Some think the bassoon set them off. Others note the turned-in feet of the dancers. Whatever the spark, “The Rite of Spring” lore tells us that patrons became rioters at the Stravinsky ballet’s 1913 premiere in Paris. But the myth of that night rarely includes details about what the dancers wore, how they sweated through Nicholas Roerich’s wool shifts, bunched at their bellies with leather straps as belts, or how geometrical patterns on blood-orange fabric played tricks on anxious eyes in the audience.

Which is why the costumes of “Diaghilev and the Ballets Russes, 1909-1929: When Art Danced with Music” are so important to the National Gallery of Art’s exhibition, which opens Sunday and runs through Sept. 2. Borrowed from the Victoria and Albert Museum in London, the National Gallery of Australia, Canberra and Dansmuseet of Sweden, the yellowing fabrics bring the mythology of this fabled company down to earth in ways that Auguste Rodin’s sculpture of Vaslav Nijinsky cannot. With 38 costumes on display, the exhibition shows that the fashions of the Ballets Russes were just as essential to the company’s myth as the choreography or scores.

“Diaghilev proved that design wasn’t just accessory on the stage,” said Sarah Kennel, curator of the exhibition. “The company went over the top. There was a lot of imaginative creation and body-conscious designs that made the costumes daring and new.”

The costumes, pulled from the company’s two-decade run, display a broad range of fabrics and fashion aesthetics, from Henri Matisse’s satin robe for “Le Chant du Rossignol” to Coco Chanel’s knitted wool tanks for “Le Train Bleu.” The pieces helped the modernist craze spread from the stage to the street. Famous artists — Leon Bakst, Matisse, Pablo Picasso — lent their talents to the company from 1909 to 1929, bringing cutting-edge artistry to dancers and patrons as the company toured the globe. Most credit Serge Diaghilev, the charismatic impresario and director of the company, with recruiting Left Bank artists to design for his company.

The costumes complement the choreography, showcasing the extended movements of the dancers’ bodies. Alexandre Benois designed a traditional ballet costume for the Sylph in “Les Sylphides,” but the long white tutu wasn’t stiffened in the traditional manner, an innovation still seen on stage today.

“It’s a softer silhouette that some of the late 19th-century’s ballet tutus,” Kennel said. “It would flow with the dancer, showing this new idea of costume extending the movement of the body and complementing the body shape.”

Pieces from opulent ballets such as “Scheherazade,” a ballet adaptation of “The Arabian Nights,” illustrate how the company strived to balance historical accuracy with the audience’s appetite for spectacle. The jeweled and feathered costumes of “Scheherazade,” which Kennel said launched the craze for the Ballets Russes, drew on the history of Orientalism to bolster the company’s own lore as a group positioned between East and West. The costumes for the Polovtsian Dances from “Prince Igor,” a dance adapted from the opera about the nomadic Polovtsian tribes in present-day Russia, for example, included authentic silk ikat tunics woven in Uzbekistan.

“The Ballets Russes understood that French saw them as something incredibly exotic,” Kennel said. “They used the relationship between Eastern dress and Orientalism to revive the fantasy of Orientalism.”

Sometimes art overtook the structure of the costumes. Some pieces were impossible for the dancers to move in. Picasso’s cubist-inspired constructions in “Parade,” for example, were made of cardboard, a material that does not lend itself well to dance.

And as is the case with old clothes, worn costumes of the most popular ballets were less likely to survive after the company deteriorated in Monte Carlo in the 1930s. Many of the gilded costumes worn by Nijinsky have disappeared with time, leaving us with costumes of lesser characters and dancers.

Perhaps that is why the company’s most enduring design influence is not on display at this exhibition. Rather, it is being exhibited on stages, right now, in opera houses across the world. The company left a model for collaboration between designers and dancers, posing a challenge that artists continue to take up a century later.

In September, the New York City Ballet invited Valentino Garavani, now retired from his eponymous Valentino house, to design tutus and costumes for the company’s Fall Opening Gala. The company has worked with Stella McCartney, Joseph Altuzarra, Oscar de la Renta and Gilles Mendel. Marc Happel, the ballet’s director of costumes, sees the fashion industry’s interest in ballet as a relatively recent revival of this collaboration model.

“The Ballets Russes was much more artist-oriented,” Happel said.“ I think it’s more recent, in the last several decades, that fashion designers are putting their talents on stage.”

But whether fashion designer or artist, this collaborative approach to building the pageantry of the ballet is the lasting influence of the company. Without it, Picasso’s curtain, Chanel’s bloomers and, yes, even Valentino’s crisp red tutus of 2012 may have remained hidden in sketch pads, awaiting another muse.