Tony Bennett accepted the boundaries of his universe.

In the last few decades of his life, the period of his greatest success, he never tried to do a Rick Rubin/Johnny Cash-style album of recent pop and rock hits tweaked to suit his voice. Instead, he transported the contemporary artists he worked with — Lady Gaga especially — to his preferred musical arena: the Great American Songbook classics of Johnny Mercer, Irving Berlin, Rodgers and Hart, the Gershwins, Harold Arlen, and so many more. Without seeing the cover, you’d never even know his “MTV Unplugged” album was an “MTV Unplugged” album just by listening to it. His last studio album, “The Silver Lining: The Songs of Jerome Kern,” speaks to his appreciation of the craft of songwriting embodied by the entire Great American Songbook era, and how a singer can work in dialogue with that songwriter even decades after their death to create meaning.

As his collaborator Bill Charlap said in an extraordinary CNN interview this weekend about Bennett, who died Friday at the age of 96, the singer, whose other great artistic love was painting, brought a painterly sensibility to his interpretation of songs: shading each word he sang with just the meaning he intended, calibrating his enunciations to produce just the tone and feeling he wants, as if applying careful brushstrokes.

Just like any painter, what Bennett chose not to paint was essential for defining his artistic ambitions and their limits. That meant, unlike many other singers, an acting career was something he decided not to aspire to. He had bit parts on “The Danny Thomas Show” and “77 Sunset Strip” but a poor experience making his feature film debut, “The Oscar,” made him give up acting altogether. He focused instead on where he could have absolute mastery. There’s a possibly apocryphal quote attributed to Chopin where the Polish composer of small-scale piano works said, “My kingdom is rather small, but within it, I am truly King”. That was Bennett. His artistry was scaled just as it needed to be scaled.

That doesn’t mean Bennett didn’t have an impact on the movies, though. In fact, his voice helps power one of the greatest moments in American cinema. “As far back as I can remember I always wanted to be a gangster,” Ray Liotta’s Henry Hill says after taking part in a grisly murder at the start of “Goodfellas.” He slams the trunk of his car shut to hide the body from view and then orchestra leader Percy Faith’s big-band trumpets fire up a blast of Pax Americana bombast, setting up Bennett’s voice: “I know I’d go from rags to riches,” he sings. “If you would only say you care / And though my pocket may be empty / I’d be a millionaire.” Saul Bass’s credits ricochet across the screen, and, quickly, we’re seeing young Henry Hill’s deep-green iris as he looks out his bedroom window imagining what his own life as a gangster could be.

Bennett’s recording of “Rags to Riches,” written by Richard Adler and Jerry Ross, was already 37 years old by the time it unspooled in “Goodfellas” to kick off this legendary flashback montage that shows how Hill came to be. His recording is full of exactly the swagger and yearning that define the Hill character himself. It wasn’t the first time Bennett’s music was used in a movie for a particular dramatic effect: Cybill Shepherd’s character in “The Last Picture Show,” despite living in a Texas town, listens not to Hank Williams’ “Cold, Cold Heart” but Bennett’s cover of that song — director Peter Bogdanovich chose Bennett’s version to show how she aspires to a more urbane life outside of her rustic environs. Bennett always conveyed sophistication, yes, but in both “The Last Picture Show” and “Goodfellas” his voice was something more: it was the sound of American aspiration itself.

Obviously, the “Goodfellas” version of American aspiration is its dark side. And Bennett himself, though pictured with Scorsese over the years, including at a 2004 Tribeca Film Festival panel about the music in Scorsese’s films, expressed that he “didn’t like” being associated with “Goodfellas.”

In a 2015 Vulture interview, Bennett said of the association, “I didn’t like it. I know how great the actors and the story were, but it’s not accurate because every nationality has an underworld. It’s not just the Italians. The British, the Germans, the Irish — there’s an underworld throughout the whole universe. They’re doing evil things. The absurdity of that strong prejudice that came out of that movie…”

Certainly, many Italian-Americans have expressed frustration at “Goodfellas,” “The Godfather,” and other mafia movies for linking their diaspora to criminality. For Bennett, it must have carried a particular charge when you consider this: to achieve mainstream music success he assumed the name Tony Bennett, rather than attempt a career under his birth name Anthony Benedetto, the name on his dog tags when he helped liberate a sub-camp of Dachau in 1945 and, as he wrote in his autobiography, “saw things no human being should ever have to see.” In no way had Bennett ever tried to cover up his Italian-American heritage, and as he had number-one hits in the ‘50s, the Italian-American community embraced him enthusiastically. But having to change his name showed the kind of efforts Italian-Americans did have to make to “fit in” — and now decades later, he’s being associated with a mafia movie.

That discomfort with “Goodfellas” is completely understandable, but “Rags to Riches” does speak a bit to Bennett’s own journey. A seven-decade career in the public eye is bound to have ups and downs, but Bennett’s were unusually pronounced: by the late ‘60s, as his style of interpretative, unadorned crooning had become unfashionable, he fell on hard times. In 1970, he actually did record an album of pop/rock covers, “Tony Sings the Great Hits of Today!” which Time magazine likened to William Shatner’s infamous cover of “Lucy in the Sky with Diamonds.” Bennett said he vomited before the initial recording session. In the ‘70s he was even without a record deal for a time, and struggled with a cocaine addiction that led to a near-fatal overdose in 1979.

By 1986, Bennett began his comeback simply by trying not to be anyone other than himself, and that comeback was in full swing by the time “Goodfellas” featured him to such stirring effect. Of the 20 Grammy Awards he won during his career, 18 of them he won after 1993. A rags-to-riches story indeed.