Fellini, who described a changing scene as a “volta”, and their love of science fiction. Their debut album, the Rick Rubin-produced Deloused at the Comatorium, was based on Julio Venegas, an El Paso poet and artist who went into a coma after a deliberate drug overdose, recovered and later committed suicide. While touring, Ward died of a heroin overdose.

“One day, we were all getting high, and Jeremy asked me if I could see he had worms in his head,” Cedric recalls. “I never touched the stuff again. His passing was the final nail in the coffin. We never went back.”

The creative connection between the two is almost spooky. “We both have addictive, curious personalities. We rely on impulse and instinct,” Omar explains. “We are locked into a sound because I write the melodies and Cedric has a very particular voice. We experiment to keep a healthy relationship. My biggest inspiration and challenge is Cedric, I want him to hear something and feel he has to do something new. I record the music, then I give it to Cedric, he writes his lyrics, then I record him and we tweak a little bit. That is where the telepathy aids us — when I give him the music, he knows exactly what I mean by it. ”

Cedric is no fan of real-life, “I went to the pub”-style lyrics. He has a fondness for Frank Zappaesque humour and writes in English, Spanish, even Latin. “I love to take common sayings, pervert them, mutate them a little. So you think I am singing one thing, but when you read it, it is different.”

“Perhaps Octahedron is a new birth, maybe a new era,” Omar grins. “An aggressive album, a far-out album. We are self-indulgent, we do what we want.”

Cedric likens the Mars Volta to Werner Herzog’s Fitzcarraldo, permanently hauling the boat over the Amazon hill, except that he insists: “I never want to reach the top. Otherwise we’ll stop trying.”

Octahedron is released on Mercury; the Mars Volta play Somerset House, WC2, on July 13

Explore Music

• CD Reviews

• Live Reviews

• Classical

Editor's choice

• The 100 Best Films of the Decade
• 70 facts you didn't know about Marvel
• The 50 Biggest Movies Of 2010