Was it perversity or indifference or a mixture of both that led the New York City Ballet to schedule the Kennedy Center premiere of George Balanchine's "Robert Schumann's 'Davidsbundlertanze'" last night in the middle of the second week of a two-week run, and then to trot out this enormously challenging, not to say perplexing, 45-minute work at the tail end of a long, weighty program that also included Balanchine's "Brahms-Schoenberg Quartet" (four movements), his "Concerto Barocco" (three movements), and the Washington premiere of Jerome Robbins' "Suite of Dances" (from "The Dybbuk Variations"), to a particularly knotty Leonard Bernstein score?

Whatever the motivation, the placement cannot have been much help toward the perception of "Davidsbundlertanze," which is taxing enough to need all the enhancement it can get. The tepidity of the audience reaction may have been partly due to fatigue, which is perfectly understandable, and partly to bafflement, which is undeniably an appropriate reaction upon first encounter with the new opus.

Advance reports had led one to expect something unusual, even strange. But even the strangeness is elusive -- there's nothing shocking or kinky or radical-looking here. Yet "Davidsbundlertanze" is unsettlingly different from any other Balanchine work one can recall, and even more different from anyone else's ballets, in both atmosphere and style.

If you're looking for elucidation or appraisal, you won't find much of it here; this is a ballet that decidedly demands multiple viewings for both appreciation and comprehension. In one sense, it is very simple -- a series of dances for four couples, (Karin von Aroldingen and Sean Lavery; Suzanne Farrell and Jacques d'Amboise; Sara Leland and Ib Anderson; Heather Watts and Peter Martins), set to the cycle of piano pieces by Schumann from which the ballet takes its name, dances by turns contemplative, troubled, vivacious, romantic, mysterious and melancholy.

Balachine himself has warned against looking for latent philosophical or biographical significations in the work, despite the fact that the "Band of David" of the title was the composer's imaginary league of warriors against artistic philistinism. Yet if the feeling persists on seeing it that the ballet has aspects of romantic allegory, the reasons are visible enough. When the curtain goes up, one regards a stylized ballroom (designed by Rouben Ter-Arutunian) with Art Nouveau touches, a pianist in 19th-century garb seated at a grand, and as a backdrop, an eerie landscape containing a wild, wind-bent tree, a body of water, and hovering above it, a shimmering apparition of gothic arches and spires.

Lavery (in the role created by the indisposed Adam Luders) has an odd distraction about him from his first entrance; toward the end, he's given a turbulent, disturbed solo into which there suddenly intrude a number of ominous, silhouetted specters in stovepipe hats bearing huge tomes and raised writing quills. It's impossible to escape interpreting the specters as Schumann's Philistines, and the scene itself as an adumbration of the composer's madness. Similarly, the final dance, in which Lavery recedes slowly into darkness as von Aroldingen inclines into a tearful pose, inevitably evokes Schumann's end.

The choreography per se is the strangest part of all. Within a recognizable classical mold, colored by elements of social dances like the waltz, the ballet looks as if Balanchine had decided once and for all to eliminate steps from dancing -- or rather, not steps, but "steppiness," our awareness of basic, combinatory units. There is as much walking in the work as "dancing," and a great deal of sustained posing as well. The women shift from dance slippers to toe shoes after the first few dances, but the change is almost imperceptible, and thereafter they dance on quarter and half as often as on full point. But if Balanchine has relinquished the borderlines between steps, he certainly hasn't given up on movement; if anything, this new fluid, erratic idiom of his has more poetic effect than ever.

If the ballet seems to be "about" anything, it may be degrees and shades of romantic attachment. In any case, despite passages that are animated, even tumultuous, the impact of the whole is curiously muted in statement. This may be Balanchine's subtlest ballet, and perhaps one of his most beautiful; easy, however, it's not.