With mere hours until the release of her new album, Madonna sits behind a closed door in a suite at Interscope Records’ office near Times Square. A stylist darts into the room for a few touch-ups. “She wants to look good for you,” Liz Rosenberg, Madonna’s longtime publicist, tells me. I pass a pair of security guards, then wait to be beckoned into the makeshift chamber. Not much has changed since 1984, when Madonna promised to “rule the world” and subsequently invented modern pop stardom. She is still the one to decide when, where and, most importantly, how we see her.

Over the past few months, however, a hacker challenged Madonna’s right to govern her own image. “Living hell” is how she describes the multiple Internet leaks that plagued her 13th studio album, “Rebel Heart.” For someone who approves every thread of her dancers’ costumes before a performance, this was Madonna losing control, the very thing that made her the star she is. So it makes sense that the singer, who did almost no press for her previous album because its release was sandwiched between a Super Bowl halftime show and a world tour, has been ubiquitous in her promotion of “Rebel Heart,” which was released March 10. The high priestess of reinvention maintains her relevance with the headline-making narratives that grow from each hit album, single, video, film and performance — distinct story lines that expand Madonna’s brand. Like the sexual dare of “Erotica,” the spiritual-enlightenment yarn of “Ray of Light” and the political racket of “American Life,” the new album now carries with it another chestnut to add to Madonna’s biography. It’s just not one she invited.

To create “Rebel Heart,” the 56-year-old collaborated with the likes of Diplo, Avicii, Kanye West, Nas, Nicki Minaj, Chance the Rapper, Mike Tyson, Toby Gad, DJ Dahi, Ariel Rechtshaid and Ryan Tedder over 18 months. Two days after Thanksgiving, a pair of demos leaked online. Then, a week after other journalists and I previewed 13 tracks one evening in early December, the full album leaked as well. What can the most exacting and famous pop icon on the planet do when hackers threaten her power? What she’s always done: reclaim control.

It’s not dissimilar from what I glean during our 30 minutes of face time, which Madonna begins by offering me a Red Vine. She may not know what questions she’ll be asked, but Madonna asserts herself simply by making it clear which ones she likes and which ones she does not. She’s cognizant that even professionals flinch in her presence. Coy smiles give way to skeptical frowns as the conversation unfolds, underscoring the art of Madonna’s protracted self-awareness.

Stars in Madonna’s orbit (L to R): Michael Jackson (1991), David Letterman (1994), Rosie O’Donnell (1998), Britney Spears and Christina Aguilera (2003), then-husband Guy Ritchie with son Rocco and daughter Lordes (2007)

In an age when pop stars feel like ephemera — Britney Spears turns into Katy Perry, John Mayer gives way to Ed Sheeran, Janet Jackson yields to Rihanna — Madonna is the only one to promote a persona that demands every move become another indelible page in the story she’s writing about herself. That’s tougher nowadays, when trends don’t last as long. So, as usual, Madonna concocts her own tale: She releases mastered versions of six leaked songs with no announcement, becomes the first major artist to premiere a video on Snapchat and runs a contest that allows fans to chat with her on Grindr. Just don’t think the leaks somehow benefited Madonna — she scowls when I imply there’s solace in their prompting her to stretch “Rebel Heart” from 13 tracks to 19, meaning she eliminated less from what at one point might have become a double album.

“It was really hard on everybody,” she says of the leaks. “Everybody became very paranoid. It was like, ‘Oh, it could be anybody. It’s got to be somebody close.’ I was worried it was an engineering assistant or somebody that had access to everything.” (It was a 39-year-old man from Israel. He has been arrested and indicted.)

Celebrity image control has evolved wildly since Sire Records president Seymour Stein signed Madonna after listening to her debut single, “Everybody,” from his hospital bed in 1982. That Madonna has molded herself for the Instagram era despite having cut her teeth before social media was conceivable is a chief source of the “she’s irrelevant” potshots her critics sling. Before she leapt onto the social-media bandwagon, which has served devotees-turned-counterparts like Beyoncé and Taylor Swift well, Madonna’s control was born in the music-video era, when performers molded their personas primarily through MTV rotations. In Kanye West’s eyes, for example, she is “the greatest visual musical artist that we’ve ever had.” Instagram, then, is another visual platform where Madonna can craft her career narratives.

I tell Madonna that West has paid her such a compliment and ask whether she agrees. She looks at the floor, chuckles knowingly and looks back at me. “That is a trick question,” she smirks. “Um. I think Kanye is a …” — and here she morphs into an exaggerated English accent — “… brilliant man. Brilliant, brilliant. He says some very pithy things sometimes.” (In an interview with the New York Daily News, Madonna tried her hand at pithiness, too: “Kanye is the black Madonna,” she said.)

Others say things Madonna doesn’t find quite so amusing. Case in point: Giorgio Armani. The designer fashioned the cape that led to her nasty tumble at last month’s Brit Awards. A week after Madonna took to Instagram to thank Armani for the costume, he told the Associated Press she is “very difficult to work with.”

“That was kind of disappointing because I don’t think I was difficult to work with,” she tells me. “I never blamed my cape for not being able to untie it. In fact, the day after it happened, I posted a drawing, a beautiful drawing, of the cape and thanked them for my costume. I didn’t blame what happened on anyone, so I don’t really know why they did that. I think that was a knee-jerk reaction on their part thinking they were going to get criticism, so they just had to make me the bad guy. Not very elegant, I don’t think.”

This pendulum — a tick-tock between fierce loyalists and unforgiving detractors — swings with every major moment in Madonna’s career. Out of the reactions, the narratives are born. With the post-breakup anthem “Living for Love,” the lead single from “Rebel Heart,” Madonna fell down (literally and figuratively) and carried on, just as the lyrics promise. A “tumultuous” few months led to many sleepless nights as Madonna tied bows on the album, now according to her hacker’s schedule. As a result, “Living for Love” emerges with the type of potent backstory the singer hasn’t seen since 2005’s “Hung Up,” the heralded dance canticle whose John Travolta-influenced video marked a return to form after the departure of “American Life.”

Throughout these recent obstacles, Madonna used Instagram to reach the fans who rallied behind her. That instant-access culture has taken interesting turns for the singer, though. In January 2014, she posted a photo of son Rocco, then 13, with a caption that included the hashtag “#disnigga.” The backlash was swift and ended in a rare apology from the very woman who has a new song called “Unapologetic Bitch.” After refusing to douse infernos involving alleged religious blasphemy (“Like a Prayer”), nude streetwalking (the Sex book) and smooches planted on Britney Spears’ and Christina Aguilera’s lips at the 2003 MTV Video Music Awards, why cave now?

Madonna explains that she only apologizes “when I see that there’s a huge fire that’s about to blaze through the center of the universe and I have to put the fire out — especially if it comes to my children.”

As with everything in the second half of her career, Madonna has straddled motherly enlightenment and relentless envelope-pushing, ensuring that we see her as an evolved artist who remains true to her initial priorities, even in the face of ageism and sexism. In the case of the N-word gaffe, Madonna says it was Rocco who told her how to caption the photo. “It was the one time that I listened to my son,” she says. “It was his idea. I was like, ‘What caption do you want me to put on it?’ And I did. I wasn’t thinking.”

This controversial Madonna is a theme on “Rebel Heart,” with songs that probe some of the more audacious moments of her 33-year career. On the title track, she sings about “all the things I did just to be seen,” echoing criticism predating the time she rolled around on the VMA stage in 1984, when hardly anyone had even heard “Like a Virgin.” It also reminds us that almost all of those contentious moments, whether she regrets them or not, contain layers that most pop stars are lucky to achieve once or twice in their career. Still, it pays to be meditative, and that’s the chief tune Madonna has sung since the mid-’90s, when she made “Evita,” began studying Kabbalah and had her first child, Lourdes.
“Sometimes I just did shit, you know? Just to, like, throw a firebomb in the room.”

“There’s a part of my character that’s on automatic, that just likes to be a provocateur. And to a certain extent, maybe some of the things that I did didn’t really have any thought process behind them necessarily, but they got attention,” Madonna says. “I wasn’t really thinking of anything specific. I mean, I could even think of shows that I did on the Lower East Side, when I was first starting in punk-rock bands. I can’t say that every creative decision I made was altruistic or came from the deepest part of my soul or with the best intentions or was really well thought-out or anything like that. Sometimes I just did shit, you know? Just to, like, throw a firebomb in the room.”

Times have changed: We don’t see those firebombs from today’s biggest pop star, Beyoncé, whose carefully curated image does not allow for the same spontaneity. Instead of subscribing to a traditional, interview-based press strategy, the “Flawless” singer perpetuates her offstage persona primarily through Instagram and Tumblr. Madonna says she’s unaware of Beyoncé’s PR tactics, in part because Bey is not among the 57 people she currently follows on Instagram. A more obvious pop comparison may be Miley Cyrus, whose Robin Thicke-accompanied twerking at the 2013 VMAs faced minstrel-show accusations and electrified the cultural conversation for weeks. Cyrus seemed like she could become the decade’s biggest star by courting controversy in a very Madonna-esque manner. Two years later, we’re not paying much attention to Cyrus — something you can never say for Madonna, whose doggedness stokes incomparable intrigue and avoids pop-culture limbo.

We don’t like our pop stars to thrive for too long, anyway. Instant castigation awaits those who try too hard, seem insensitive or appear to appropriate other cultures for their own gain. Out of that came another Madonna apology, in January, after she reposted fan-made Instagram photos of Martin Luther King Jr., Nelson Mandela and Bob Marley with the same thin black cords that envelop her head on the cover of “Rebel Heart.” Detractors accused the images of conjuring the chains of slavery. She acknowledges the political-correctness policing that has materialized over the past few years but was unaware that Cyrus, too, attracted such backlash after the VMAs. Way back in 1998, when Madonna opened her own VMA appearance with the Hindu ode “Shanti/Ashtangi,” she surrounded herself with East Asian dancers and donned the religion’s traditional facial markings. A quiet protest from the World Vaishnava Association ensued, but the Internet was nascent and the controversy — tame compared to the Blonde Ambition Tour’s simulated masturbation or a coffee-table book containing near-pornography — barely registered. Today she wouldn’t be so lucky, as we saw with the troublesome Instagram posts.

“Oh, they can kiss my ass,” she says of critics who might accuse her of borrowing other cultures’ fixtures. It’s a topic she seems interested to discuss. “I’m not appropriating anything. I’m inspired and I’m referencing other cultures. That is my right as an artist. They said Elvis Presley stole African-American culture. That’s our job as artists, to turn the world upside down and make everyone feel bewildered and have to rethink everything.”
“That’s our job as artists, to turn the world upside down and make everyone feel bewildered and have to rethink everything.”

But the fact is that Madonna can get away with more than anyone else, not only because of longevity, but because her entire image has been manicured to remind us that her outlandishness always contains a story. Well before the hackers interceded, she made a calculated decision to expand her ubiquity to the Instagram audience. (And she does maintain her own account. When I mention that some celebrities hand off their phones for others to post on their behalf, she knowingly says, “Yes, they do.”) Now, in between that mass networking and the exhausting press tour she’s conducted since the start of the year, Madonna will “fine-tune,” over just one week, four different performances for next week’s “Ellen DeGeneres Show” residency. Then she’ll continue to craft the various themes she’ll incorporate on the “Rebel Heart” tour, which launches in August. In a few years, no doubt, she’ll do it all over again, and a new narrative will rise.

At this point in the interview, Liz Rosenberg tells me I have two minutes remaining. Over a lightning round of quick hits, I ask Madonna to pick her favorite Instagram filter (X-Pro) and five most iconic songs (“Like a Prayer,” “Like a Virgin,” “Ray of Light,” “Express Yourself” and “Vogue”). She thinks Katy Perry’s Super Bowl halftime show looked “exhausting” (“That drunk shark!” she says) and would “rather not” list which musical acts she’s listening to at the moment. I tell her it’s David Letterman’s final year on the air (she wasn’t aware), and Rosenberg interrupts to say Madonna will be making an appearance because “she loves him.” With one question left, I inquire about the best party she’s ever attended — excluding her famed Oscar soirée. Her answer: “None.”

Thirty-three years ago, she extended to the world an invitation. Times have changed, but we haven’t left the dance floor.

“Only I throw good parties,” Madonna says.