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Imagine an alternate reality, one where Kendrick Lamar's sterling To Pimp a Butterfly didn't just feature George Clinton and Snoop Dogg and a Tupac interview but also Prince. Now imagine that reality being a hair's width away from our own, because it is.

In a new, head-scratchingly brief oral history of Butterfly at the GRAMMYs' website, Kendrick explains how Prince was in the studio while they made "Complexion (A Zulu Love)," the standout song featuring Rapsody, but didn't end up laying down vocals.

Rapsody and Kendrick reflect:

Lamar: Immediately when I heard the beat I heard [Rapsody's] voice and vocal tone. But what made her special was that I knew that she was going to bring the content from a woman's perspective about complexion, being insecure and at the same time having gratitude for your complexion.

Rapsody: He said he wanted to talk about the beauty of black people. I told him to say no more. What tripped me out is Kendrick originally said that he didn't want to do a verse on there. He wanted me to do two verses and Prince to do the hook.

Lamar: That's true. Prince heard the record, loved the record and the concept of the record got us to talking. We got to a point where we were just talking in the studio and the more time that passed we realized we weren't recording anything. We just ran out of time, it's as simple as that.

Running out of time adds up, considering how busy Prince was in 2015, releasing albums in both September and December. In 2013 he lent his voice to Janelle Monáe's The Electric Lady.