NEW YORK – There is little obviously similar about Arcade Fire and LCD Soundsystem.

The former is an anthemic Montreal-based indie rock band whose dress and instrumentation is more Baroque than Brooklyn. The latter is a dance punk outfit whose fusion of synthesizers and rock sensibility is unquestionably contemporary.

But despite any sonic differences, the two bands have proven unlikely friends and collaborators. They are currently touring together on a twin bill that had the indie blogosphere salivating for months in advance.

They’ve also created a split seven-inch vinyl disc featuring a song from each group, which they are selling along the tour. And James Murphy, the leader of LCD Soundsystem and founder of DFA Records, is planning a remix of Arcade Fire’s song “Black Mirror.”

“We’re coming from pretty different worlds,” Win Butler, the lead singer and songwriter of Arcade Fire, said in a recent phone interview from the band’s tour bus.

“In a sense, we have similar production aesthetics,” he explains. “What’s strong about James’ stuff is he’s working in a kind of dance-y medium, but making stuff that sounds organic. And I think we have a somewhat similar approach. We really try to make things sound organic.”

The two bands first met several years ago at a festival in Europe. They each shared an admiration for the other’s music, though that connection wasn’t immediate.

“When I first heard about them, I didn’t pay attention to it, which I think happens to bands a lot – I’m sure it happens to my own band,” Murphy said by phone on his way to an ultimate fighting match. “It’s one of those things where you hear almost too much about something and you just presume ‘This isn’t going to be for me.'”

But once Murphy finally listened to Arcade Fire’s sensational debut “Funeral,” he says it “grew on me enormously.”

He says the two bands had wanted to do something together for a while. They earlier talked about Murphy producing Arcade Fire’s sophomore album (“Neon Bible”), but the band’s long recording schedule made it impossible with Murphy’s own record to make.

“It’s very physical,” he explains of Arcade Fire’s music. “The way they play is very much about building energy – songs build and build and build. We do something very similar, but with a slightly different arsenal.”

That effect might be best heard on LCD Soundsystem’s continuously swelling “All My Friends,” a single off their critically hailed album “Sound of Silver,” released earlier this year.

Oddly enough, the band’s arsenals overlap on LCD Soundsystem’s “Someone Great,” which incorporates a standard Arcade Fire instrument: the glockenspiel.

“It’s not very often you tour with a band who has a glockenspiel,” laughs Murphy.

The overlap has led to one of the several on-stage collaborations on the tour, though Murphy notes the guest appearances are mostly a one-sided affair since Arcade Fire tends to fill up a stage with its many members.

In contrast to the large shows in amphitheater-sized venues, the split seven-inch is a distinctly punk kind of disc to produce. It features two covers: LCD Soundsystem playing Joy Division’s “No Love Lost,” and Arcade Fire playing Serge Gainsbourg’s “Poupee de Cire” – which the band originally recorded while making “Neon Bible.”

Butler, whose band began touring “Neon Bible” in small churches early this year, says the seven-inch reflects both his and Murphy’s “independent streak.”

More than anything, both Murphy and Butler felt combining forces was a good way to spice up concert-playing after nearly a full year of close to nonstop touring.

“We’re both at a place in our respective careers where we just want to have a good time,” says Butler. “We don’t really want to be on a treadmill.”