Oh, what a little moonlight will do. Halfway through Tony Bennett’s performance of “Fly Me to the Moon” at the Monterey Jazz festival featured in the “American Masters” (8 p.m., PBS, check local listings) salute “Tony Bennett: The Music Never Ends,” the singer looks up to see the clouds have parted to reveal, as if on cue, a gorgeous full moon.

Produced by Clint Eastwood, directed by Bruce Ricker and narrated by Anthony Hopkins, “Music” traces Bennett’s many influences and evaluates his place in the 20th-century musical pantheon.

Author Gay Talese and director Martin Scorsese describe his Italian-American musical heritage. Scorsese also discusses his use of Bennett’s “Rags to Riches” to set a tone for his mob masterpiece “Goodfellas.”

Harry Belafonte recalls Bennett as a natural ally to the civil-rights movement and a friend to Dr. Martin Luther King, Jr. At a rally marked by folk ballads and gospel songs, Bennett turned the up-tempo Broadway tune “Just in Time” into a call for social justice.

The film uses a wealth of vintage television clips to compare Bennett performances from decade to decade. And there are scenes from “Saturday Night Live” and more contemporary shows to demonstrate how Bennett, helped by his business manager and son, Danny, reintroduced himself to a whole new generation of fans.

I had a chance to speak separately with Bennett and Eastwood about the film. Bennett is a passionate advocate for the songs he sings, the product of a musical flowering now referred to as the American songbook, a beloved catalog of standards created during a revolution in Broadway musicals and at a time when the microphone was allowing singers to record and perform with conversational intimacy. “Bing Crosby taught us a lot,” Bennett observed.

When I asked Bennett if he wasn’t a little jealous of singer-songwriters like Paul Simon and Paul McCartney who churned out hits and owned their own songs, he said: “They wrote some good songs. But they’re not George Gershwin.”

The film is filled with performance footage of Bennett’s contemporaries and influences, including Frank Sinatra, Dean Martin, Judy Garland, Fred Astaire and Jimmy Durante. If the film at times seems to lose singular focus on Bennett, Eastwood has no problem with that. “We wanted to tell Tony Bennett’s story as a way to remind people of this great musical era.”

In a 1965 Life Magazine article, Sinatra praised and anointed Bennett. “For my money, Tony Bennett is the best singer in the business. He excites me when I watch him. He moves me. He’s the singer who gets across what the composer has in mind, and probably a little more.”

“That changed my life,” Bennett told me. And we learn in the documentary, Bennett never forgot his responsibility as an heir apparent and as a keeper of the flame. “He’s really the last link,” Eastwood says, “to this great tradition of singers and musicians.”

But if Sinatra had an air of swagger and even dangerous cool, Bennett exudes the contented confidence of a happy ambassador for his music. “Is Tony Bennett cool?” I asked the lifelong jazz buff Eastwood. “Sure,” he replied. “Tony Bennett is cool because he doesn’t have to act like he’s cool.”

Tonight’s highlights

• The new 13-episode series “Most Daring” (7 p.m., Court) recalls real-life rescues.
• Tennis brat John McEnroe (as himself) falls under suspicion on “CSI: NY” (9 p.m., CBS).
• Tommy and his father relax on “Rescue Me” (9 p.m., FX).
• Airplane food on “Top Chef” (9 p.m., Bravo).
• “Inside the NFL” (9 p.m., HBO) enters its 31st season.