As Frank’s fame grew, his swagger turned bolder. He was a short, slight man, hypersensitive and brilliant, and an Italian-American in an era when that ethnic group was low in the social order. As a young entertainment phenomenon in the early and mid-’40s, Sinatra was a kind of proto-hip-hopper: he strutted around Manhattan and then Hollywood with a pre-Rat Pack posse (known as the Varsity) of hangers-on high and low: songwriters, comedians, former boxers. He loved bling — he is said to have given away $50,000 worth of gold cigarette cases and lighters before he turned 30. He lived his life precisely as he pleased; consequences were for others to worry about.

Still, the engine of Sinatra’s fame, what really makes him endure, is the contradiction at the heart of this tough-seeming genius: his exquisite way with great American popular songs. He could always — still can — make you feel he is revealing emotional truths to you and you alone. He worked enormously hard on the technical aspects of singing that facilitated this impression: breath control, diction, deep study of the lyric.

But ultimately, his vulnerability is at the core of his magic. There was an operatic intensity to Frank Sinatra’s existence. His life mistakes were legion; he was, always, at the mercy of powerfully oscillating emotions. The conflicts filter into the molecules of his music. We hear, we respond.

Rap, of course, would seem to be about outer rather than inner conflict: swagger and defiance don’t just set the tone, they shout it. And yet the best rappers expose the sorrow and humanity that underlie the swagger. Eminem’s hymn to recovery “Not Afraid” is both brutally self-critical and self-transcending, reaching out to listeners who’ve been down the same addictive path.

And Jay-Z’s “Empire State of Mind,” which begins by trumpeting the rapper’s importance to the big city, modulates to sympathy for those who get lost in it: wayward girls from small towns, ball players and rap stars hooked on Ecstasy and addicted to the limelight. When the Swedish interviewer asked Jay-Z, “What is your talent?” he answered shyly. “I guess, telling the truth in rhyme,” he said. “It’s all about emotion — the detail and emotions in the songs that I sing just connect to people all over.”

Frank Sinatra often said much the same thing, in slightly different words, about his own music. Still — obligatory compliments aside — he wasn’t apt to be generous about the music that followed. According to his former valet George Jacobs, Sinatra expressed his true feelings about rock one day in the mid-1960s, when the Doors’ “Light My Fire” came on the car radio for the umpteenth time: He reared back and kicked the radio with the heel of his shoe. Now, that’s gangsta.