The all-ages audiences for City Center’s Fall for Dance festival are a democracy’s dream. People are so buzzed from having snagged the $10 tickets that sell out in a day that they’re rapturous about everything they see – and keenly attentive. For master puppeteer Basil Twist’s glorious take on Fokine’s 1911 Petrushka, they burst out laughing whenever the balsawood Ballerina made a finicky adjustment to her refined pose, weightlessness and her vanity perfectly matched. (“Wrong!” shouted a rabid balletomane – proof of Twist’s parodic precision.) Everyone understands that this two-week, five-programme dance smorgasbord is a present to us.

Vibrant precision: Ballet West’s staging of ‘Les Biches’

But it’s also supposed to be a gift to dance – encouraging people to try another show some time (at City Center, with luck). That’s the rationale for the buffet approach: with a slice of modern and a side of tap, everyone’s going to like something.

In my experience, no one likes anything as much as when the menu coheres. So it’s an improvement that Fall for Dance comes with a timely theme this year: Diaghilev’s Ballets Russes, riffed on and reconstructed, on the centennial of the company’s birth.

The reverberations from the fantastical and propulsively dramatic works that Diaghilev commissioned (from 1909 until his death in 1929) from Fokine, Nijinsky, Nijinska, Massine and Balanchine have stretched far into ballet and modern dance. To take one example, dance has long exploited the tension between the mechanical and the natural: a dancer spins like a top, then bows like a prince. The Ballets Russes opened up where the emphasis might fall, so the mechanistic was no longer confined to technique. It might shape style, too – the angle of the arms, a gesture’s rhythm. Track just this one effect, and you could fill all 20 spots on the Fall for Dance roster without breaking a sweat.

The festival producers, however, didn’t even mine the Russes-related repertory of City Center’s own resident companies. Rather than Christopher Wheeldon’s engrossing Pulcinella, in which the dancers’ hips and ankles convey as much harlequin sauciness and wile as their shoulders and arms, we got Lightfoot León’s ghoulish Softly as I Leave You as our Morphoses provision. In place of Paul Taylor’s Rite of Spring, a comic-book noir take on the Nijinsky ballet that retains the original’s horror and sadness, we were treated to his cotton-candy Offenbach Overtures, a spoof of that other Paris, of Napoleon and dancehall dames. The drag queens of Les Ballets Trockadero de Monte Carlo were funny and delectable in the Balanchine spoof Go for Barocco – but imagine if the looming Katerina Bychkova had gone toe-to-toe with Diana Vishneva in The Dying Swan!

Still, the bits of Ballets Russes we were privy to irradiated out to touch every work susceptible to their influence. Everything missing from Boston Ballet’s stultifying reconstruction of Nijinsky’s Afternoon of a Faun, for example, showed up that night in Ohad Naharin’s B/olero: voluptuousness, unleashed in jagged riffs; frieze-like flatness, in the two dancers’ window-wiper arms; and even that Cubist habit of pointing out that it’s running nature through the heartless mill of artifice.

Naharin’s self-conscious use of Ravel’s Bolero does that. To keep the famous score from hypnotising him into treading the same path of least resistance that Béjart and others have taken, Naharin chooses a kitschy electronic version and sends it zipping from speaker to speaker like a wispy ghost. Haunted by this emasculated relic the way a night is haunted by a gnat, the dancers grow preternaturally alive.

The Ballets Russes choreographers subject one kind of movement to the rigours of another, thereby exposing how the very art we are watching is made. The fourth and most smartly curated programme brought this elusive fact home. In Nijinska’s stateside-scarce Les Biches – the festival highlight, danced precisely and vibrantly by Utah’s Ballet West – classicism takes the giddy mannerisms of 1920s high society through its paces, and both sides gain clarity from it. This 1924 ballet features a party hostess undulating with self-importance; an impassive “page-boy” girl, all flat lines and endless balances; three muscle-flexing brutes; two girlish lesbians; and and a spritely chorus of flappers. Nijinska creates these caricatures and mysteries – dancers flattened and dancers deepened – with a cornucopia of fascinating steps.

After Les Biches, Jerome Robbins’ Four Bagatelles looks especially thin. Why weren’t we treated to his Faun? It would have been the perfect companion to Mark Dendy’s Faunes, which recounts the aerobic frenzy, at once Dionysian and compulsive, of two golden boys.

To cap the evening, Mark Morris’s Grand Duo evokes Nijinsky’s Rite in its exhilarating tribalism and finger-pointing. It also serves as a warning and spur to survive, dance needs to be evolving and inventing (more than revolving and revolting) all the time. It can’t wait for another Diaghilev.

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