One night in 1986, I tuned in “Saturday Night Live” to see Paul Simon, who back in those early years was practically a regular. He had a new album to promote. At the appointed hour, out he came with an enormous band of African musicians, launching into “You Can Call Me Al.” What the hell was that?

Soon enough, I learned that it was the first single from “Graceland,” Simon’s masterpiece, a deft and compelling blend of South African and American music. It’s hard to come up with enough superlatives for this album; 34 years after its release, it still sounds fresh. The title track, “The Boy in the Bubble,” “Diamonds on the Soles of Her Shoes,” “Homeless” — these are all wonderful songs, a completely unexpected gift from a musician who was already a superstar on the basis of his ultra-polished folk-rock as half of Simon & Garfunkel and the gospel-, jazz- and even Bach-inflected pop of his early solo career.

“Graceland” was not without controversy. For one thing, by traveling to South Africa to record the album, Simon had violated the boycott called by many of his fellow musicians who were fighting against that country’s apartheid regime. (And let us pause here to watch “Sun City,” by Artists United Against Apartheid, one of the three or four greatest music videos ever.) For another, Simon was hit with charges of plagiarism that were not only well-founded but also completely unnecessary. Everyone understood that “Graceland” was a collaborative effort, and a number of the songs have co-writing credits. Why not be more generous?

Simon followed up with another album of world music, “Rhythm of the Saints” (1990), focusing on the music of South America — and damn if it wasn’t almost as good as “Graceland.” Throughout his long career, from the 1960s right up until recently, Simon has made a lot of great music. But “Graceland” will stand as his singular achievement.

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