On a snowy morning in February, Violette Verdy walked into a well-lit rehearsal studio seven stories above Broadway. At 81, the former ballerina, best known for her 20-year collaboration with George Balanchine at the New York City Ballet, is a striking woman, petite and vivacious, with eyes the color of stormy seas. (“My mother said they change with the weather,” she told me.) She wore her signature work attire: matching tights, knee-length skirt, and top, all in the same shade of dark blue, and complemented by a pair of bright-red ballet flats. If one looked closely, one might have noticed that her shoes were held in place not by elastics or ribbons, but by matching rubber bands, the kind shelved next to the paper clips at Staples. Verdy displays the pragmatism of someone who is utterly comfortable in her skin.

As soon as she entered the room, Verdy was surrounded by friends and admirers. Some had shared the stage with her or watched from the wings during the 1950s, ’60s, and ’70s, when she was one of New York City Ballet’s most celebrated dancers in what she calls the “19th century and a half” repertory, by which she means ballets that make reference to 19th-century themes and traditions while applying the innovations and refinements of 20th-century technique. Verdy had a word for each person who approached her. Hers is an irrepressible friendliness.

Verdy and one of her former dance partners, Jean-Pierre Bonnefoux, were in New York to work with Ashley Laracey and Chase Finlay, two young dancers from New York City Ballet, on the finer points of Sonatine, a work that Balanchine had created for Verdy and Bonnefoux in 1975. The session was to be taped and edited by the George Balanchine Foundation for its video archives, part of an effort to preserve and document the subtleties and details of style that define each of Balanchine’s ballets. (“It’s about a very tenuous thing called atmosphère,” Verdy explained.) Such nuances are the first thing to fray when a ballet is passed on from one dancer to the next. If care isn’t taken to explain and preserve them, or at least consider them, choreography becomes an empty exercise, a relic, like a poem loaded with forgotten allusions, or a painting retouched by too many hands. It just fades away. “Ballets are like butterflies,” Balanchine said, and he wasn’t wrong.

Videotaping can capture an impression of a performance, but it fails to elucidate the reasoning behind the steps, or the feelings they were meant to evoke. Notation, when it is used, offers an abstracted score, a guide to what happens when. But nothing can replace the guidance of a person who has danced the role many times and knows its secrets. In ballet, these coaches, or ballet masters, embody an oral, body-to-body tradition that has existed for centuries. (It is central to most forms of dance.) In the case of works from the 19th century—say, Swan Lake—the ballerina is imparting the accumulated wisdom (and sometimes the excesses) of her predecessors. But in the case of 20th-century dances, many of the original interpreters, like Verdy and Bonnefoux, are still with us. They worked with the choreographer and remember what was said—or left unsaid—in the room as the steps were made. Like the annotations of a biblical scholar, their insights illuminate a shared text.

The Sonatine coaching session began. After the pianist, Elaine Chelton, played the opening melody of Ravel’s 12-minute piece—while the dancers listened—Laracey and her partner calmly walked forward from a corner of the studio, arm in arm as if embarking on a leisurely stroll. Three times, on a lilting, descending four-note figure, Laracey stepped pensively onto the tip of one toe, then tilted off, as if testing her balance or toying with a thought. In her prime, Verdy was known for the pinprick quality of her pointes and the beautifully turned-out line of her legs, exposing an expanse of strong, pulled-up thigh. Clearly, Balanchine had wanted to show off these qualities in Sonatine. Verdy stopped the dancers after a few steps, as if experiencing a rush of memories. “It’s like a walk in the park,” she said to Laracey, “more natural, less held.” In a blurry old film at the New York Public Library, one can see exactly what she means: Verdy’s trajectory has an unstudied, natural feel. She looks windswept; the movement’s impulse seems to come not from her well-developed muscles but from outside of her body.

Verdy encouraged Laracey to sway her hips more as she walked and to take liberties with the timing, “as if you’re singing to yourself, inventing it on the spot, and you’re not onstage at all.” During the second movement, a minuet, Laracey carefully unfolded one leg in such a way that the action appeared perfectly smooth, uninterrupted. Verdy stopped her: “Remember, not too lyrical, a little more folk.” The dance’s Slavic folk elements—a turned-in knee, a hand on the hip, a little horselike prance—began to come into relief, accentuated by pauses and minute changes of timing. The steps developed a flavor. “Feel the slight syncopation here,” Verdy pointed out, referring to the way an accented step slightly anticipated and held the beat. Through these touches, Balanchine and Verdy had turned Ravel’s lilting minuet into a kind of modified mazurka. The dance alternated between French nonchalance and the earthiness of Slavic folk dance. It was this blending of styles that made it interesting. As Verdy said later, “It was a delicious zakouski.”

Something else Verdy seemed intent on drawing out of the dancers was a more palpable sense of interplay. Often, with practice, the push and pull of partnering disappears; the dancers know what’s coming next, so they prepare in advance, anticipating the next move. “Show resistance here,” Verdy suggested to Laracey as Finlay pulled her toward him, “and then spin.” That way, the passage no longer looked like a smooth, well-executed series of partnering moves, but like a call and response, a conversation between two people. “It was almost like listening to Violette when we danced it,” Bonnefoux explained in an interview after the session. “My whole body was listening to what was happening to Violette’s body.” This feeling of attunement is what makes the steps resonate with deeper meaning. Take the dancers’ exit at the end of the first movement: The woman faces forward, toward the wings, the man backward. He is behind her. Their arms are joined overhead. Slowly, gravely, she pulls him into the wings. He can’t see where he’s headed, but allows himself to be led all the same. The audience sees an image of obligation and trust, of a man’s subjugation to a woman. The image adds a note of mystery and wonder to an otherwise sunny duet.

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Sonatine was the last ballet Balanchine made for Verdy before she retired, in 1977. She was 43 and had already suffered for years from various dance-related injuries. By then, Verdy had been dancing for all but nine years of her life. She was born Nelly Guillerm, in 1933, in the small medieval town of Pont-l’Abbé in Brittany, the only child of a shopkeeper (father) and a schoolteacher (mother). When her father died of kidney failure, only a few months after her birth, Nelly’s education was taken in hand by her capable and protective mother, Jeanne, who soon decided that the child’s highly strung, sensitive nature should be channeled into an edifying activity: ballet. With this in mind, she packed their bags and moved them to Paris. It was 1942, the middle of the Occupation.

Because the Paris Opera Conservatory of Dance was not taking auditions, Madame Guillerm was directed to Carlotta Zambelli, an Italian-born former opera star who now ran a private studio. (Verdy’s early training is vividly evoked in Victoria Huckenpahler’s 1978 biography, Ballerina.) Through the grapevine of ballet mothers, she heard of Rousanne Sarkissian, an Armenian teacher with Russian training. Young Nelly acquired different skills from each: strength and technique from Zambelli, an almost religious devotion to the art from Sarkissian. “She had a great spiritual dimension,” Verdy told me recently, “so from the start, I had a vision of ballet as a high activity.” It was a vision that would guide her through her dancing career and on into her work as a company director and teacher.

In her early teens, Nelly began to tour with Roland Petit’s Ballets des Champs-Elysées and later with his Ballets de Paris, dancing small roles at first, then the leads. She was the loving young bride in Petit’s Le Loup (a retelling of “Beauty and the Beast”) and the sexy, doomed gypsy in his adaptation of Carmen. One of her companions on these tours was Leslie Caron, who would go on to star in An American in Paris and Gigi. (“I felt rather bland next to her,” Verdy said.) The dancer’s theatrical flair, adaptability, and unmannered classical technique led to a starring role in a film, Ludwig Berger’s Ballerina, as well as stints with the London Festival Ballet and Ballet Rambert and, eventually, in 1957, to an invitation from American Ballet Theatre in New York. By then, she had become Violette Verdy, a name that, to her ear, sounded more sophisticated than Nelly Guillerm. It was in New York, at a performance of Birgit Cullberg’s Miss Julie, that Balanchine noticed her. When ABT briefly shut down operations—it was always disbanding and getting back together in those days—the choreographer asked her to join his company, New York City Ballet.

The offer came as something of a surprise. Balanchine was known for his love of tall, leggy, and fearless American dancers whom he had trained in his own, more dynamic, streamlined technique. They were cool and didn’t overlay the steps with their own personalities. He preferred to let the steps speak for themselves. With the exception of her fearlessness, Verdy did not embody this type at all. “I was more of a French poodle than a borzoi,” she likes to say. Her technique was Old World, her stage personality strong. She liked to flavor the steps. And yet, Balanchine wanted her. As she explained in the oral biography I Remember Balanchine, he “may have wanted to work with me because of a certain clarity in the articulation of the feet and legs”—a characteristic of the European school in which she had trained—“some sort of eloquence, a pronunciation of the dancing. Something to be joyous with…. What he had to do was to tone me down a little bit. I had a little too much garlic. He had to keep me quiet and busy.”

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To keep Verdy occupied, Balanchine made witty, joyous ballets for her to dance, like the buoyant Tchaikovsky Pas de Deux, La Source, and, of course, Sonatine. Often, but not always, they were set to French music. They seemed to reflect her temperament and her past. Of La Source, a sparkling, hyperfeminine work that took as its inspiration the ballet music of Léo Delibes, Verdy told her biographer that it was like a “transfusion out of my own blood.” Balanchine also cast her in other ballets, works that relied on charm, esprit, and brilliant technique, like Donizetti Variations, Allegro Brillante, and Stars and Stripes. To all, she brought her own particular accent, at times even daring to add her own twist to the choreography. Huckenpahler recounts that at a performance of Donizetti—a frolic set to infectious melodies by the bel canto composer—Verdy peppered a series of turns with little hops, like popping champagne bubbles. As she came offstage, Balanchine, who stood in the wings at every performance, bowed semi-seriously and commented: “Spécialité de la maison!” To which she responded, without batting an eye: “Plat du chef.” This kind of tac au tac was anything but typical in the company.

Balanchine and his fellow choreographer at New York City Ballet, Jerome Robbins, quickly realized there was more to Verdy than sparkle. Both created roles for her that called for introspection, complex emotions, and the ability to suggest layers of buried subtext in the steps. In his 1969 Dances at a Gathering, set to Chopin piano pieces, Robbins cast her as a woman in green who appears halfway through the ballet, an isolated figure who dances for her own pleasure, giving herself airs, reveling in her own charms, perhaps remembering past conquests. With small pauses, sudden changes of emphasis, flashing glances, and alternating staccato and legato movements, Verdy was able to evoke a wide range of emotions, both real and affected: insouciance, self-importance, vulnerability, an underlying loneliness. The woman in green became a multidimensional character, despite appearing onstage for only a few minutes. Verdy was particularly skilled at navigating the fine line between sincerity and affectation. During a coaching session captured in the film Violette and Mr. B, she explains the difference between two moments in a pas de deux from Balanchine’s Liebeslieder Walzer. “Pretend to be submissive here,” she says to the Spanish dancer Lucia Lacarra. “But, you know, I think the second swoon is for real. Like something out of Max Ophuls’s [The Earrings of] Madame de….”

How should a dancer show such things, without words? In part, by using the music. But then, not all dancers are particularly musical. They are trained to listen and count and follow certain cues, to start with the first note of a phrase and end with the last, but this is a superficial definition of musicality. A musical dancer helps you to see and feel the music in your own body; a dancer with a superior musicality goes even further, playing against the music, entering into a conversation with it, bending it to her own wishes. This is the kind of dancer Verdy was. Such musicality is innate. Verdy already had it as a child; when she heard music on the piano, “I just had to participate, I had to do something about it,” she told an interviewer. Having studied piano and violin, she had a grasp of the structures that underpin music: rhythm, the mood evoked by certain tonalities, the workings of counterpoint, the excitement of syncopation. And she understood phrasing, the changes in topography that give music its character. “It’s like speaking,” Verdy told me. “If you’re going to emphasize a certain thing, then you can slide over something else. Phrasing is a recognition of the values of talking, of thinking; it’s an evaluation, an itinerary.” Like her explanations, Verdy’s dancing was articulate.

Imagination is the alchemy that turns musical values into meaning. Take “Emeralds,” the opening section of Balanchine’s Jewels, a triptych inspired by the contrasting sound worlds of Fauré, Stravinsky, and Tchaikovsky. The choreographer created a solo that began with Verdy admiring the movement of her own arms. In the film Violette and Mr. B, she explains, “Je faisais des ondes” (“I made waves”). She demonstrates the effect, showing the character’s diaphanous, billowing gestures. Then she begins to delve into the dance’s deeper layers:

It’s an exploration of two themes, aspiration and resignation. It’s about hope, aspiration, desire in all its forms, and resignation, more or less noble, more or less consensual, more or less aloof, more or less calculated, more or less innocent. You can see the aspiration here in this fouetté [she shows a decisive pivoting of the body with arms raised]. And here you see the resignation, in this little thing [a falling back of the upper body], and in the arms that say, “No, I can’t. But wait, maybe after all I can—one never knows.” Then you seek elsewhere: “Maybe it’s here— or here.” You play with elements of doubt and conviction.… After all, the sorrows of life can be turned over, like a crêpe suzette. It was Shakespeare who said, “Sweet are the uses of adversity.” Disappointments, limitations, can be turned into beautiful things.

All this, in a minute or so of choreography. The explanation is typical Verdy, a mixture of the intellectual (Shakespeare), the physical, the emotional, and the domestic (food, a frequent point of reference for the former ballerina, who knew hunger during the war). Like Laracey during the Sonatine taping, the young dancer on the receiving end of this deluge of references strains to keep up with her train of thought, to sift through it for ideas with which to color her own performance. Verdy’s mind is like a ticker tape, clicking incessantly, a never-ending stream. It’s impossible to grasp it all, but even a tiny fraction can profoundly change a performance. “I just walked away with a new sense of self and perfumes to play with onstage,” Laracey told me of working with Verdy. “It’s like nourishment; I still try to think about it daily.”

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Shortly after her retirement from the stage, Verdy returned to France to lead the Paris Opera Ballet for three tumultuous years from 1977 to 1980. It was a difficult time: She was overwhelmed by the politics of leading a large, state-run company, the difficult negotiations with unions, the administrative responsibilities, the need to make ruthless decisions about casting and dancers’ careers. Then, after a change of leadership at the Opera, she was replaced. From there, she went to direct the Boston Ballet. Again, there were problems, particularly the constant need to raise funds that kept her from the place she wanted to be: in the studio with the dancers. She lasted four years. “I discovered that it wasn’t for me to be a director,” Verdy told me. “I’m not made to be the number one of anything. I’m a very good number two, and if I have to be number three, I might not even protest, if I’m working hard enough. I’m interested in a form of humanity that you cannot have when you are a director.”

Teaching suits her best. Since 1996, Verdy has been on the faculty of ballet studies at Indiana University, Bloomington, the only program of its size and importance at an American college. (Many students graduate with a combined degree in ballet and a field of academic study.) She still travels to coach dancers and to teach elsewhere in the United States and in Europe. Last winter, I watched her gently put a class of 16- to 18-year-olds through its paces at the School of American Ballet, the training program associated with New York City Ballet. Verdy has a knack for finding just the right words with which to cajole a young dancer toward a fuller understanding—and thus execution—of a step. (“It’s like a horse who’s having a very good time!” she said to one girl as she launched into a series of small, sprightly jumps.) “Her body fell into that way of moving, but she can articulate it in a very methodical way,” explains Kay Mazzo, the cochair of SAB. “It’s all very well-thought-out, with the energy and the musicality combined.” Verdy’s smiling voice encourages improvement for its own sake; it also reflects an undimmed love for the art of ballet. “She’s very playful,” says Mazzo, “and the students adore her.” Like the Advaita Vedanta school of Hinduism she has quietly practiced since the ’60s, ballet, for Verdy, is a spiritual pursuit: “I feel the obligation to make people consider that this is not just a physical activity, a physical technique, but that it points to something higher,” she told me. This belief bound her to Balanchine, in whom she intuited a similar idealism. “If you’re going to have a guru in the world,” she added, “Mr. B was it.”

Soon, Verdy thinks, she might like to teach less and devote more time to gathering materials for her memoirs. She’s not sure whether she will stay in Bloomington—she doesn’t drive—or return to her hometown of Pont-l’Abbé. Where does she belong? Verdy was married briefly, in the ’60s, to Colin Clark, a British filmmaker (and the author of My Week With Marilyn). It didn’t end well. She has no children. Ballet has been an all-consuming pursuit, leaving little space for family or anything else. “The family I have in Paris is not that much,” she reflected recently. “In Brittany, I have more, but they have complicated lives. So, in a way, I’m more or less by myself. I’m a bit of an odd number now.”