Merce Cunningham (1919-2009) and John Cage (1912-1992), ca. 1965. (Jack Mitchell/Courtesy Merce Cunningham Dance Company)

John Cage could play on cowbells, rice bowls, car parts and temple gongs, smashing a wine bottle where an ordinary percussionist might strike his cymbals. But the one thing this musician who got his start as a dance accompanist couldn’t (or wouldn’t?) do was keep time.

“John couldn’t keep a beat and couldn’t follow the phrasing of the dancing,” said Remy Charlip, who as a founding member of the Merce Cunningham Dance Company endured Cage’s idiosyncratic accompaniment in the 1950s.

Cage’s out-of-sync piano playing might have been a liability in the eyes of some dancers. But not for Cunningham, who shared Cage’s drive for newness. And so was born one of the great partnerships in dance. As Fred was to Ginger, and Fonteyn to Nureyev, so was Cage to Cunningham.

Since Cunningham went on to become the king of modern dance, it follows that the art form would not be the same without Cage, his longtime musical adviser, artistic collaborator and life partner. Nor would Cage be the same without dance. You wouldn’t know this from the meager dance references in the upcoming John Cage Centennial Festival.

In fact, Cage created his most famous invention, the “prepared piano,” for a dance.

Back in 1940, when he was a dance accompanist at Seattle’s Cornish School, a dance student named Syvilla Fort asked Cage to write the music for her graduation concert. Cage wanted to use a full percussion ensemble for one of the pieces he composed for her, called “Bacchanale,” but there wasn’t room in the theater. So he brought the percussion into the piano, laying screws, bolts and bits of leather on the strings so they thudded and pinged as he played.

What Cage did with the piano that night long outlasted what Fort did onstage (though she would go on to an important career in her own right, performing with Katherine Dunham and teaching Marlon Brando and James Dean how to dance). But what he gained from that concert was even more important than the curious new sound. In the creative problem-solving that working with dancers required, Cage discovered an immensely satisfying and fruitful process. This is what fueled his half-century of collaboration with Cunningham, which began in earnest a few years later.

Cage had already tapped the tall, elegant teenage dancer, also a student at Cornish, to be one of the members of his all-percussion sextet at the school. (All the “musicians” in the group, except Cage, were dancers. Maybe that was because Cage needed vigorous movers to thump around on the washtubs, tortoise shells and pipe lengths that he scrounged for them.)

By 1945, Cage had talked Cunningham into leaving his first professional gig as a member of the Martha Graham Dance Company and going solo, with Cage at his side. After all, the two men had so much in common. They both wanted to defy how it’s done.

Cage’s lack of interest in timekeeping or other musical conventions (“I certainly had no feeling for harmony,” he once acknowledged) suited Cunningham just fine. As Cage adopted chance operations in his music, tossing coins to determine the pitch, volume and duration of sounds, Cunningham realized he could also use a coin toss to order sequences of steps and numbers of dancers, and revolutionize his field.

And why expect the music to follow the dance? Both elements could be created separately and brought together at the performance. These concepts — chance and the independence of design elements — grew out of Cage’s quirky way of working and became fundamental to Cunningham’s art. What results from these methods, as Cage wrote in a program note for an early Cunningham performance, is theater that doesn’t “say” something, but rather simply “presents” activity.

“This can be said to affirm life,” Cage wrote, “to introduce an audience not to a specialized world of art, but to the open, unpredictably changing world of everyday living.”

Indeed, it was in the realm of everyday living where Cage displayed his true mastery. His renown for whimsical sound experiments was one thing, his debatable merits as a composer another. But as the music director of Cunningham’s company and, for many years, its de facto manager, chief fundraiser, tour cook, bus driver, resident philosopher, morale-booster and liaison between the moody, introverted choreographer and his dancers, Cage was the indispensable sherpa who kept Cunningham and the artists around him relatively sane.

“John was like everyone’s father, in a way,” said Susana Hayman-Chaffey, a Cunningham dancer in the 1960s and ’70s.

Cage’s influence over Cunningham’s art continued beyond his death in 1992. In 2003, the British rock band Radiohead accepted Cunningham’s invitation to compose for a new dance. (The piece was called “Split Sides,” and yes, Radiohead, which sold out Madison Square Garden at around the same time, performed as the dance troupe’s pit band at the Brooklyn Academy of Music.) The band didn’t know much about Cunningham’s choreography, their manager, Chris Houfford, told me at the time. What clinched the deal was that for bandleader Thom Yorke, Cage was one of his “all-time art heroes.”

Lately, little recognition has been paid to Cage’s connection to dance. That is, until July, when, in homage to Cage, the Bill T. Jones/Arnie Zane Dance Company performed an engrossing piece called “Story/Time.” It was modeled on Cage’s 1958 work “Indeterminacy,” in which he sat alone onstage, reading aloud a series of one-minute stories he’d written. In the engagement at Wolf Trap, Jones took on the Cage role, reading from his own one-minute stories, selected and ordered by chance. Dancers from Jones’s company performed as he read. It was a lovely tribute from one experimental artist to another, a bow across time to a man who was a great friend of dance.