The Royal Ballet’s new triple bill, first seen on Wednesday, offers Balanchine’s Agon, made in 1957, the acquisition of Glen Tetley’s Sphinx of 1977 and Wayne McGregor’s new Limen. With bright-eyed insouciance, a programme note declares that “Sphinx can best be described as modern ballet”, a statement wholly wrong-headed about this display of turgid gymnastics nailed to an unsuspecting Martinu score. Agon is the quintessential “modern ballet”. From the middle of the 20th century it looks both forward and back, as does its score.

Stravinsky’s music speaks of past and present – and future. No less so Balanchine’s dances, rooted in the glorious past of his St Petersburg schooling, displaying the glorious present of his American ballet and (for those with eyes to see) proposing glorious journeys into a future, dance as clear in purpose as Stravinsky’s music. Agon is the single most significant ballet of the 20th century, its roots firm, its fruits a nourishment we ignore at our peril. In this revival it was handsomely danced, Melissa Hamilton’s intense line notably effective in the great duet with Carlos Acosta, its ensemble clean-cut.

And Agon was a reproach to what ensued: the vacuities of Sphinx and the portentous manoeuvres of Limen. As a version of the encounter between Oedipus and the Sphinx, Tetley’s ballet has the dramatic urgency of a meringue. It claims dubious parentage with Cocteau’s La Machine Infernale and is performed while Martinu’s music is played, but neither party recognises the other. It has three roles, that of the Sphinx wasting Marianela Nuñez’s time, and Rupert Pennefather saddled with the blanknesses of Oedipus’s choreography. Only Edward Watson (pictured), very fine as Anubis, turned posturing into theatrical art.

About Limen, I note that it has a video-installation setting by Tatsuo Miyajima, vestigial costumes by Moritz Junge, Kaija Saariaho’s intriguing cello concerto as companion, and it lasts 29 minutes. Fifteen dancers are involved in McGregor-ish activities that feed intermittently on academic dance, and Steven McRae has a dazzling little solo. The lighting is complex and, I would hazard, not a little expensive, and does nothing for the ballet save confuse the watcher’s eye. Agon, with no décor, is light-filled, light-giving. Real amid unrealities.

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