If Bjork isn’t pretentious, then who is? It isn’t a hostile question: In an anti-intellectual age, pretentiousness isn’t the sin it used to be. And for an artist such as Bjork, continually restless and inventive, success means navigating the shoals of doing too little and daring too much, which means some amount of pretentiousness is almost inevitable.

There is a heady mix of insouciant charm, playful irony and risible pretentiousness throughout the Museum of Modern Art’s new Bjork retrospective, which opens on Sunday. The exhibition surveys more than 20 years of the 49-year-old Icelandic pop star’s videos, music, costumes and collaborations with designers, producers, writers and other artists. Perhaps the most ridiculous moment comes in a new video installation, “Black Lake,” directed by Andrew Thomas Huang and created for the exhibition, in which the singer mourns the loss of her longtime relationship with artist Matthew Barney. Wandering through a lunar landscape of black lava, she cries “I am one wound,” while repeatedly beating her breast in the manner of a 19th-century tragedienne.

Opera singers, so given to melodramatic cliches, gave up this sort of thing at least half a century ago. But you have to admire the strange alchemy of pop artists who manage to borrow the most hackneyed gestures, the most threadbare aesthetic moves of yesteryear, and make them seem almost profound and new.

The MoMA show is testament to Bjork’s blazing success as an artist who has built a diverse audience and brought a distinct sensibility — visually and musically — to everything she does. Anyone who loves Bjork will enjoy much of this show, while those who fret about the direction and mission of MoMA will wonder if the museum is merely pandering. Even those who try to keep an open mind will be befuddled: Where is the critical distance, the objectivity, when it comes to assessing the oeuvre of an artist who is sometimes brilliantly original, and often ridiculously pompous and self-obsessed?

It’s unfortunate that the bulk of the show is contained in a series of small galleries that must be experienced while wearing headphones pre-programmed with a lamentably jejune — and pretentious — voice over by Sjón, the Icelandic writer who is also a longtime Bjork collaborator. The faux-naïve text is billed as a lightly fictionalized “psychographic journey through the first seven albums of Bjork,” but its sing-song narrative and storybook cadences cloy from beginning to end: “once there was a girl . . . a girl . . . who lived alone . . . in a lava field . . . in a forest . . . by the ocean . . .

A new exhibition at the Museum of Modern Art in New York chronicles Icelandic pop star Bjork's career using her music, videos, costumes and collaborations with other artists and designers. (Reuters)

This journey, also documented in the catalogue, takes us from Bjork’s early days as a girl in Iceland, raised in a bohemian environment, to her emergence as a major artist in London in the 1990s, up to the present day, ending with wordplay on the figure of “heart” and “earth,” with a not so subtle suggestion that Bjork has reached some kind of primitive animistic transfiguration. Among the visual elements are handwritten lyrics and old photographs, and costumes (some of them recreated for the exhibition) that are instantly recognizable to anyone who knows either her videos or her iconic appearances on the celebrity stage. Cleverly placed to give visitors a brief view into the larger architecture of the museum (a welcome punctuation from the otherwise claustrophobic warren of small galleries) is the swan dress she wore to the Oscars in 2001. This was Bjork at her best, winsome and witty, yet daringly indifferent to the rituals of the larger entertainment industry.

Other artifacts include the shiny carapace of Alexander McQueen’s 2004 “Bell Dress” and several of the fanciful folk- ­inspired costumes from “Wanderlust.” But the galleries are bare of physical objects, and the obligation to wear headphones that drone Sjón’s ridiculous ­pseudo-poetry gives one little chance to think. Bjork may implore her listeners to “Declare Independence,” but this exhibition is a perfect example of how the experience economy has invaded the museum, enforcing a single, rigidly determined, pre-interpreted encounter with the art. (If you go, be sure to take off the headphones to enjoy the full, rich ridiculousness of the red vulva room, where a neon light fixture with a very recognizable form alerts visitors to the artist’s psychojourney through love and motherhood.)

The galleries are laid out chronologically, with brief sketches of feminine awakening to desire, self discovery, love, birth and betrayal. In this, they follow the general pattern of a romantic song cycle, say Schumann’s “Frauenliebe und -Leben,” which celebrates the traditional chapters of femininity without any overt sense of feminism. But it also has the arc of a bildungsroman, a drama of self discovery and gestation, liberation and transcendence, as the artist discovers her powers and forges her own path. The word isn’t invoked, but throughout the exhibition we are invited to think of Bjork as a genius, in the rather shopworn 19th-century sense of the term: A rebel and innovator whose life, face, body and psyche are so intimately interesting that the most mundane things are transformed as they flow through her ecstatic consciousness.

Visually, this idea is presented in myriad ways. In the 2007 “Declare Independence” video, directed by Michel Gondry, Bjork chants through a megaphone that also serves as a conduit for tightly stretched cords or ropes that function both as musical strings and a kind of belt drive for some sort of perpetually looping industrial machine. This symbolizes connectivity with her audience, but also a circular loop of inspiration and admiration, flowing through the artist and among her admirers. In another video, “Hidden Place,” tears flow from her eyes only to be reabsorbed through her mouth and nose, changing colors and consistency, another cycle of outflow and intake, in which the artist’s face is the canvas for a hermetic drama of pain and self-nourishment.

Fluids in general are an obsession for Bjork, as they often were for Barney. The fixation among this generation of artists on bodily fluids probably arose out of the 1990s, when AIDS was ravaging the creative underworld of cities such as New York and London. But fluids were also an obsession for Wagner, whose fascination with wounds is remarkably close to some of the darker passages of Bjork. And, of course, fluids are fascinating to children, a source of endless self-absorption, which is the weakness Bjork is most inclined to indulge.

Fortunately, the pretentious Bjork isn’t the only Bjork. There is also the trippy, manic, playful Bjork, forever a child with an impish child’s boundless energy and whimsy. This is more on display in the earlier videos, when she presented herself as a proxy for larger feelings of ironic alienation rather than a grand symbol of herself. The exhibition includes a theater playing a cross section of her most famous and influential videos; it would have been wise for MoMA to limit the show to this material, which is the core of her creative contribution and far more appealing than the efforts to structure a gallery experience around her life and personality.

Perhaps it’s inevitable that artists turn inward and find themselves more fascinating than the world at large. Bjork’s expressive power is strong enough that I’m more than willing to follow her yet deeper and hopefully one day out of this labyrinth of solipsism, through the only thing that really matters: her music. The exhibition at MoMA, however, raises troubling questions that go far beyond Bjork and the narcissism so many artists are prone to.

The problem is the Pop Industry. Bjork doesn’t need MoMA to find an audience, and she isn’t well served by the exhibition’s shift of focus from her music and video work to the larger personality cult of Bjork. The Pop Industry, however, doesn’t care about the dwindling resources of the non-commercial cultural realm. It is simply voracious, and it plays by different rules. The primary aesthetic claim made by this exhibition is that Bjork is daring to cross lines between art forms and genera distinctions. This boundary crossing is presented not simply as an expressive freedom she indulges, but as a virtue in and of itself. Unfortunately, this claim serves the Pop Industry all too well. Like the colonialists of another era, Pop is always in search of raw material, which it can repackage and sell to new audiences. It needs you to believe that there is no history to the ideas and influences that Bjork appropriates, because it functions by presenting everything, especially cliches and pretensions, as eternally new.

MoMA is, or should be, in exactly the opposite line of work, making distinctions, tracing history, educating audiences.

The only danger Pop faces is a remote one — that an educated audience will unmask its haphazard borrowing and call foul on the emptiness of the whole aesthetic enterprise. Bjork is, of course, better than that. And relative to other music artists, she has struggled to maintain her independence and creative freedom from an industry that is ruthlessly leveling.

Bjork’s creative accomplishment makes her immensely appealing to people who would like Pop to be better than it is; but Pop isn’t about to get better, it seeks only to get larger. It’s difficult to see how the ultimate mission of MoMA and the endless appetite of Pop can work together; MoMA will simply become one more venue for entertainments that have already reached near ubiquity.

It’s sad that it would be an exhibition of Bjork — so independent, and often so good — that crystallizes this for the larger art world. But spend time with this strange exercise in hagiography, and you may wonder what exactly MoMA brought to the table, except its reputation, legitimacy and prestige.

“Bjork” is on view at the Museum of Modern Art in New York City beginning Sunday through June 7. For more information visit www.moma.org.