Katy Perry tries to deliver “purposeful pop” on her new album “Witness.” (Rich Fury/Getty Images)

Sometimes, a pop star drops a single so soupy and ill-conceived, it makes you wonder if the artist ever had any understanding of their own appeal to begin with. For Katy Perry, that song is “Chained to the Rhythm,” a half-throttle disco ditty that scolds us for dancing our nights away while the republic crumbles: “Put your rose-colored glasses on and party on.” Somewhere in Donald Trump’s America, the left-shark’s googly eye sheds a single tear.

Perry calls this new approach “purposeful pop,” implying that her previous music didn’t have a purpose. Obviously, it did. Her biggest singles provided affirmation (“Roar”), promoted uplift (“Firework”), encouraged abandon (“Teenage Dream”) and embraced goofiness (“California Gurls”). And while the edgeless bluster of her voice often made Perry sound more like a hit-making conduit than an autonomous personality, the songs usually got the job done. Purposeful or not, her music has been therapeutic.

On her new album, “Witness,” Perry is abandoning all of that — her frivolity, her wink-wink sense of humor, that brassiere that shot Reddi-wip. “We’re living in a bubble-bubble,” she sings on “Chained to the Rhythm,” offering to topple our divisive American thought silos. “So comfortable, we cannot see the trouble-trouble.” But throughout “Witness,” Perry refuses to articulate what that “trouble-trouble” might actually be. We get the sense that bad forces are on the rise in America, and that we should feel proud of ourselves for noticing them, and . . . that’s it, congratulations, we’re officially woke!

Yes, perhaps change starts from within, but there’s a song on this album titled “Mind Maze,” and it would have made a good title track for this collection of songs, so bland in their production and so lost in their own doublespeak. If you’d like to join Perry in tsk-tsking the “wasted zombie” that stumbles drunkenly through the refrain of “Chained to the Rhythm,” be sure to close your ears during “Roulette” when Perry longs to “have a few rounds and just let go.” If you want to believe in her political awakening during “Bigger Than Me” (“If I’m not evolving, I’m just another robot taking up oxygen”), you’ll have to ignore her stay-the-course platitudes on “Pendulum” (“Don’t try and reinvent your wheel . . . You’re too original”). And during the feminist rah-rah-rah of “Hey Hey Hey,” when Perry boasts about “karate chopping all cliches and norms, all in a dress,” please excuse the cliche she’s just evoked.

Equally confounding is how frequently Perry lets her words get in the way of her voice. For her choruses to properly take flight, her verses need to feel like smooth rides down the tarmac — but she’s a clunky lyricist, and rhythm isn’t her forte. If you saw her dancing alongside the Atlanta rap trio Migos on “Saturday Night Live” a few weeks back, you know how tricky it is for Perry to locate the beat.

And when Perry isn’t leaning on her guests, she’s leaning on her past. “Miss You More,” a lurching ballad about lost love, finds her cooing about plastic in the breeze — “I saw a balloon floating away/I thought, ‘Did somebody let go, or did they lose it?’ ” — echoing that plastic bag that went drifting through the opening lines of “Firework.” And during “Swish Swish,” an alleged diss-track about Taylor Swift, Perry boasts that “A tiger don’t need no sleep,” conjuring the “eye of the tiger” cited in “Roar.” (And don’t forget that Perry got that plastic bag idea from the 1999 film “American Beauty,” and the tiger-eyeball line from the 1982 motivational-rock hit by Survivor.)

All of this makes the opening lines from “Bigger Than Me” feel especially confounding. “Can’t go with the flow, got to make waves/Even though I look at the sand, and I’m just one grain,” Perry sings. “But my intuition says there’s a bigger mission I must embrace/So I’m . . . pushing my thoughts to a new place.”

What a demented thing to say on such a solipsistic, flow-sustaining, unwavy, missionless, momentum-deficient, same-old-place kind of pop album. At best, Perry sounds like she’s trapped in a purgatory, pantomiming progress, giving an endless pep talk to her own reflection. She wants to look out into the world, but she can’t look away from the mirror.