Coincidence and mutual appreciation led to the band FFS, the surprising union of Scottish dance-rockers Franz Ferdinand and the eccentric LA duo Sparks. In a way, the first seed was planted back in the mid-’90s, when future Franz Ferdinand frontman Alex Kapranos was foraging for used records.

“I’d go down to this big flea market that we’d have in Glasgow and buy a stack of records that I didn’t know anything about,” says Kapranos, 43. One was “Amateur Hour,” the 1974 single by Sparks brothers Russell and Ron Mael. “It didn’t sound like anything I’d heard before, Russell’s falsetto vocal soaring above this staccato piano that was insistent, and the lyric was unconventional. It made me laugh.”

A decade later, Franz Ferdinand was riding high on their 2004 debut single “Take Me Out.” The Mael brothers heard the song and noticed a magazine story where Kapranos cited Sparks among his favorite bands. They met for coffee and spoke of working together. But Franz Ferdinand was busy, and nothing came of it for another decade—until Kapranos broke a tooth and was walking down the street in San Francisco, looking for Huey Lewis’ dentist. “I heard this voice: ‘Alex, is that you?’ And I turned around, and it was Ron and Russell.”

This time, they didn’t let serendipity pass them by. The Mael brothers presented Franz Ferdinand with a draft of the tongue-in-cheek “Collaborations Don’t Work,” and soon both bands were trading lyrics over the Internet, sealing that song with zingers like “I don’t need your navel gazing / I don’t get your way of phrasing.”

“We share a certain sense of humor, and that definitely made the process easier,” Kapranos says from London. “Songs went back and forth very quickly, and before we knew it, we had a whole album’s worth.” FFS released their self-titled album in June and launched an extensive tour that hits the Orpheum Theatre on Oct. 2.

“It’s been a completely amazing experience,” Sparks singer Russell Mael, 66, adds from LA. “Both sides push each other.”

The resulting songs represent a smart hybrid of each band’s sound, even if Sparks’ imprint stands out more for its idiosyncratic sensibilities. For more than 40 years, the Mael brothers have juggled bandmates and styles, grandly fusing multi-tracked bits of synth-pop, cabaret, disco, opera and musical theater. “We thought that a band should have all those elements covered,” he says, citing musically and lyrically provocative British bands with “a strong visual image” like the Who and the Kinks. In the U.S., people didn’t notice much beyond his brother Ron’s Hitler-like mustache, and the Maels decamped for a time to London. “It’s more from the American perspective that people think more that [the music] is oddball or that sort of thing, because in Europe, it’s really more openly embraced,” he says. “Things are still as conservative as ever in the States.”

Which perhaps makes a song like FFS’ “Piss Off” more delightfully apt, with lines like “Most will listen and take the hint / Know that this ain’t a compliment.” That attitude is doubled with Kapranos and Mael sharing dual vocal leads, tradeoffs and harmonies, honed in rehearsals before hitting the studio with producer John Congleton (St. Vincent, Swans).

“The other roles within FFS don’t overlap,” says Mael, whose keyboardist brother Ron supplements Franz Ferdinand guitarist Nick McCarthy, bassist Bob Hardy and drummer Paul Thomson. “We wanted to find a way to integrate the two vocals into just about every song, so it could make seamless transitions.”

The tandem proves entertaining at live shows, with Kapranos largely ditching his guitar to go toe-to-toe with Mael. FFS also plays a few Franz Ferdinand and Sparks songs to satisfy their respective audiences.

As to whether FFS represents a lucky one-off or a new course for their separate bands, neither singer will predict. “Neither camp really knows what the future will hold for FFS,” Mael says, while Kapranos offers, “I didn’t know whether it would be an album, and I certainly didn’t think we’d end up touring it.… That’s one of my favorite feelings in the world, not knowing what’s going to happen next.”

FFS plays the Orpheum Theatre Oct. 2.