There are four guys in Coldplay; their new single "Every Teardrop Is a Waterfall," has six co-writers, though: the four members, alongside Peter Allen and Adrienne Anderson, who wrote the song's distinctive piano riff 35 years ago. As for how it came to Coldplay--well, that's a story.

Peter Allen was one of those old-fashioned showbiz types who don't turn up much any more: a cheerful Australian gentleman with a receding hairline, a bunch of MOR songwriting credits feeding his bank account (he co-wrote "I Honestly Love You," "Arthur's Theme" and "Don't Cry Out Loud," among others), and some high-powered connections in the business. (The musical The Boy From Oz is based on his life.) In the '60s, Judy Garland and her husband took Allen under their wings; Allen was married to Garland's daughter Liza Minelli for a few years, although he ended up in a much longer relationship with an American named Gregory Connell.

Allen never made much of a dent on the American charts. (From a 1979 New York magazine profile of him: "None of Allen's own witty, sophisticated albums has ever sold more than 50,000. In the trade they say he has 'no radio voice.'") His sole U.S. chart hit was 1981's "Fly Away"—that link is to a live performance from a few years later that involves a lot of sweat and some situps—which only made it to #55.

Back home in Australia, though, he was a star. "I Go to Rio," released in 1976, was a massive hit—that's the song the "Every Teardrop" riff comes from. (It was co-written by Adrienne Anderson, who also contributed to easy-listening hits like Barry Manilow's "Daybreak" and "Could It Be Magic.") It was a cheeful, swinging bit of fake samba that let Allen show off his piano-pumping charisma and tropical shirts on stage.

The song's power, arguably, comes from the suggestion that Allen's not naturally the kind of guy who'd be grinning, wiggling his hips, shaking hand percussion and unveiling... what he unveils 2/3 of the way through this cheery live TV performance.

("Rio" stands in for "sexual freedom," of course: it's done that in American pop culture for a long time, from Fred Astaire's 1933 Flying Down to Rio to this year's Rio, possibly the only G-rated animated film ever to revolve around the question of whether the protagonists are going to have sex already or what.)

"I Go to Rio" caught on internationally through a handful of covers. In France, for instance, it was Claude François' "Je vais a Rio" that was the hit—the video features the normally serious-minded chanteur (another songwriter, who wrote the French song that became "My Way") getting down, surrounded by scantily clad dancing girls. The American hit version of "I Go to Rio" was Pablo Cruise's soundalike cover, which came out in 1978. Even the Muppets got in on the act.

At some point, a decade or so later, the story gets slightly more complicated. Circa 1990, somebody got the bright idea of building a pop-house track around Peter Allen's "I Go to Rio" riff, which was yay-close to a typical house piano groove anyway. (Compare, for instance, Black Box's "Ride on Time" or Marshall Jefferson's "Move Your Body.") The song was called "Ritmo de la Noche," but it's not entirely clear who recorded the first version of it.

Chocolate's "Ritmo de la Noche" has a bit more of a Gipsy Kings vibe (although their song of the same name is a different one). Mystic's version—which allegedly had some kind of involvement from Simon Cowell—appears to have been a bit later, although still in 1990. The Sacados' version was a big club hit in Europe, and threw in some James Brown yelps and rhythm samples from Lyn Collins' inexhaustible "Think (About It)." Araja sped up "Ritmo De La Noche" a little—by the time they got to it, the riff didn't sound to have come from anywhere near an actual piano.

Lorca's version of "Ritmo de la Noche" was part of the same cluster of recordings of the song (and includes the same "It Takes Two" whoop-loop as the Sacados).

That's the version that Alejandro González Iñárritu included in his 2010 movie Biutiful, in a scene set in a club that's apparently having some kind of retro night. The origin story of "Every Teardrop Is a Waterfall," according to Coldplay's own site, is that Chris Martin went to see Biutiful, heard that piano riff, and was inspired to write a song of his own around it. (It's not clear at what point the band found out that it had its origins in "I Go to Rio.")

It's surprising, then, how much the lyrics to "Every Teardrop" echo the lyrics to "I Go to Rio." One singer gives in to the rhythm (the erotic surrender associated with Rio), the other feels his "heart start beating to my favorite song"; one sees the sun lighting up his life, the other sees someone "emerge blinking into" light. It's Allen, though, who actually becomes a "salsa fellow," who rises out of his seat to create rhythm. In Coldplay's song, Chris Martin is trapped "underneath the rubble" with his records--trying to dig himself out from the detritus of time and space, while a Mexican director's repurposing of a Spanish replaying of an Australian songwriter's evocation of American illusions of Brazil plays on an infinite loop.