The premiere of Stravinsky’s “The Rite of Spring” in 1913 is often cited as a flash point in the divide between new music and its audience. People began shouting, booing so loudly that the dancers could no longer hear the orchestra. The audience, conventional wisdom had it, still cared about contemporary music, and was outraged when it got too strange, dissonant, “ugly.” From this point on — so the claim goes — the chasm widened between composers pursuing their own agendas and audiences wishing they could just be left alone to hear Mozart.

This claim, however, is grossly incorrect. It’s not just that the detractors in the opening-night “Rite of Spring” audience were reacting to Nijinsky’s angular, jagged choreography as much as, if not more than, Stravinsky’s music; the piece returned soon thereafter and met with widespread interest. And while the work is often and correctly cited as one of the artistic milestones of the Ballets Russes, it would be an egregious misrepresentation to say that the Ballets Russes turned people off new work. It was just the opposite: rather than dividing the audience from new music by ramming the avant-garde down people’s throats, it created something brand-new and made it wildly popular throughout European society.

Indeed, the Ballets Russes’s relationship with music is, if anything, a story of synthesis. The company’s use of music paved the way for dance to have the easiest relationship with contemporary music of any of the performing arts — at least in that dance audiences are less likely to shrink back at the prospect of a contemporary work. The Ballets Russes also helped shape the 20th-century musical canon. Of all the arts that were fused in the glorious synthesis that was the Ballets Russes, music is the easiest to replicate, and while the dances are only sometimes reconstructed, many of the scores are familiar concert-hall fare.

This is partly because the Ballets Russes was a catalyst for musical masterpieces. Picasso worked on five different productions for the Ballets Russes, but no one would place his curtain for “Le Train Bleu” on a par with, say, “Guernica,” his 1937 painting protesting the Spanish Civil War. By contrast, Maurice Ravel’s “Daphnis and Chloé,” written for the Ballets Russes in 1912, is one of the highlights of that composer’s oeuvre, and the same could be said of Prokofiev’s “Prodigal Son” (1929) or of the Stravinsky ballets — notably “Rite,” but also “The Firebird,” “Petrushka,” and several others — that helped launch both the company and Stravinsky’s career.

Serge Diaghilev, the visionary impresario who made the Ballets Russes such a dominant artistic force, had an eye for talent. He also had an eye to good box office. Like the Italian opera impresarios of the 19th century, he was running a for-profit operation. He was committed to seeking out the greatest and newest art, but he also wanted to find things that would make people want to buy tickets. Music lovers today, quick to condemn commercialism as the enemy of art, should perhaps consider that some of the most significant works in the canon were created on a commercial, money-making basis — including “The Rite of Spring.”

They were also, for the most part, narrative ballets. You wanted music that told a story, conveyed a rhythm, and had some melody (“Daphnis and Chloé” fits the description). Praising the 1925 “Zéphire et Flore” by the young composer Vladimir Dukelsky, Prokofiev called it “harmonically beautiful and not too ‘modernist,’ ” and meant the words as approbation, not disparagement. Dukelsky did indeed have an ear for melody; he later changed his name to Vernon Duke and made a big career as a songwriter.

Rather than signaling the start of the divide between art and populism, the Ballets Russes represented one of the last healthy syntheses of the two. It also represented a chance for some artists to make real money. Stravinsky made multiple versions and revisions of his early Ballets Russes scores, especially “The Firebird,” not because he was rethinking his original work a la Bruckner, but because the works were in copyright and he needed to be able to make money from them. The United States, where he settled in the late 1930s, did not recognize European licensing agreements. For “Petrushka,” the composer created a significantly different score for smaller orchestra in 1947, but the main purpose of his 1945 revision of “Firebird” was to make money.

As for “The Rite of Spring,” this unpopular, divisive work ended up being the centerpiece of a Disney film (“Fantasia”) — the quintessential mass-market medium. Amid all of the discussion that has accompanied the centennial of this seminal work, it’s helpful to lose the idea that this piece drove audiences away from contemporary music and recognize that the Ballets Russes in fact represented, if anything, the populist side of the equation.