Imagine a world where Madonna hates being photographed, where she considers quitting her career and admits to suffering haunting demands that she “act like the other girls.”

It’s the same world where pigs fly and figure skaters crowd the deepest recesses of hell.

Yet, somehow, that’s the world occupying significant parts of Madonna’s revelatory new album, “Rebel Heart.”

More credibly than any previous work, Madonna’s latest pulls back the curtain on her life, letting us see her hurt and yearning.

It also finds her licking her wounds over a breakup with a far less powerful boy toy — presumably the decades-her-junior dancer Brahim Zaibat, who she saw for three years, ending in 2013.

Maddy has said that she chose the album’s title to express two sides of her character: the defiant warrior and the aching lover.

While a decent portion of harder, bitchier odes do turn up, the album as a whole presents the softest, most sincere portrait of the star we’ve ever had. In the process, “Rebel Heart” coheres, offering a swift rebuke to whoever prematurely dribbled out its tracks in a dizzying variety of leaks.

It also marks a clear move away from Madonna’s last two works — “Hard Candy” and “MDNA.” Both soared on energetic pop, creating two of the most enjoyable, catchiest albums of her career. “Rebel Heart” goes for something more substantial and — dare I say? — mature.

Along the way, the long, 19-song album offers its share of groaners, missteps and songs more indebted to trendy production than solid craft. But its best moments boast some of the most finely structured pop melodies of Madonna’s 32-year career.

The slam-dunk opener, “Living for Love,” stands with her great gospel-soul songs of the past: “Like a Prayer” and “Express Yourself.” Of the ballads, “Ghosttown” rates with her best: “Live to Tell” and “Crazy for You.”

The way the producers recorded Madonna both bolsters the melodies and lends her depth. They’ve honeyed her voice: Madonna hasn’t sounded this rich since the sumptuous “Evita” soundtrack. In “Ghosttown,” her deep tone has some of the autumnal ache of Karen Carpenter.

All this isn’t to say Madonna doesn’t chirp, sneer and bray in places. In “Holy Water,” she’s in late-period Joan Crawford mode, putting down all comers with an unseemly pride. Then, in “Bitch I’m Madonna,” she nicks a slogan from someone far beneath her, referencing Ms. Spears’ old “It’s Britney, Bitch” line.

Madonna’s harder side finds a focus in “Unapologetic Bitch,” where she plays a spurned sugar mama. She revels in banishing an entitled young stud back to his impoverished past, a mirror, most likely, of the breakup with Zaibat.

The same scenario reels through two other songs: “HeartBreakCity” and “Living for Love,” though in the latter, the loss becomes a spur to celebrate a love that may yet come.

The music in “Living for Love” implicitly references the past, but in other passages Madonna invokes it directly. The lyrics to “Veni Vidi Vici” offer a virtual career retrospective. The title track brings an even broader life assessment — looking back at her attempts to fit in as a youth, as well as her years of acting out with provocative gestures for their own sake. Never before has Madonna copped to the latter motivation in a song. In the end, she accepts the consequences, and embraces the bravery, of her character fully enough to create her own answer to “My Way.”

The beauty of the song’s melody helps ease its self-involvement. As a lyricist, Madonna has always had trouble making her personal songs universal.

On the other hand, her persona has such cultural resonance at this point, it has become part of all pop fans. Her name is a metaphor for strength and endurance. That makes her potent enough to admit where she’s weak in “Joan Of Arc.” Here, she says that each critique drives her to private tears. In “Wash All Over Me,” she ponders either running from, or accepting the end of, her career.

It’s hard to imagine Madonna expressing things like this before, let alone making them ring true. That’s “Rebel Heart’s” peak feature: It presents a 56-year-old woman who, in the best possible sense, sounds her age.

jfarber@nydailynews.com

NY Daily News