Milwaukee-born Neumeier, 79, who has been artistic director and chief choreographer of Hamburg Ballet since 1973, has not only choreographed and directed this opera, but he also designed the sets, costumes and lighting, giving new meaning to the word, “Gesamtkunstwerk,” German for “total work of art.” With only three singers, Orpheus (the marvelous tenor Maxim Mironov), Eurydice (the clear-toned soprano Lisette Oropesa), and Amor (the engaging soprano Liv Redpath)—and a formidable chorus, led by Los Angeles Master Chorale artistic director Grant Gershon—the opera, based on the Greek myth of a singer able to bewitch hell’s Furies is, in a nutshell, about an artist and the transcendent power of art.

Make no mistake, though, “Orpheus” has long been a vehicle for choreographers, with L.A. Opera having mounted a production helmed by Lucinda Childs in 2003, and Mark Morris directing and choreographing the work with the Boston Handel and Haydn Society, which was performed at UCLA in 1996. And, in 1975, Pina Bausch tackled the opera with her own danced version.

Neumeier has updated his staging to the present, with Orpheus, the son of the god Apollo, a choreographer instead of a crooner, and his wife Eurydice, the troupe’s feisty star ballerina. The opera opens with the company rehearsing his latest work, “The Isle of the Dead” (also the name of Arnold Böcklin’s Orpheus-inspired painting of the same name, an image that is on view throughout the opera). Eurydice arrives late and the couple quarrels, prompting the prima to rage out of the studio, after which she slams her car into a tree (yes, the crushed vehicle—and tree—appear onstage), with Eurydice’s lifeless body sprawled nearby.

This scenario provides the jolt of shock and grief that sets the opera in motion. And what motion it is! Orpheus, wracked with guilt and singing, “Ah! Dans ce bois tranquille,” the forest spirits spinning around him as he tries to process his unthinkable loss, ultimately has a breakdown and imagines himself traveling to Hades to rescue his wife from the Elysian Fields. The doomed duo is splendidly doubled by Eurydice’s Victoria Jaiani and Orpheus’ Temur Suluashvili, the dancer’s real-life husband, with their moves as lyrical and incandescent as the singers’ luxurious voices.

Neumeier’s vision proves ideal for dance, with nearly four dozen members of the Joffrey embodying the characters’ inner lives, as well as helping provide scene transitions: The mostly movable sets are mirrored, with the chorus in the raised orchestra pit, occasionally allowing the conductor, L.A. Opera’s indefatigable music director, James Conlon, to be reflected on stage.

The Goddess of Love, a jeans-clad Amour (the only wardrobe misstep of the evening), offers Orpheus, who unfortunately—and unnecessarily—clings to a headshot of Eurydice (how does it even read in the upper tiers of the 3,600-seat venue), accompanies him into the underworld. There he confronts the 10 angry Furies and will be allowed to lead a revived Eurydice back to earth. Of course, that deal comes with a big caveat: At no time during their return together can Orpheus look upon his beloved’s face.

Neumeier’s otherwise inventive costuming includes wispy, earthen-toned gowns for the women and flowy, culotte-type garb for the men, as well as a green and silver-scaled version of Cerberus, the monstrous three-headed dog who guards the gates of Hades, here a trio of The Shape of Water aka “Grinding Nemo”-type monsters, poignantly danced by Yoshihisa Arai, Dylan Gutierrez and Alberto Velazquez. Seven barefoot couples offered thoughtful unisons as the Blessed Spirits of Elysium, their arms wielding Nijinskyesque patterns to the familiar but always lovely music (L.A. Opera Orchestra sounded particularly crisp and dreamy), with an octet of Shadows adding to the terpsichorean flow.

In the end, of course, the tenor doesn’t get to spend the rest of his days with his woman, as Gluck (but not the Greeks) intended, at least not in the normal sense: Here, Orpheus’ deceased wife will remain with him, but, alas, only in his heart.

And while the first “L’Orfeo” was composed by Monteverdi in 1607, with numerous iterations since, it is curious to note that at the turn of the last century, Böcklin’s painting was also extremely popular, finding its way into works by late Romantic composers and the playwright August Strindberg, while copies of the painting were even displayed on walls by such disparate types as Freud and Lenin. Neumeier, whose alluring and exquisitely rendered portrait of an artist in crisis, can now add his name to the list of “Orpheus” interpreters, with his emotionally charged, albeit fiercely delicate aesthetic making him an auteur of the highest order.

Postscript: The Chicago-based Joffrey Ballet, under the artistic directorship of Ashley Wheater, is doing double duty while in town, also performing the balletic tragedy, “Romeo and Juliet” (two more performances, March 17). However, as choreographed by Krzysztof Pastor for Scottish Ballet in 2008, this updated version that includes scenes of fascist Italy in the 1930s, the starchiness of the 1950s and a nondescript ode to the 1990s, is a complete misfire. After all, how can Romeo (Dylan Gutierrez seen by this reviewer in the March 11 performance), be taken seriously sporting a pair of Dockers, while Jeraldine Mendoza’s Juliet pouts and preens in an elevator—or what set and costume designer Tatyana Van Walsum has crafted to be a balcony. Going down …