The nearby lunch tables were filled with gallerists and businessmen, but Diamanda Galás put down her biscotto, opened her mouth slightly and proceeded to hold a single note — a low, plaintive note — for what felt like an eternity.

It was a bright day, and she was singing in full view of others at the Trestle on Tenth in Chelsea. Some ignored her and others turned to watch, but Ms. Galás was completely oblivious.

“I can do that for four minutes,” she said, gripping her water glass. Dressed in all black, Ms. Galás perused the menu, pointing to items with her left hand, which has the words “We Are All HIV+” tattooed on sequential fingers.

This was her first New York performance in eight years, completely impromptu. Her next one involves considerably more planning.

On Tuesday, as a part of the Red Bull Music Academy Festival, Ms. Galás — the enigmatic composer and vocalist sometimes described as the Maria Callas of avant-garde music — will return to the New York stage with her nine-foot Steinway in tow, playing at St. Thomas the Apostle Church in Harlem for three nights. She is calling her piece “Death Will Come and Will Have Your Eyes,” named for the poem by Cesare Pavese.

Ms. Galás, who would not disclose her age because she feels “it’s irrelevant in the face of an entire career of making music,” was back in New York, where she lived for decades before uprooting in 2011. Since 2014, she has been an artist in residence at the Grotowski Institute in Wroclaw, Poland, putting the finishing touches on a new conceptual piece tentatively titled “Das Fieberspital” (The Fever Hospital), which is named for a poem by Georg Heym. She hopes to perform it in the United States as soon as next year.

For more than 40 years, Ms. Galás has used her voice like an eagle’s talons, with frenetic performances on dark topics like AIDS, vengeance and genocide.

“There is nothing like her work anywhere, in my opinion,” said Henry Rollins, the actor, writer and singer. “There are vocalists, avant vocalists, but nothing with the depth, power and force.”

The performance artist Marina Abramovic remembers the first time she saw a piece by Ms. Galás. “She was covered in blood,” Ms. Abramovic said. “The audience and her became one beast together.”

It’s that vim that has propelled Ms. Galás to continually breach the limits of music, improvising, mixing classical bel canto singing with demonic shrieks, muttering and glossolalic runs. Her vocal range is stunning, though the precise parameter is unknown. Theories put it at anywhere from three and a half octaves to eight octaves, and, like the Gyuto monks of Tibet, she can invoke more than one at a time.

Raised in San Diego by a Greek mother and an Egyptian father, she has been honing her sui generis craft since she came to the world stage at the Festival d’Avignon in 1979, where she starred in “Un Jour Comme Un Autre,” an opera by the experimental composer Vinko Globokar about imprisonment and torture.

Mr. Globokar, 81, remembers the young Ms. Galás, who was then a college student. “She had a technique of singing where everything was allowed,” he said.

A few years later, she released her first album, “The Litanies of Satan,” a rending 30-minute maelstrom of weapons-grade solo voice and electronics. In 1982, Bernard Holland, a classical music critic for The Times, described a live performance of the album as “grating screeches, hisses, strangled sighs, pants and gaggings, all delivered imaginatively and with great personal force.”

It set the tone for Ms. Galas’s career. Shortly after, her attention turned to AIDS activism and the group Act Up, which inspired several of her most famous, as well as profane and horrifying, albums including “Plague Mass” and “Vena Cava.”

Her most recognized work is arguably “Masque of the Red Death,” an operatic trilogy about society’s indifference toward the AIDS epidemic, which had its premiere at Alice Tully Hall in Lincoln Center in 1989. It was a personal battle that hit home when her brother Philip Dimitri Galás died of the disease that year.

Her brush with popular culture would come in 1994, when she teamed up with John Paul Jones of Led Zeppelin on “The Sporting Life,” a collection of homicidal love songs that combined Mr. Jones’s signature heavy grooves with Ms. Galás’s malevolent ravings about castration, rape and torture. The two toured extensively and even appeared on “The Jon Stewart Show” on MTV.

After a decade in which she continued to release albums every few years, Ms. Galás, who was a longtime New Yorker, quietly moved away. The circumstances of her self-imposed exile were a mystery. The last time she played New York was in 2008, at the Knitting Factory in TriBeCa. Since then, one-off shows in faraway places like Warsaw and Zaragoza, Spain, have appeared intermittently on her website.

The reason for her departure, it turns out, was death, a recurring theme in her work. “My father died in 2010,” Ms. Galás said. “The second time I saw my mother after that, it was clear to me that she had become extremely fragile.”

Ms. Galás had moved to San Diego to take care of her. “I am a Greek daughter,” she said. “This means that I do not question my love for my mother.” She added that this impulse was a continuation of her AIDS activism: “You do not abandon the loved one when he or she is dying.”

When her mother’s health improved last summer, Ms. Galás slipped back to New York, into a Midtown apartment where she lives alone. Her days are filled with a rigorous schedule of voice lessons, contract negotiations, booking tours and arranging music.

Promoting her art is something she does with great care with help from her small inner circle, which includes the artist Stephanie Loveless, who is her assistant.

At the restaurant, one hour turned into four. The stories Ms. Galás tells, even about the most mundane facets of her life, have a way of protracting to Wagnerian proportions, such as her distaste for marauding flight attendants who stand watch at airplane lavatories. “They monitor how long you’re in there,” she said. “I’m traumatized.”

Ms. Galás is garrulous not only about her work, but also about the world as she sees it. Despite her dark wardrobe and wolflike rapacity on stage, she has a softness in person. She laughs a lot and engages the people around her. She noticed that the waitress had a Teutonic accent, and so she struck up a conversation with her in German. It ended with both in stitches.

She is still driven by politics and social ills, as one would expect. These days, the rise of the Islamic State is a subject that gets her going, as is feminism as it relates to Hillary Clinton’s presidential bid. To Ms. Galás, the link is indubitable. “She has been in the trenches for decades,” she said, adding that “a woman who disavows feminism is a woman who does not realize the great amount of work done.”

And her art remains informed by her politics. “To be an artist is to be equal to the present,” she said. “Because mediocrity is so largely rewarded and broadcast ubiquitously, like a swarm of mosquitoes, by obese and tone-deaf accountants, the public is unable to learn about, let alone hear, see and digest the art of the present.”

Ms. Galás channels something much more primal. “The only thing that works is distilled rage,” she said.