On Tuesday evening the New York City Ballet explored its experimental side with Balanchine’s “The Four Temperaments” and Christopher Wheeldon’s “Polyphonia.”

Both dispense with many of ballet’s conventional trappings (tutus, for instance, in favor of camisole leotards and muscular T-shirts). Unsheathed, the bodies of the dancers are like weapons in their sharp, angular combinations, but both choreographers wield them scrupulously to promote the classical virtues: a plumb line, balance, and precision.

For this abstract ballet, Balanchine relied on a clearly deployed structure, taking his cue from the medieval doctrine of the four humors, each one corresponding to a variation in Paul Hindemith’s commissioned score for piano and orchestra. But the tidiness of the organization, which in the hands of a lesser choreographer would spell boredom or worse, demonstrates Balanchine’s remarkable ingenuity. There is no space-filling cartilage; the structure never overrides the beauty and rich suggestiveness in the dancing.

Many of the images that fill the opening “Themes” have become icons of the repertory. Standing beside each other, Faye Arthur and AndrewVeyette cross their arms repeatedly. Their simple gestures introduce a counterpoint already suggested by their black-and-white uniforms. With an ear-high kick, Ms. Arthur announces the score. Holding her body rigid, Mr. Veyette torques her in a quick promenade. She forms an attitude with her right leg, hooking him first between the knees and then over his neck.

Peter Boal impressively embodied Melancholy. He leaps childishly at first, one arm sticking to his extended leg, and then collapses, losing heart. Although he is not as limber as he was in previous seasons, he brings his experience as an expressive dancer to the role. His long arms can move insinuatingly, gaining dramatic force with each stride. He stammers his feet noiselessly until the ensemble enters, perfectly deadpan, kicking their legs high into the air and jutting out their hips.

Alexandra Ansanelli replaced the injured Sofiane Sylve in her duet with Charles Askegard as the sanguine couple. Although the height difference between them exaggerated their partnering, Ms. Ansanelli acknowledged the fact proudly in their fleet backward shuffle and giddy high-step. Albert Evans chased an evasive object as the phlegmatic figure, folding his arms gill-like. He displayed real ambivalence, trying to pump himself up like a runner at the starting line and eagerly accepting the ensembles’ offered hands. But once the cadence picks up, his spine goes flaccid. Teresa Reichlin stridently interprets the choleric woman. Spurning her partner, she feverishly scoops and swivels, leaping and shivering, before collapsing from exhaustion. Both invention and nuance give these otherwise static personifications an uncommon grace.

In “Polyphonia,” Mr. Wheeldon produced a suite that adds up to more than the sum of its parts. One of his first pieces, it is his most successful, confirming with each new performance his ascendancy in the ranks of the company to become its first resident choreographer. With the exception of Miranda Weese, Amar Ramasar, and Andrew Veyette, the original cast performed, having matured in their roles. Clearly, Mr. Wheeldon has drawn upon each dancer’s strengths, whether Alexandra Ansanelli’s warmth in her introspective solo or Wendy Whelan’s flexibility in her duet with Jock Soto.

Greek for “many voices sounding simultaneously,” “Polyphonia” lives up to its name.

Gyorgy Ligeti’s score is a challenging selection of 10 excerpts from six works arranged for a regular and prepared piano. Cameron Grant and Susan Walters both gave committed performances. The avant-garde composer did not shatter the musical conventions of melody and harmony so much as melt it down into a molten flow of rhythmically dense, chromatic textures.

But the choreography smartly anticipates the music, blending vigorous displays of classical steps with quirky hand exercises, contemplative tableaus, and swooning romantic partnering. Each section is paced to rivet the viewer: two etudes introduce a recognizable waltz; a jumpy allegro slows down to a measured legato.

On a stage, dramatically front-lit, the ensemble of four couples leaps to life in propelling combinations. As they step forward, their flickering shadows loom larger on the wall behind them. A duet between Ms. Whelan and Mr. Soto follows. Gripping each other’s hands (pointing ahead to the waltz?) they gesture together in a diving motion. Ms. Whelan assumes her signature role as the ballerinacum-contortionist, floating on Mr. Soto’s knees as if asleep. Her flexibility elicited gasps from the audience. To a selection titled “Arc of Heaven,” she lay on his outspread palms, bending backward, and slowly dialing over him pensively.

The theme is repeated in their second duet near the end, enclosing the work. Only the haunting music gives Ms. Whelan’s extensions a menacing look. Covered in shadows, the two crouch together, appearing almost egglike – tender and possibly even fragile. But Mr. Soto pries her limbs apart. Only her legs are visible as he tilts her frame around like a compass needle. A lurid, sexual aura settles on their final stretches.

Ms. Ansanelli adds a much-needed delicacy to the work in her adagio with Craig Hall. She wafts around him like a flag around a pole. Her solo, however, was even more enchanting. She raises her hands in a suppliant gesture, circling the stage. Her movements were unemotional and hieratic, but also with a touch of vulnerability.

But the key to the unity of “Polyphonia” can be found in the fluid transitions and ensemble patterns. We see Miranda Weese, Jennifer Tinsley, and Alexandra Ansanelli leaning forward doing what might as well be warm-up exercises, but they visually match the syncopation in the score. The same is true for the skating duets and horizontal lifts. Physical motifs, uninteresting in themselves, are amplified by a group in unexpected ways.

“The Four Temperaments” will be performed again May 25 & 28 at 8 p.m.; “Polyphonia” will be performed again May 21 at 2 p.m. & May 28 at 8 p.m. (Lincoln Center, 212-870-5570).