Lady Gaga blew through Saturday Night Live over the weekend, weaponizing boisterous vocal runs and skinny fringe dresses that suggested the 38-year-old singer-songwriter, producer, and actor had put in the proverbial 10,000 hours studying zesty mid-20th-century variety shows. But the best skit didn’t employ her impressively interchangeable pop-star skill set. “Little Red Glasses,” a short piece near the end of the episode, was a daytime-TV ad ribbing a specific flavor of New York progressivism that has wilted since the ’90s. “I was ahead of the curve on gay marriage,” Sarah Sherman shouted, “and that’s where it stopped.” “Me too!” affirmed Gaga.

The quips, the Sheryl Crow parody soundtrack, and the backdrop of tree-hugged Central Park steps lampooned the star’s own class of millennial Manhattanite. It was a lived-in self-burn. The city figured into a few of the diffuse projects from Gaga’s hyperactive year: It was the setting for the widely panned comic-book anti-musical Joker: Folie à Deux, which cast the American-standard enthusiast as its reckless, singing Harley Quinn (who hails from the Upper West Side, just like Gaga); the deluge of interviews about Gaga’s new album, Mayhem, included a chat with Zane Lowe in a downtown dive where she once partied and wrote songs before the fame The Fame amassed. She’s tapping on her geological and chronological points of origin more than usual. Five years ago, Chromatica, the last mainline Gaga album, implied she was from space. Four years before that, Joanne applied for country-jukebox immortality. Talked into another pop album by her tech-entrepreneur fiancé and Mayhem co-writer Michael Polansky, Gaga whacks multiple birds with one stone. Fans attached to the work before jazz, serial horror, and silver-screen drama invaded what was once a much more steady stream of club bangers get a ride with Gaga 1.0, and if she absolutely must drag her Ms. Hyde back into the light, she’s going to make it fun for herself.

Even the draining portions of the new album are trying to figure out resolutions for the lengthy referendum on What We Even Want Out of Lady Gaga.

It took a few years to coax Gaga back into the bop factory, between expeditions into songs written during the Great Depression and depictions of larger-than-life 20th-century characters. Our hang-up with the pop-star persona she created appears to have complicated a larger, deeply considered Stefani Germanotta Project — a versatile one cooked up in a yearning Big Apple adolescence and codified across sweaty lower Manhattan bars. Sleek dance-pop grooves but also classicist balladry, fey art-rock, and drag-amenable camp all play crucial but disparate parts. But the constituency will always yearn for a return to the club banger. You suspect the obligation wears on her sometimes. Gaga belongs as much to the worldview of millennial and zoomer Monsters as to the school of Carol Channing, a master of comic absurdism and musical-theater panache. Mother Monster is another oddball capable of playing it arrestingly straight. She didn’t necessarily pick these skills up on the job, like genre conquistador Taylor Swift, who marched through country and synth-pop on the way to kitchen-sink adult contemporary. Nor is she Madonna, liable to return from time off singing the praises of Jewish mysticism or suddenly speaking with a regal British lilt. Gaga is a textbook Manhattan overachiever, beholden to conflicting but deeply held passions. Every unruly stretch of activity for this milieu — a Tony Bennett tour, a country album, A Star Is Born — is pulling on a thread that’s always been there: The city kid who by hook or by crook has their artistic interests engaged early on, always trying to bushwhack the space to be as formless and flowing in public as they feel in their heads. Mayhem slingshots Gaga from the toxic love story of Todd Phillips’s New York Bat moll back to her original form.

Mayhem centers Gaga’s raucous beginnings in its sound and promotion, prodding layers of artifice and performance. The lyrics examine relationship trauma from a place of newfound stability, cruising for a trouble that in real life the singer wants no part of.. The album is — to the extent that anything the pop auteur creates can break the attraction to an uplifting hook — a bit dark, reflective of a press run that saw her alternate between white blonde and all-black glamour and frame Mayhem as a “return to Gothic dream.” But songs like “Disease,” “Bad Romance”’s daughter, serve stock Gaga self-loathing that feels more parodic than in earlier work. Last tour, she sang Chromatica’s icy “Alice,” a grim(m) vision of Wonderland lore, while tied to a brutalist stone obelisk. The Fame Monster — the 2009 project whose runny-mascara alternate art foreshadowed Mayhem’s monochrome menace, unsubtle Black Flag’s Damaged airs notwithstanding — cruised down the same intersections of synth distortion, bombast, and heartbreak the newer work is visiting. Mayhem, like Justin Timberlake’s Everything I Thought It Was or Katy Perry’s 143, is a survey of past selves and sounds also trying to remain astride of modern trends. It’s both a commercial nostalgia initiative and one of the tighter pieces in the pool of self-evaluative millennial pop.

Of course, the goth shit was a put-on, one of a multiplicity of masks in play this cycle. Gaga always torches the script: The folksy Joanne plunked the screaming Kevin Parker and Mark Ronson thumper “Perfect Illusion” smack in the middle. Born This Way broke for the mariachi-house romp “Americano.” Mayhem has largely had its fill of crunchy riffs and sweetly disconcerting chord progressions by the fourth song. “Perfect Celebrity,” its most overtly Reznorian endeavor, imagines Nine Inch Nails peeling half of the trebly distortion and low-sample-rate skronk off of the Lost Highway soundtrack gem “Perfect Drug” to foreground the melodies. “Celebrity” and the lead single “Disease” employ the forbidding textures of industrial music to sing of the pits of notoriety and the peaks of rocky relationships. The root ideas of “Bad Romance” and “Paparazzi” come back around with sharper edges, but Mayhem gets outclassed in pure loudness by the more KMFDM-ish false metal EDM bleat of 2012’s Born This Way. Gaga must’ve tired of the flat, breathy anti-singing of the Joker movie — which jumps out when you compare versions of songs from the film and last year’s tie-in Harlequin one-shot — and designed a project that offered several pathways to wowing the listener with her instrument. Melisma and the time-displaced tastes of a devoted student of mass entertainment history are the themes uniting the Evanescence bops, the nods to ballroom culture, and the international array of synth- and Europop strains Mayhem threads together.

A handful of Mayhem tunes land like acorns that rolled downhill from another album’s tree and took root. “Don’t Call Tonight” ponders “Alejandro,” lifting the older hit’s “don’t call dah dah” cadence and also the beat that tries to pass Greco-/Italo-disco off as Latin pop, a gesture to “La Isla Bonita.” The self-referential tracks carry a hint of David Bowie checking back in on Major Tom. As noise tapers off after “Perfect Celebrity,” Mayhem blasts across time. “Killah” basks in plastic funk, drum machine clatter, and percussive flows, its verses cribbing the almost-funk-rap delivery from Prince’s 1987 State of the Union jam “Sign O’ the Times.” “Zombie Boy” blends a “Hollaback Girl” — or, hey, maybe “Mickey” — chant with a beefy disco strut revealing Chic, or at least the Daft Punk songs with Nile Rodgers involved. A focus on humanity and process throughout the rollout mirrors callbacks to ‘70s music business pomp surrounding 2013’s Random Access Memories, a session player’s paradise and a La La Land-ish swansong album about the importance of albums. Mayhem might scan as the same kind of tacit musical autobiography, or like a Confessions on a Dance Floor, if Gaga didn’t spend the back half disappearing into her peers’ signature moves.

In “How Bad Do You Want Me,” Gaga channels Taylor Swift via the bloopy bass of Reputation’s “Gorgeous,” the repeating vowels of Lover’s “ME!,” and the heartbreak hunting of 1989’s “Blank Space.” But Mayhem retreats into the precocious bookishness of mid-2010s Swift, where melodies make their way toward cloyingly sunny resolutions. “Bad” gently role reverses her good-girl-meets-bad-boy songwriting conceit, and later, “The Beast” tries on the skeletal, moonlit trap-pop of Midnights. In these songs, Mayhem’s restlessness feels a touch self-conscious. But the trickle of studious knockoffs also lands like an alpha vocalist play, a Best Actress nominee asking, “What do you want from me? The old me? The new her?” As with the rock star signifying, the message is that if you come for one flavor, you misunderstand the depth of the Gaga palate.

Still, you can smell the business moves. Cirkut and Gesaffelstein worked on Brat, and have collaborated with the Weeknd, whose ‘80s pop deconstructions meet their match in the Olivia-Newton-John and Pat Benatar vibes of Gaga’s “LoveDrug.” The track’s Ratatat-ish closing dual lead guitar riff dovetails with Andrew Watt’s production work, which yields either instant vintage or pre-distressed jeans and nothing in between. Mayhem is a tug of war between genres, between pop and rock impresarios’ pet sounds — none more experienced on the job than the singer and producer herself. The skeleton crew assisting Gaga and her fiancé feels calculatingly assembled, and it’s the right group for the task. But when Mayhem’s versatility starts to feel like the artist second-guessing her own musical tics, the album flashes its credentials as a member of a class of artists concerned with the futures of their creative legacies. From an eagle’s view, even the draining portions of the new album are trying to resolve the lengthy referendum on What We Even Want Out of Lady Gaga now. After revisiting arty Upper West Side abandon and old-world class over Folie and Harlequin, Gaga decided we can handle all her tastes at once.

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 Mayhem isn’t quite the return to form it’s being sold as.