Van Hove and De Keersmaeker had never worked together before, but they anticipated the uncertainty of joining forces with characteristic composure. “I have to get out of my comfort zone to work with her,” van Hove told me. “She has to get out of her comfort zone to work with me.”

Their collaboration replicates an important aspect of the original “West Side Story,” which sprang from a group of ambitious, restless artists who recognized, in one another, forces of equal and opposite weight. For years, Robbins had been talking to the composer Leonard Bernstein and the playwright Arthur Laurents about a musical based on “Romeo and Juliet” that would seamlessly combine dance, music and storytelling. Discussion of the project began in the late 1940s — they first toyed with a story about Jews and Catholics on the Lower East Side. Over the next several years, as the three were diverted by other projects, none of them entirely lost sight of it. It was a shared fantasy — still inchoate but somehow powerful.

One day in 1955, according to most accounts, Bernstein and Laurents were lounging by a hotel pool in Los Angeles. Bernstein was in town conducting; Laurents was working on a screenplay. The subject turned to the headlines in that day’s paper about Chicano gang violence. The two fell to talking. What if they revised their original idea of an East Side story and made it about white and Latino teenagers? Bernstein, who was married to Felicia Montealegre, a Chilean, was immersed in Latin music, and he could immediately hear rhythms and melodies. When they told Robbins of their new idea, he seized on the dance possibilities. Getting away from their own experiences, as descendants of immigrant Jews, and mapping their sense of outsiderdom onto a different set of tribal animosities proved freeing. All three were gay men in various states of acceptance of their sexualities, and a story of forbidden love may have been a way to write clandestinely about their own lives. They set to work.

Soon after a pair of experienced lyricists turned down the project in 1955, Laurents ran into Stephen Sondheim, who was then only 25, at a party and remembered having heard him play a few songs from an unproduced musical shortly before. He invited him to audition for Bernstein. By that point, Bernstein had written lyrics to a number of songs, but he quickly understood that Sondheim was the superior lyricist and was eager to work with him.

All four men had uncompromisingly high standards but different strengths. Laurents, who honed his skills writing radio plays for the Army, was economical, tart and resistant to sentiment. Bernstein married emotional warmth to operatic bravura, and his capacious musical intelligence could synthesize Beethoven, bebop, mambo and Puerto Rican seis. Sondheim had a knack for embedding plot in lyrics and a playful, prickly sense of language. Robbins brought his fearsome perfectionism, his sense of search, his impeccable showman’s instinct for contrast and mood.

Working together was not always easy. During the rehearsal period, Bernstein would sometimes retreat across the street to a bar to avoid Robbins after a particularly unpleasant argument (though there are also stories of the two of them together, Robbins with his hand on Bernstein’s shoulder as he sat at the piano, revising music measure by measure, as if they shared one intelligence). Robbins was a fierce editor of the material until the very end, scrapping and reworking songs (“Something’s Coming” was written just a few weeks before the play debuted) and driving the actors to tears. The four collaborators gradually arrived at a shared vision, discovering what Sondheim later called “a wholeness” — a synthesis of dramatic language, music and dance.

Think of “Maria,” one of the most affecting love songs written for the stage. It’s so familiar now that it’s hard to hear its strangeness, the haunting tritone of the song’s first word, “Maria,” the very same notes that can be heard in the prologue (what has been called “the shofar”), establishing an atmosphere of threat. The tension in the music is softened by the lyric, which is reverent but also sensual, with Tony invoking Maria’s name over and over, as if the word could be made flesh. Or think of “Cool,” a song whose breezy slang (“Boy, boy, crazy boy, get cool, boy”) pulls against its thrashing melodic line — and also quotes that same tritone — evoking barely contained adolescent aggression that explodes into dance. Or the way “America,” an escalating argument between the Puerto Rican men and women about the humiliations and advantages of moving to the United States, culminates in a dance-off.