A Sumptuous Cultural Past

This island is something special. The strangest, most tragic things have happened here. — Miguel Barnet, Rachel’s Song

Lionel Hampton, the great jazz bandleader, got a wake-up call one night in 1951. He was playing a gig in Brooklyn on a bill with a small Cuban-style combo led by an as-yet-obscure drummer named Tito Puente. Hampton’s 18-piece band failed to inspire the crowd, which turned out to be mainly Latino, but Puente’s complex rhythms roused them into a dancing frenzy. When the Americans took the stage again, they were forced to spice up the beat. “Play Latin,” Hampton ordered, and they managed to redeem themselves.

The story, told originally by saxophonist Jerome Richardson in Quincy Jones’s autobiography (both musicians played in Hampton’s band), is repeated in Cuba and Its Music, a fascinating survey by the New York musician and producer Ned Sublette. Although Puente was...