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Think Ke$ha has no place on a Flaming Lips song? How about Coldplay’s Chris Martin? Think again. Wayne Coyne and his group of merry pranksters may have picked an odd group of collaborators, but everyone seems more than willing to take part in the band’s magical mystery tour, resulting in an album that coaxes psychedelic charm out of the most unlikely of duet partners.

“2012,” an electronic rewrite of Iggy Pop’s “1969” featuring Ke$ha, opens the album with a bawdy bang, and “Ashes in the Air,” an atmospheric combination of computer noises, guitar chords and Bon Iver’s free-floating voice, shoots the listener into outer space. Few of these tracks are traditional songs, per se, and even fewer hold up on their own. When viewed as part of a larger whole, though, they deliver a warped, head-spinning punch, making “Heady Fwends” one of the Lips’ best song cycles in years.

There’s another cover on the track list, and it easily steals the show. “The First Time I Ever Saw Your Face,” a Grammy-winning No. 1 single for Roberta Flack in 1972, is stretched into a 10-minute epic, with Erykah Badu singing the song’s familiar melodies through some sort of trippy echo filter. Blasts of electric guitar noise echo in the background, and gauzy keyboard chords drape themselves over the whole thing like silk, allowing the song’s beauty to shine through cracks in the fabric.

Throw in some additional guest appearances (Yoko Ono, Jim James, Nick Cave, Edward Sharpe) and a handful of half-serious song titles (“Supermoon Made Me Want to Pee,” “I’m Working at NASA on Acid”), and you’ve got a scattershot, oddball album that feels oddly cohesive. “The Flaming Lips and Heady Fwends” may be wacky, but like the best of the band’s work, it stands up to close scrutiny, too.