Wendy Whelan has had a date with Balanchine’s “Bugaku” for many years, but it wasn’t until this month at New York City Ballet that the rendezvous came to fruition. May marked Ms. Whelan’s debut in this ballet that contains significant links in the series of knotty and complicated duets that Balanchine created during the late 1950s and early ’60s. In this repertory, Ms. Whelan had for years tangled her legs into the most extreme and unorthodox of cat’s cradles. But she had not yet availed herself of the opportunities presented by “Bugaku,” to turn her entire silhouette in on itself in an ingenious reimagining of the archetypal centripetal stances of Asian dance and theater. At NYCB’s performance last Friday, she was able to immerse herself in this material.

“Bugaku,” made in 1963, was inspired by the Japanese Imperial troupe of Gagaku musicians and dancers, who shared bills with NYCB during a New York visit in 1959.

The ballerina and her partner, who was danced Friday by Albert Evans, each trail a retinue of four men or women. They are all confined to the parameters of a pavilion-like inner stage, thus reminding us of their status as entertainers and highlighting that what unfolds contains a note of ritualistic certitude. The “Bugaku” ballerina can seem like courtesan, or a bride who is virginal or not. Ms. Whelan had a sophistication that indicated that this was anything but a deflowering; rather, it was as if a treaty was being ratified. Ms. Whelan had brought to the marriage lands, titles, hereditary honors, as well as many qualities of personal charm and authority.

Ms. Whelan may have gained a little weight to dance this ballet; minute as the extra poundage may have been, it nevertheless better allowed her to look uncommonly sensuous when, following a disrobing by her handmaidens, she began a climactic duet of connubial consummation.

NYCB’s “World Tour” program continued after an intermission with three short ballets by Peter Martins and Christopher Wheeldon. Mr. Wheeldon’s “An American in Paris” gives us inarguably fetching and enduring but nevertheless familiar emblems of Parisian street culture. The show highlights the costumes by Holly Hynes, which seem lifted from couture styles contemporary to the Gene Kelly movie rather than to the date of Gershwin’s musical creation. “An American in Paris” is certainly slight, but diverting enough, particularly as danced on Friday with charm by Damian Woetzel — a prototypical painter and both observer and participant in life — Tiler Peck, his gamine muse, and Sara Mearns as a boy-girl Beatnik.

In Mr. Martins’s “Valse Triste,” Darci Kistler is a woman of parts, whose eloquent recollections of a man in her past, or, perhaps, in her imagination, flit back and forth before our eyes. Ms. Kistler and Jared Angle repeated and even improved upon their excellent performances of last season. Mr. Angle was both dominant in Ms. Kistler’s consciousness but recessive, subject to the vagaries of memory. This was followed by Mr. Martins’s “The Chairman Dances,” performed to John Adams music composed for, but ultimately dropped from, his opera “Nixon in China.” Teresa Reichlen fearlessly led a cast of what seems to be thousands that was actually only 16 women strong, taken to the streets or the stadiums of mass popular pageant. Paraded as “Chairman” progresses is the tucked-in flower petal imagery we’d seen in “Bugaku,” as well as arm swishes and averted head positions, lightly draped over an athletic minimalism boldly essayed by Ms. Reichlen and her sisterhood.

Friday’s performance closed with Alexei Ratmansky’s “Russian Seasons,” in which Ms. Whelan returned to dance another bride of sorts. She moves in this ballet from integrated member of a community to the slightly off-center position of local eccentric and then finally to victim of romantic betrayal or delusion. Here she is garbed in a white dress with a white chaplet on her head, but this is a more barren white than the filmy, pale draperies that had accompanied her triumphant progression throughout “Bugaku.” Her arabesques are wonderfully descriptive here: Her torso is lifted but her working leg trails desolately. Mr. Evans, who had earlier been her “Bugaku” consort, now is also in white, attending her as doctor or counselor. Also outstanding in this performance was Georgina Pazcoguin, dancing a kind of jostling incitement to revolt that contains some of Mr. Ratmansky’s best choreography in the ballet.