A low, sullen warehouse building, 299 Meserole Street sits in a straggle of industrial units not far across the Williamsburg Bridge in Brooklyn. This afternoon, the cool, dark space within is in the process of being transformed with palm trees, portable toilets and a makeshift bar. Mirrorballs spin out over the empty room as three men scatter handfuls of multicoloured paper – tiny flickers of pink and blue and silver cellophane – on to the concrete floor. When they are finished, they scrunch up red plastic drinking cups and throw them on to the ground too. The effect is of a party recently ended, of a room still ringing with merriment, laughter and dancing.

Up on a small stage, Arcade Fire are soundchecking, running through their potential set for the night to come: a selection of new songs – Reflektor, Supersymmetry, It's Never Over – as well as a couple of steady favourites: Neighbourhood #3 (Power Out), Sprawl II, Wake Up. The preparations here today are part of the band's album launch extravaganza, two semi-secret shows for 3,000 people, that will be replicated in Los Angeles and Miami, with attendees requested to dress up in their finery, and for which tickets have been swapping hands for up to a rumoured $5,000 (£3,100).

It was 2004 when Arcade Fire emerged out of Montreal with their extraordinary, mysterious debut album, Funeral. A six-piece band comprising of Win Butler, Will Butler, Régine Chassagne, Tim Kingsbury, Jeremy Gara and Richard Reed Parry, as well as a moveable feast of other players, over the past nine years and two more albums – Neon Bible (2006) and The Suburbs (2010) – they have built a reputation for both the intrigue and intelligence of their songwriting, as well as for live shows that can seem ecstatic, desperate and electric all at once.

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Across those nine years, much has changed about the band: members flitting in and out, the focus of their songwriting shifting to accommodate other talents — Butler's brother Will, multi-instrumentalist Richard Reed Parry, and bassist Tim Kingsbury among them – and with each album a musical turn that has at times unsettled their devoted following.

On Monday they will release Reflektor, a double album that has already startled many who have heard it, with its sheen and its unabashed splendour: there are shades of Studio 54, of disco and glam rock, as well as Talking Heads, Blondie and ska. There is the obvious influence of David Bowie, who guests on one of the new songs, and of LCD Soundsystem, whose James Murphy produced the record, along with the band's long-time collaborator Markus Dravs. And beneath it all, lyrics that speak darkly of a relationship in disarray, of disappointment and disillusionment and sudden flares of hope; of falling apart and coming back together, of two lives that can never quite unravel. "And now you're older, Butler sings on one track, "you will discover, it's never over."

"When Régine and I met, I was 19 years old," says Win Butler, lying back in what he refers to as a "therapy pose", with his long legs draped over the arm of the sofa. "We spent so much of our life working on records, working on music, and it was the idea of putting all of this life on to a little piece of plastic." Now 33, Butler has seen not only his own life alter, but the music he makes physically change, from the records, tapes and CDs of his teenage years to the world of iTunes and MP3s. "If [The Beatles'] Revolver is about the LP, and Reflektor is about the end of the CD era," he says, "it was feeling: 'If we were making the last CD, how would we make it?' Because the medium of something kind of always impacts on it a little bit. And it was also kind of a way of understanding the times, and life, and how I feel about myself, men, women, relationships, you know … all the different things."

Many hearing the album for the first time have been preoccupied by its musical volte-face, and have drawn comparisons with U2's 1991 album Achtung Baby, noted on its release for its defiantly experimental sound. Yet Butler dismisses the comparison. "With Achtung Baby, they have these characters that have been created of themselves and they were making an effigy about culture," he explains. "And I don't think that is what we're really trying to do. I think what we're driving at is a little bit different. I think [Reflektor] was more about allowing ourselves to be transformed, musically, allowing ourselves to be changed, trying to connect in a new axis."

Régine Chassagne. Photograph: Douglas Mason/Getty Images

It began with rhythms, with the influence of Haiti – the country Chassagne's parents had fled during the dictatorship of Papa Doc. These rhythms had been tangible even from Funeral, but in recent times, particularly since the devastating earthquake of 2010, the band had begun to explore the country's musical heritage, performing there at festivals and playing with Haitian musicians. In the summer of 2011, Chassagne, the Butler brothers and some of the drummers from the Haitian band RAM spent two weeks in New Orleans working specifically on rhythm. "We just recorded beats," says Chassagne, in her slow, sing-song voice. "We were interested in doing hybrid beats that could translate stuff that I know from my family background in Haiti. I was always interested to try to find rhythms that mean something, to communicate emotion through rhythm and music. Because rhythm is almost like a vocabulary."

The rest of the band could not replicate Chassagne's more primal relationship with Haitian rhythms, but their response was nonetheless instinctive. "To understand or to feel them is immediate," Win Butler says. "It's like putting you finger in an electric socket." It also offered rich new ground for musical exploration. "They are very different from the rhythms I grew up with," says Kingsbury. "You see the historical sweep from Africa, but African-American music from North America is also very different. The emphasis is very different. So it does put you in a different headspace and it does make you engage with the music in a different way."

Will Butler recalls the particular delight of working with the RAM drummers and overcoming their mutual linguistic hurdles. "My French is not very good," he says sheepishly, "and my Creole is even worse than my French, but it was actually very good for my musicianship to be in a room with people I couldn't really communicate with except through music. Most of us are pretty heady most of the time, we love talking about music, everyone's an ethnomusicologist at some time, so it was very good to only have hand gestures, to play what you meant. It was very valuable."

Wrapped around what Chassagne refers to as "voodoo rhythms" were other influences too. Reed Parry mentions Fela Kuti and James Brown before describing the finished record as in no way resembling James Brown and "not sounding anything like Fela Kuti". Will Butler explains how some of the sounds that in many ways fired the album didn't even make it to the final cut. "On The Suburbs we said that Depeche Mode and Neil Young were approximate poles of the album, and this album too has poles," he says. "One of those poles was the Haitian rhythms. Synth string drones is another. But we also recorded a ton of punk rock stuff that isn't on the album, that is just abrasive like nobody's business, so that is actually a core of the album too." There are remnants of it still, he points out, on tracks such as Normal Person and Joan of Arc. "Just a bit in some of the edginess of it, it's still there."

Win Butler. Photograph: Tim Mosenfelder/Getty Images

But for the most part, the roughness is counterbalanced by sheen. "I think in order to realise some of the songs fully, we realised we had to really polish them," Will explains. "That rough form was really powerful, but the back of your eyeballs were dry after you'd listened to it. And it was actually really fun to go down that road, to get out the really sharp-skinned sandpaper and make everything shine again."

The tension between the scuffed, crackling side of the record and glistening keys is one of the many dualities on Reflektor. It is there also in the mirroring of the album title, of course, something also alluded to in the track Supersymmetry, and as on previous albums, some tracks appear to sit in pairs, and there are retakes of earlier songs – in this case Here Comes the Night Time. "I think every album we write about what's happening to us at that time," Chassagne says. "And sometimes there's a lot [to say], and there's like a second wave … the same idea, and so then you get this," she holds one palm up, "and that," she raises the other. It is often, Will adds, a case of "just attacking the same concept over and over".

The duality of the album's title track is broken, oddly enough, by the presence of David Bowie. "He just needed the work," Kingsbury says soberly. "It's really sad actually." In truth, Bowie was roped in while visiting the Electric Lady studio where the band were working in New York. "The song is better for having a third voice in it," says Will. "So it's not just these two voices talking to each other, so it's not just Islands in the Stream, there's a third voice at the end, an outside perspective."

Working with Murphy had been a hope for Arcade Fire since as far back as Neon Bible, but it was only for this album that their schedules aligned. Will recalls with amusement that, in the early years of their careers, they danced around one another with some scepticism. "I always imagined he and LCD would be kind of insufferable," he says. "And he actually said the same about us – that people were talking so much about Arcade Fire before he had heard or seen us that he was like: 'Oh goddamnit … why are these stupid bands doing stuff with xylophone?' And then he saw us and thought: 'Wait, that's Arcade Fire?' And I did the same: 'Wait, that's the guy that I thought would be this hipster douchebag that I wanted to punch in the face and the balls at the same time? Great!'"

For Chassagne, Murphy's role was to help realise the great dance record she believed the album could be. "I really wanted to get the right feel to the songs and be able to dance, really dance to them," she says, suddenly lit up. She talks passionately about dancing in Haiti: "When Win and I were staying in this place that had windows but no real doors and some drummers started playing, and more drummers came and more drummers came, and they were playing these roots, voodoo rhythms, and we just danced til 5am, and when we were too hot, we just ran and jumped in the ocean."

And she remembers with a sudden tenderness the sight of her mother dancing: "I always have this memory of my Mom dancing in the kitchen all the time," she says and starts to laugh. "We had a really bad radio – so bad you had to put your finger in it to change the music, so you were always at risk of being electrocuted every time you went to change the channel. And the songs would come on in the kitchen and my Mom would just dance, and she was always sad. I suppose it's the experience a lot of people have as immigrants. She loved to dance so much and was so sad because she always thought people didn't dance enough. She was a Haitian woman. She was round. So I don't exactly dance like that, but not completely different either."

She is not, she insists, the band's greatest dancer. "I think Will," she says. "Ritchie as well. Everybody! Everybody can dance!" But the problem with going out dancing these days, says Will, is that it's hard to find a place that plays the music that makes you want to dance. Chassagne agrees: "I don't get it, because dance music, sometimes it's so dumb! Why does it have to be that dumb? The thing is I find either it's danceable and really stupid, or it's brave and artful and thoughtful, but you can't dance to it. But I want to have both!"

The aim of the evening ahead, with its dress-up code, short, hour-long set of new songs, and a DJ set from Murphy, is that it might just lure people into dancing. They have even invented an alter ego band named The Reflektors, in which they perform wearing giant papier-mache heads of themselves, to add to the levity, and perhaps also to relieve the weight of what it means to be one of the world's biggest bands.

The party, in all its bright fun and silliness, is in some way an extension of the record. "It's hard not to get people out of their comfort zones and just alienate them," says Will. "I think a lot of art and a lot of the stuff we make, we get people out of their comfort zones by being extremely confrontational. And it's great that art's really confrontational, but there's something to be said about lifting people out of the day-to-day, that makes them excited about dancing instead of just feeling horrible about the government. But it's also valuable to feel horrible about the government." He laughs. "You want people dancing and being like 'The government sucks.'" He shoulder dances as he sings a little ditty: "The government sucks."

Shortly after 9pm, I am sitting in a white limousine at the back of the venue, wearing a papier-mache head of Chassagne. Win has implored the driver to find the worst kind of bass-heavy chart dance music he can on the limo's radio, to wind down the windows and turn it up loud. It is to this soundtrack that we all make the short journey round to the front of the building, to where the crowd has assembled and a red carpet has been rolled out.

We climb out to shouts, whistles and cheering, and the rush of it is faintly terrifying – through the head's giant nose holes, I can see little, breathe less, and wonder quite what my feet are doing. Win takes my hand and leads me along the queue, posing for photographs with fans as we go. Ahead of me, he is just a blur of sequinned jacket that I follow into the venue to where the rest of the band, in their wild suits and giant heads, have occupied the dancefloor. As I watch them dancing, I see how it liberates them, how charged they seem by rhythm and music and anonymity, and how thrilling it is to watch them caught in this sudden flare of hope.

• This article was amended on 6 November 2013 to correct a description of Arcade Fire. The original called the band "a loose circle of musicians orbiting husband and wife duo Win Butler and Régine Chassagne". In fact they are a six-piece band, as well as a moveable feast of other players.