Prince's Around the World in a Day immediately announced itself as something completely different with its opening, Middle Eastern-influenced title track. "Open your heart," Prince sings. "Open your mind."

No, this wasn't going to be Purple Rain, Part II. In fact, Prince had purposely stepped off that hurtling juggernaut – ending what should have been a fame-confirming world tour after just six months – in order to complete its 1985 follow up.

"I think the smartest thing I did was record Around the World in a Day right after I finished Purple Rain," Prince told Rolling Stone. "I didn't wait to see what would happen with Purple Rain. That's why the two albums sound completely different. ... You know how easy it would have been to open Around the World in a Day with the guitar solo that's on the end of 'Let's Go Crazy'?"

Mystical and deliriously bizarre, in particular for anyone expecting that kind of arena-funk, "Around the World in a Day" invites listeners on a magical, mystical journey where "laughter is all you pay." Originally constructed in instrumental demo form by Revolution band member Lisa Coleman's brother David, this circuitous, flute-driven track's psychedelic feel – so redolent of the Beatles circa 1967 but still very much its own unique thing – set the musical tone for the determinedly iconoclastic album that would follow.

Prince had been standing with feet in two different worlds – one, that of a superstar; the other, a flinty cult favorite. "Around the World in a Day" made it clear which direction he intended to head.

"I sorta had an f-you attitude – meaning that I was making something for myself and my fans," Prince told a Detroit DJ about the period, "And the people who supported me through the years, I wanted to give them something, and it was like my mental letter. And those people are the ones who wrote me back, telling me that they felt what I was feeling."

Around the World in a Day was wrapped by Christmas Eve 1984, and in stores just two weeks after the final show on the abbreviated Purple Rain tour. That kind of turnaround surprised even members of the Revolution, who at first didn't understand just how quickly things were moving in Prince's fertile imagination.

"I wasn't totally aware that he had been tracking that album,” keyboardist Matt Fink memorably admitted. "I was not involved in it. I was okay with it, but at the same time, you always want to be in there if you can."

The project became a multi-platinum smash – and Prince's best-selling post-Purple Rain album – while also producing two Top 10 hits in "Raspberry Beret" and "Pop Life." Still, those numbers paled in terms of what came before. For every bedrock Prince fan who may have delighted at his individualistic nerve, he probably drove off dozens more.

That, as the wider world would soon learn, was a template not a career aberration. Around the World in a Day (with its first-song admonition to "Come here and take my hand, I'll show you; I think I know a better way, y'all") wouldn't be the first time Prince frustrated our desires in service of his own muse.

"More than anything else, I try not to repeat myself," Prince told Rolling Stone. "I think that's the problem with the music industry today. When a person does get a hit, they try to do it again the same way. ... But I always try to do something different and conquer new ground."

Prince Albums Ranked in Order of Awesomeness