Cheerful and competent, Perry favors a look like that of a fifties bombshell. Illustration by Stanley Chow

Katy Perry has become one of the biggest pop stars in the world by not making us worry about her. We usually see our alpha pop stars—Beyoncé, Rihanna, Lady Gaga, Eminem—as characters with a story, or as heroes with a mission. Lady Gaga likes to change her look every few months and has become probably the most visible (and credible) defender of L.G.B.T. rights in pop culture. Rihanna has grown into the Clint Eastwood of pop—slow of step, eagle-eyed, and unbiddable. But Perry is more like a talk-show host, the face for a team of professional entertainers, chipper and on time. We don’t worry that Perry has lost herself to this cult or to that bad boyfriend, because she’s never hidden the fact that she’s not staking her life on her public persona. (The exception to this theory of allegiance is younger listeners, who identify strongly and specifically.)

Though her personality is consistent, her style changes from album to album, like a lineup of guests or of TV backdrops. Her shape-shifting has paid off: “PRISM,” her new album, entered the Billboard 200 at No. 1, and her first single, “Roar,” has been at the top of the charts in several categories, both purchased and streamed. Her previous album, “Teenage Dream,” equalled Michael Jackson’s “Bad” by generating five No. 1 singles.

Perry, born Hudson, made a Christian-pop album as a teen-ager, which immediately sank from view. (Though she still mentions God in interviews, he rarely shows up in her songs these days.) When she returned for another crack at pop stardom, she worked with one of the industry’s most reliable hit generators, Glen Ballard, who has written songs with Alanis Morissette and Michael Jackson. Perry was signed and then dropped by a couple of major labels, and the collaboration with Ballard was abandoned. Eventually, shuttling from label to label, she had the luck to end up with the team that has dominated almost twenty years of chart pop: New York’s Lukasz (Dr. Luke) Gottwald and Sweden’s Max Martin, along with the producer Cirkut.

Her first single, “Ur So Gay,” released in 2007, was a serious misstep: it is either homophobic or a clumsy approximation of how teens spell and talk, or both. A bomb, it was followed by the hit “I Kissed a Girl,” a sort of cleaned-up Katy Gone Wild. Though the song was probably not convincing to girls who actually kiss girls, it was more than sufficient for boys who hold their red Solo cups high. For this pop fan, it was neither heartening nor intense enough to distract me from worthier artists. Perry’s voice is a steady, not particularly distinctive alto—it’s strong and bright, but it’s not enough to capture you without a killer hook. Her default backing track is a crunchy guitar sound that reaches back to Morissette, was recharged by Kelly Clarkson, and now mostly belongs to Perry. (“PRISM” dials through some variants of dance music but rarely with the jubilation that she brings to guitar rock, so this may have been a wise, and possibly lucky, early choice.)

In the course of her career, Perry’s look has mostly been a series of variations on the fifties bombshell; she carefully dials up and down the sexual innuendo, depending on what hour of the evening her performance airs. Openly discussing her songwriting teams, popping up on red carpets and morning shows without sulking, Perry doesn’t throw her lot in with any single age or style. There’s very little of the suffering artist about her.

“PRISM” could also be called “Now That’s What I Call Perry! Vol. 3.” It’s an omnibus of what the kids are listening to, while supposedly also being for those kids. Since “Teenage Dream,” she has solidified her version of good clean American fun. She might shade into something heavier than hard cider, but she never flirts with the kind of P.R. disaster that Madonna encountered when she blithely decided, onstage at Miami’s Ultra Music Festival, last year, to give a shout-out to the drug Molly. If Perry has edged away from the teen-age insouciance that characterized her previous album, it’s perhaps a recognition that she no longer resembles a teen.

The album is driven by “Roar,” a pop monster that could have gone to No. 1 even if it were sung in Romanian. The verses have a springy bounce and a chattering piano, and a noncommittal, easy line about being “scared to rock the boat and make a mess” that remains cheerful. The chorus enters with the subtlety of a Michael Bay plot point, drums veering toward Zeppelin, guitars geo-locating Slash, and it rides straight up the scale: “ ’Cause I am a champion and you’re gonna hear me roar.” Once, in conversation, Gottwald told me that Martin’s facility with melody was unmatched: “If you only have one swing with the axe to take the tree down, Max is the guy to do it.” That swooping Valkyries moment is Martin’s trademark. The lyrics openly quote Survivor’s “Eye of the Tiger,” and the “champion” in the chorus is likely a Queen reference, a group that Perry has often claimed as a touchstone. (Her fragrance is called Killer Queen, so this may be Perry’s most solid statement of aesthetic loyalty.)

The video for “Roar” depicts Perry (safely) crash-landing in a wholesome, goofball kind of Disney jungle landscape, where she befriends the animals and loses her hapless male-model co-pilot. The exposed flesh is very PG, as if Perry has decided to back away from anything approaching nudity. (In the booklet for the CD of “PRISM,” Perry looks thoughtful and gauzy, as desexualized as she’s been on a cover yet.) In a recent interview on NPR, she called on other female performers to “put it away”—one of the few times her good-natured sensibility has slipped. What if Miley’s having a nude kind of year? Let your peers make that call, Katy. Her stance typifies her soft-serve feminism. On “PRISM,” Perry takes strong positions, and almost none of her songs depict the singer as forlorn or as waiting for some dumb boy. But you don’t get the sense that she is going to match the Dixie Chicks, who, on “Goodbye Earl,” from 1999, sang about killing an abusive husband. Just like a good network player, Perry skews toward the middle.

“This Is How We Do” is an odd patchwork of dance-music textures over an awkward tempo that seems to have been slowed down to accommodate Perry’s semi-rapping about “checking out hotties” and singing Mariah Carey songs at karaoke. The Carey reference sounds out of date, as does the title of “Double Rainbow,” a reference to a YouTube meme that’s roughly three years old. The interlude on “This Is How We Do” is a clue to this time trap: “Yo, shout out to all you kids, buying bottle service with your rent money!” It seems unlikely that the people in Perry’s target demographic are paying their own rent, and she appears to be playing to the parents as much as to the kids, who are less likely to be buying concert tickets. “Walking on Air” sounds like Eurodance from 1990, and “Birthday” is a Prince soundalike, circa “Dirty Mind,” from 1980.

Two confusions come together on “Dark Horse,” a track with the m.c. Juicy J, best known as part of the Memphis group Three 6 Mafia. The track is bassy and airy, and Perry’s voice dips slightly lower, where it often sits naturally (as on “Fingerprints,” from her pop début, “One of the Boys”). But the lyrics are like a charm bracelet assembled in the dark, with Perry claiming to be Aphrodite, magic, and a horse. Juicy J is more family-friendly than usual, but he still sounds as if he’s wandered onto the wrong track. Why not put him on a rowdier song? With Perry alleging some sort of mythical strength, the rapping guy doesn’t seem necessary, and the album makes no other concessions to hip-hop.

In these songs, Perry doesn’t approach the new minimalism that has trickled down into pop through dubstep, or use any sounds that are in any way unfamiliar. “PRISM” reflects the very practical realization that teen-age dreams last only one cycle, but adulthood is a lifetime subscription. ♦