It’s some kind of paradox — he probably thought of it as a joke played on him by the gods — that Christopher Plummer, the impishly irascible, velvet-voiced star of stage and screen who died Friday at 91, was one of the great Shakespearean actors of the 20th century, as well as a notorious rapscallion who spent decades living the dissolute high life, yet the first thing that most people think of when they hear his name is “The Sound of Music,” the timelessly beloved 1965 musical that’s the sugary quintessence of G-rated Hollywood wholesomeness. “The Sound of Music” is not a hip movie to like. Critics have spent half a century taking snide swipes at it, and Plummer himself liked to call it “The Sound of Mucus.” Yet as an unashamed fanatic for it, I’d argue that “The Sound of Music” carries the hint of a more turbulent inner quality than it usually gets credit for. That goes back to what Plummer brought to it.

The grand cornball saga of Maria, the singing nun who comes to look after the seven children of Captain von Trapp, was played by Julie Andrews and Plummer as a classic ingenue-meets-older-man-of-the-world romance. Yet the two actors were just six years apart, and there are moments when their on-screen connection doesn’t so much melt through the saintly squareness as heighten it. Just watch the scene where they first dance together, and look at the light in Plummer’s eye. Von Trapp isn’t just swooning for Maria — he’s shocked at the feeling that’s taking him over. Plummer had a ripe sensuality that the legendary Shakespeareans of the time (Olivier, Gielgud, Redgrave) did not. Andrews’s radiant Maria is the soul of goodness (and no one gave goodness as much soul as Julie Andrews), but it’s the way Von Trapp the family autocrat becomes good that propels the movie. It’s the film people remember Plummer for because it was staggeringly popular, but also because he was great in it, too.

In the late ’60s, Plummer enjoyed the status of a leading man, mostly in clunky late-studio-system genre pictures (“Triple Cross,” “The High Commissioner,” “Lock Up Your Daughters!”) that weren’t nearly as good as he was. Yet during that time, he failed to land another big-screen role that defined him in the popular imagination the way “The Sound of Music” did. His passion for the stage was part of the reason; so was his passion for carousing. He became, in essence, a character actor, and in films like “The Man Who Would Be King” and “Murder By Decree” and “A Beautiful Mind” and “The Girl with the Dragon Tattoo” (or playing historical characters like Tolstoy, F. Lee Bailey, and FDR), he could always be counted on to show up and gleam, to flash that leer, to cock an eyebrow of insinuation or flex a muscle of hidden power, to pierce the screen with a haughtier cynical knowledge than that of anyone around him. He was an impeccably named actor whose very presence was plummy, because he always seemed to be taking such mordant delight in what he was doing.

If you want to see a movie where Plummer really pops, watch “The Silent Partner” (1978), the contemporary Hitchcockian thriller he made in his native Canada with Elliott Gould. He plays a psychopathic thief who matches wits with Gould’s bored Toronto bank teller, who tries to double-cross him, and the cocksure vitality of Plummer’s villainy is positively outrageous. It wasn’t a big movie (though it had a script by the young Curtis Hanson), but Plummer, as he approached 50, was doing something unexpected: getting in touch with his aging inner bad boy. In 1981, he did the highbrow version of that when, after decades of playing Hamlet, Macbeth, Marc Antony, and others, he gave what was to that point his most revered Shakespearean performance, playing Iago opposite James Earl Jones in “Othello.” I regret to say I never saw Plummer on stage, but those who did rhapsodized over the heady humanity of his joyful backstabber.

Plummer was a quintessential scene-stealer, because whenever he showed up in a movie, he had a sinister playfulness about him that could dictate a scene’s morality. In hindsight, it seems like destiny that in the wake of the Harvey Weinstein/#MeToo earthquake, he replaced Kevin Spacey as the billionaire J. Paul Getty in Ridley Scott’s “All the Money in the World.” When you watch the film, it’s hard to imagine anyone but Plummer in the role. He’s charming, he’s formidable, he’s dastardly, he’s rotting on the inside, but mostly he’s a man who thinks about money at every moment, taking a daily mental bubble bath in its lustrous value. Plummer projects the mind of corruption with the relish of someone who knows it from the inside.

Yet he had an equal and opposite ability to seize and hold a movie’s moral center. You see that in a diabolical confection like “Knives Out,” where he plays the murdered mystery novelist Harlan Thrombey, who in flashback sees right through what scoundrels his family members are; he wants to set these wastrels right (and pays the price for it). You see it, too, in “The Insider,” where he makes the “60 Minutes” reporter-god Mike Wallace the essence of righteous lawyerly showboating — but only because Plummer’s Wallace is the one who understands (maybe more than the movie does) that “60 Minutes” is a piece of journalism that’s really a piece of high theater.

The two sides of Plummer — the light and the dark, the romantic and the sleazy, the hammy and the humane — come together, quite gloriously, in “Beginners,” the sublime 2011 dramatic comedy for which he finally won an Oscar (for best supporting actor). On paper, Mike Mills’ autobiographical movie almost sounds like it was designed to win Oscars, with Plummer as the father who, in his grizzled mid-70s, after the death of his wife of 40-odd years, decides to come out of the closet. He declares that he’s gay, starts to live on the wild side…and he’s battling cancer. The fact that this all really happened is one thing. But Plummer, anchoring a splendidly flawed father-son duet with Ewan McGregor, makes the newly liberated Hal a movie character you buy in your bones. He’s a man suddenly freed from a kind of prison, and damned if he’s going to let a little thing like death get in the way. The Bard aside, it’s very possibly the performance of Plummer’s life, given when he was 82, making him the oldest person ever to win an acting Oscar. And it’s no wonder. At his greatest, he touched something timeless.