To see the José Limón company is to enter a completely different world from today’s contemporary dance. The company’s recurring message is recurrence itself — the ages of man and woman, universal life cycles. On Tuesday at the Joyce, the company celebrated a step in its own cycle of existence — the 60th anniversary of its founding.

Tuesday night’s performance opened with Limón’s “Dances for Isadora: Five Evocations of Isadora Duncan,” created in 1971, the year before he died. Limón was already ill, and since Duncan was a formative figure in his development, the creation of this piece represented a full circle of sorts. The historical overview proposed by this piece is that there are no clean breaks in the line of descent of modern dance. Duncan’s story and movement are seeded with some of Limón’s own vocabulary, which reminds the viewer of the debt all modern dance choreographers owe to Duncan. “Dances For Isadora” is a continuum of cross-referencing, chronicling the give-and-take of influence.

This treatment of a historical figure becomes a prime vehicle for the simultaneously specific and archetypal identities that mark the Limón troupe’s repertory. Duncan is given something of an Everywoman flavor, emphasized by the section titles that refer to mythological and iconographic personifications.

Different women dance to a selection of Chopin piano pieces, charting Duncan’s aesthetic epochs and episodes from her life. Kristen Foote is “Primavera,” re-creating Duncan’s neo-Attic gambols, using wending hands, hovering poses, skips, bourrées in place, and falls to the ground, with the suggestion of space as a resistant buffer. In “Maenad,” Ryoko Kudo dances in the heroic, declamatory style of Duncan’s “La Marseillaise” which here is also visualized in the vein of Martha Graham’s social protest pieces of the 1930s. There are crashing jumps to the floor, and landings with knees splayed.

In “Niobe,” Kathryn Alter is a majestic doyenne, wearing robes of a high priestess.

Her cradling movements allude not only to the mythological Niobe’s grief, but to the death of Duncan’s children. She shudders along in extremis. The lights go out, and Roxane D’Orléans Juste enters in red dress with Grecian top. Planted in second position, she sways, hoisting a red banner as “La Patrie,” thus referencing Duncan’s visits to Russia before and after the revolution, and her marriage to Russian poet Sergei Esenin, with whom she championed the birth of the Soviet state.

The final “Scarf Dance” depicts Duncan’s sodden last years. The Limón company’s artistic director, Carla Maxwell, wears a ruffled gown that could be a peignoir or a flamenco dress. Indeed, there are images of the bullfight as Duncan confronts her past and her demons.

In silence, all the previous incarnations of Isadora return for a recapitulation, and it is possible to see Limón’s integration of himself into Duncan here. The “Niobe” and the dissipated “Scarf” Isadoras face each other on their knees. Finally, inevitably, Duncan’s own scarf becomes a noose.

Doris Humphrey’s 1947 “Day on Earth,” set to Aaron Copland’s Piano Sonata, gives us the life and death of a universal family unit, from a man’s adolescent dalliance to his coupling with his mate. “Day on Earth” ends with all covered by a sheet, except the emerging future in the person of the girl who plays the couple’s daughter.

Within today’s context, “Day on Earth” runs the risk of seeming overearnest, or almost trite. But regardless of whether it skirts banality at times, “Day on Earth” makes its point and makes it kinetically. The movement is slantwise, full of legs and shapes that swing open and closed, performed with skill and dedication by Raphael Boumaila as the hero, Ms. Juste taking on the role of the mother, and Ms. Foote playing the first love; Morgana Cragnotti was the daughter.

The company closed its opening night program with “Recordare,” a new work it commissioned from Lar Lubovitch that pays tribute to Limón’s Mexican heritage. It is inspired by the Mexican Day of the Dead, in which the spirits of the dead are welcomed home. “Recordare” showcases liturgical ritual and its transference to Dark Ages theatrical spectacle, and its continued existence in the folk culture of Catholic nations.

“Recordare” becomes a celebration of immortality. The piece takes a comic view of death’s inevitability and ubiquity by employing a personification of death that cavorts like a zany jester. The curtain rises again and again on a miniature proscenium to reveal new personages who rise forth and do battle with death. “Recordare” succeeds as an homage to Limón and his cultural roots, as well as a diverting way to conclude the evening’s entertainment.

Until November 26 (175 Eighth Ave. at 19th Street, 212-242-0800).