Madonna’s albums from this century fall into two categories: the playing-it-safe ones, and the “WTF is she thinking?” ones. You might be tempted to assume the mega-weird ones are better, but nothing is ever that straightforward in the Madonna universe. Confessions on a Dance Floor was her totally safe execution of an obvious idea — why doesn’t history’s greatest disco mastermind just make a damn disco record? — but it was also brilliant. Whereas the certifiably flaky American Life was certifiably ass. That’s just one of the many reasons Madonna remains the queen of all pop queens.

Yet Madame X is so admirably bizarre, all you can do is stand back and watch the girl go. “It’s a weird kind of energy,” as she sings in “God Control” — a rare moment of Madonna understatement. She dips into a melting pot of Latin-pop styles, complete with a reggaeton jam called “Bitch I’m Loca.” It’s for fans of her loca edge only, full of experiments no other pop star on Earth would try.

She teamed up with Colombian superstar Maluma for the scandal-bait single “Medellin,” learning to cha-cha-cha in her mysterious new accent. There’s a lot more where “Medellin” came from. Like a vocoder singing The Nutcracker in “Dark Ballet.” Or the moment when she chants, “People think that I’m insane/The only gun is in my brain/Each new birth, it gives me hope/ That’s why I don’t smoke that dope.” She throws down with Quavo, Diplo and Rae Sremmurd’s Swae Lee.

Weirdest of all, there are truly great Madonna moments. Especially “Crave,” a love song with florid acoustic guitar where she plays down the accent and gets lost in emotion, or the trip-hop “Crazy.” But with her typical nerve, she buries the strongest songs deep in Madame X. To reach them, you have to endure “Killers Who Are Partying,” where she ponders political oppression: “I’ll be Islam if Islam is hated/I’ll be Israel if they’re incarcerated.”

There’s something gratifying about the way the music can trigger that familiar “worried about Madonna” feeling. Let’s face it, aren’t we proud of our Eighties mega-pop idols for still being willing to act up like this? Imagine going back in time to the Eighties and saying, “Someday, Madonna will chant ‘Bitch, I’m loca’ the same week Bruce Springsteen releases his concept album about horses.” These two legends never let us down, in their very different ways. Time will tell if Madame X has staying power or not. But if you love Madonna for her shamelessness – bitch, she’s loca.

3 out of 5 stars

With 2012’s MDNA and 2014’s Rebel Heart, it seemed Madonna was fighting, and often struggling, to stay at the centre of the pop universe. As a super-saturated blast of The Nutcracker crashes into Dark Ballet, Madame X’s second track, however, it feels like there’s been a loosening of grip and a new air of recklessness.

Madame X is Madonna’s fluid new persona – “A professor. A head of state. A housekeeper. An equestrian,” apparently – and there is a hyper-mobile flex to this record, all global pop (partly inspired by a relocation to Lisbon) and space-disco production (courtesy of Diplo and Mirwais).

Crave’s delirious swoon, featuring rapper Swae Lee, or the skin-to-skin cha-cha-cha of Medellin keep things at the micro level of human desire but more untethered are the moments where the record zooms out to look at the big picture, as on Dark Ballet’s omnipotent state-of-the-planet address: “they’re so naive, they think we’re not aware of their crimes/We know but we’re just not ready to act.” This is Madonna on top of the world, looking down on creation, God complex at cruising altitude.

It doesn’t always work. The preposterous Killers Who Are Partying is messianic in an Earth Song style, its mother-of-the-world pomposity (“I’ll be Islam/If Islam is hated” and so on) overstepping the cosmic mark. Yet I Rise, sampling high-school shooting survivor Emma Gonzalez, or the rage overload of God Control, keep pace with a world out of joint. On Rebel Heart, she recorded the uptight, authority-reasserting Bitch, I’m Madonna; here, she sings “Bitch, I’m Loca”, Madonna and the times, it seems, have fallen into step again.

4 out of 5 stars