Fox Searchlight Pictures with The Cinema Society host a screening of "A Bigger Splash"

The arrival of Ralph Fiennes in “A Bigger Splash,” the new film directed by Luca Guadagnino, could hardly be more ominous: The roaring plane carrying his character, Harry, and Penelope, his newly discovered daughter, played by a Lolita-like Dakota Johnson, literally casts a shadow over the bodies of Tilda Swinton and Mattias Schoenaerts, who play a couple sunning in retreat on the Sicilian island of Pantelleria. An ebullient music producer and former lover of Swinton's character, Marianne Lane, Harry is garrulous enough that his garbled mid-air phone call announcing his surprise appearance doesn't even give Schoenarts a chance to reveal that it's actually his character Paul, Marianne's new boyfriend, on the other line. Meanwhile, as in the rest of the film, Marianne sticks to silence: A rockstar of mythic proportions, she’s recovering from a throat surgery that could end up taking her voice, effectively ending her career.

“It was my suggestion,” Swinton said of her lack of dialogue at the film’s New York premiere at the Museum of Modern Art on Thursday. “I just thought it would be interesting to kind of ramp up the tension, particularly between Harry and Marianne, because he's always trying to engage her in some form of argument.”

Harry is quite the presence indeed, and Fiennes plays him to a tee, whether peeing on tombstones (“Europe’s a grave!” he retorts to Paul’s protests) or blasting a Rolling Stones record he helped produce – a performance that involves exhorting Penelope to get out of the pool and "hear what daddy made,” spinning tales about Keith Richards so familiar that Marianne mouths along – and gyrating with a barely clothed Lily McMenamy.

His relationship with Penelope, is perhaps equally as suggestive – enough to even coax a few angry whispers out of Marianne – though the father-daughter duo are hardly alone in their flirtations: The entire movie oozes sexual tension, just like the 1969 Jacques Delray film that inspired it, La Piscine. As for why Guadagnino decided to rework it: “Why not?” the director asked with his usual Italian gusto. “I said, you know, as far as I can make something that is personal and committed, I will do it, and I felt I was going to have that kind of level of control to let me do that."

Guadagnino shifted the setting from the Côte d'Azur to Pantelleria, an island close enough to Tunisia that the hot sirocco winds blow over from Africa, beleaguering both the film's characters and the actual cast and crew. They spent two and half months there – long enough that Guadagnino started shipping over ingredients from the mainland to add variety to their home-cooked dinners, and that everyone got stung by jellyfish at some point in swimming and exploring the thermal springs and caves.

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“It was kind of wild, occasionally a bit chaotic, but I thought that all kind of was part of the experience,” Fiennes said. “It's not an island that's used to hosting films, and it's got tiny narrow roads, and the normal requirements of a film set I think were challenging for production.”

Part of the cast will reunite soon for another remake: Guadagnino is reassembling Swinton and Johnson for his take on the Italian horror film, Suspiria. Presumably, this time around, Swinton will have a bit more to say, though it doesn’t seem like she’d mind if not: “I'm a little sick of people talking too much in movies,” she said. Pausing to reflect on her self-imposed silence, then leaning back to laugh, she added: “I'm so lazy, that's the real answer. I was so happy not to have to learn any lines.”