At Radiohead‘s recent performance at Bonnaroo, Thom Yorke introduced the song “Supercollider,” by saying “This song is for Jack White. We saw him yesterday. A big thank-you to him, but we can’t tell you why. You’ll find out.”

Jack White shed some more light on that in an interview with the BBC saying, “I didn’t play with them or produce them but they came and recorded at Third Man and I don’t know what else they want to be said about that so that’s probably all I should say.”

So what would a Radiohead 7″ cut at Third Man sound like? Although Jack White didn’t cut the record with them, typically the artists who stop over at the studio at least emulate some of his idiosyncrasies, whether it be his country twang, his Memphis soul, or his avant garde side.

Classic country and soul are far from Radiohead’s bag although they were known to through in a little peddle steel on some “OK Computer” tracks. The closest element to their sound that could be drawn anywhere near Jack White’s universe is when they decide to get gritty with their guitars. Those outbursts have become fewer and fewer in recent years but here are a few tracks that find Radiohead at their Jack White-est.

“Electioneering”

After the deadpan hum that brings “Fitter, Happier” to a close, we are welcomed to side two of “OK Computer” with a call-to-arms tambourine followed by some of Radiohead’s most swaggered interplay. With swinging beats and a walking bass line, the guitarists are free to wrangle about in a raw clanging with some surprisingly bluesy lead riffs from Jonny Greenwood. While Jack White usually steers clear of politics, Thom Yorke’s sneering vocal in this song mixed with the all-out rockitude behind it is something not incredibly foreign to the Third Man universe.

“I Am a Wicked Child”

Recording during the “Hail to the Thief” era in what sounds like a live to tape reading, “I Am a Wicked Child” finds the band in the furthest region of backwoods blues they have ever ventured. Complete with an aching groove and a smoky harmonica part, it’s one of the group’s most underrated rarities and the closest they have come to making something that could feasibly be covered by The Dead Weather.

“Go to Sleep”

The quickness in which “Hail to the Thief” was recorded lent itself to housing some of Radiohead’s most organic material. On “Go to Sleep,” the five-piece lock together tightly in an acoustic guitar-driven rocker, the type of tough jangle that can be heard on Jack White’s solo album “Blunderbuss” on songs like “Hypocritical Kiss” and “Weep Themselves to Sleep.” With any luck, hanging around Nashville will have brought some of this sound back to the band for this upcoming 45.