In the winter of 1971, The Village Voice magazine carried a small advertisement for Yoko Ono’s exhibition at the Museum of Modern Art (MoMA) in New York. Ono produced a catalogue, and in contemporary photographs she can be seen posing with some works outside the museum. Just one complicating factor: this exhibition did not exist. Ono’s accompanying book was titled Museum of Modern (F)art.In the Japanese artist’s short film The Museum of Modern Art Show (1971), several disappointed or oblivious visitors are interviewed and sound fairly blithe about her no-show exhibition of the mind, which required MoMA to stick a copy of the Voice advertisement at reception with a scrawled note: “this is not here.” Ono’s stunt is “dubious”, for sure, says one museum-goer, but Yoko is also “smarter than John [Lennon]”, according to another. A surprising reaction, because it is hard to think of an artist more persistently mocked, envied and misrepresented. Can Tate Modern’s (very real) survey do justice to her strange journey between avant-garde renown and a wild, hollowing-out sort of fame?Yoko Ono: Music of the Mind—the title is derived from her concerts in London and Liverpool, in 1966 and 1967—opens with works that seem to rely on Ono’s central presence and laconic persona. In Eye Blink (Fluxfilm No. 15) (1966), the artist’s left eye shuts and opens in a black-and-white, slow-motion close-up. There is just enough facial information to recognise her and imagine you are looking, for two minutes and 40 seconds, at something akin to Andy Warhol’s Screen Test film portraits, begun a couple of years earlier. A staring contest, in other words, between subject and medium, a test of self-possession and charisma.It is hard to think of an artist more persistently mocked, envied and misrepresentedSounding in the background as you enter the show is Telephone Piece (1964): a ringing receiver and then a voice, “hello, this is Yoko.” Yes it assuredly is; but in a way, as with the film, she is hardly there at all, or quite beside the point. These are not self-portraits. In her best work of this period, all is subordinate to action, not expression.Meeting one’s matchThe verbs are the thing, in the films, texts and performances of the first decade or so of Ono’s career. In the first room proper of the exhibition, Film No. 1 (Match) (1966) shows a match being struck and flaring: a liquid flame, in slow motion again, with visual echoes of Harold Edgerton’s photographic studies of movement—and more than a hint of A-bomb horror. (Ono was 12 years old, an evacuee in the mountains, when the atomic bombs were dropped on Hiroshima and Nagasaki.)The film is flanked by photographs of Ono at the Sogetsu Art Centre, Tokyo, in 1962: seated on stage at a piano, she strikes a match and lights a cigarette, looking down all the while. Lighting Piece is originally from 1955, when she had moved to the US and was studying poetry and composition at the Sarah Lawrence College in New York. In its first iteration it consisted of a simple instruction: “light a match and watch till it goes out.”The daring, the wit, the poetry of Ono’s instruction pieces—many of them collected in her 1964 book Grapefruit—reside in the minimal actions prescribed. At their most reduced, as in a sequence dedicated to the composer La Monte Young, the instruction might devolve to a single word: peek, rub, touch, peel, tear.At Tate Modern, the textual poverty and material profusion of such works—lines and grids of typewritten commands, sometimes handwritten in Japanese script—could easily give an impression of Ono as an austere but wry conceptualist. Photographs of her performances, alongside collaborators such as Young or John Cage, are often so coolly composed that you can get a misleading idea of control and direction. (Some of the most sheerly beautiful images were taken by her Fluxus confederate George Maciunas: photographs of Ono’s ephemeral paintings, six darkling, near-abstract studies of her enacting Bag Piece in 1965.) Read or look closer and more levels of antic variety and humour appear—also a frivolity that will not in the end quite save her work from sentiment.The balance between poetry and comedy is near perfect in a work like Snow Piece (1963), with its instruction to “take a tape of the sound of the snow falling. This should be done in the evening.” Snow Piece later gave rise to Soundtape of the Snow Falling at Dawn, which is to be played at “any speed”. Where Cage’s composition 4′ 33″ was meant to foment a subtle riot of sound amid the silence, Ono’s jocoserious gesture turns inwards—the music of the mind.Ono’s performance work Bag Piece (1964), in which members of the public climb inside a cloth bag, in the Tate Modern exhibition© TateNot so clear-cutTime and again in this show, Ono is not quite the artist you might have imagined. Renowned works turn out to be frayed at their “iconic” edges. Take Cut Piece, her most famous work (outside of certain musical collaborations, that is). The version in the exhibition was filmed by the documentary makers Albert and David Maysles in 1965 at the Carnegie Recital Hall in New York. The kneeling, implacable artist; close-ups of scissors and stopwatch; brief shot of the audience; an undercurrent of laughter; small tentative cuts to her clothes by women, followed by one man’s astonishing assault on what is left. Cut Piece looks like its reputation—a fearless study of abjection and misogyny—until you are reminded that Ono also envisaged a version in which the audience turned on each other with scissors, and only stopped when they felt like it.Her most infamous provocations are frequently twinned by such comical, excessive alternatives. This is why it does not exactly work to say that Ono’s art declined into whimsy or banality in the late 1960s, around the time her relationship with John Lennon began. Their film Fly (1970) remains a garish vanitas, a grubby Swiftian riposte to Warhol’s languorous Sleep (1964). As a small listening room with headphones and album covers reminds us, the records they made as Plastic Ono Band and as a duo are sometimes as daring as anything in the noise-rock canon.But the couple’s Acorn Peace (1968) project—mailing acorns to world leaders, in the hope of turning them towards peace—sets the tone for Ono’s later work, and for the final rooms at Tate Modern. A white boat for refugees, to be inscribed or decorated by gallery-goers. An invitation to describe one’s mother. Portions of “sky” in upturned German helmets. The final work in the show, however, is a video of a performance from 2013, when Ono was 80 years old—a whisper-scream reminder of just how stringent, not to say heroic, an artist she could be.Brian Dillon is a writer. His latest book Affinities is published by FitzcarraldoWhat the other critics saidIn The Guardian, Adrian Searle noted that Ono’s work relies often on sound and voice: “When it hasn’t been derided, Ono’s voice has been compared to that of Meredith Monk and Diamanda Galás, and her vocalisations in the film Fly reminded me of listening to a Sámi performer imitating the infuriating noise of a mosquito and the cries of the wolf.” In The New York Times, Emily LaBarge wrote: “It might be easy to link the austerity of her work to a childhood marked by scarcity, homelessness and mass destruction.”• Yoko Ono: Music of the Mind, Tate Modern, London, until 1 September• Curators: Juliet Bingham and Patrizia Dander