The programme that Ashley Page, Scottish Ballet’s director, brought to the Edinburgh International Festival this year – the third year in a row that his company has been invited to take part – was his most ambitious yet. It featured a world premiere from Stephen Petronio, the acquisition of a rare Trisha Brown, and the revival of Page’s own award-winning Fearful Symmetries. Taken together, they showcased a company of remarkable versatility and international stature.

Ride the Beast isn’t the first Petronio work in Scottish Ballet’s repertoire, but it is the first that the American choreographer has made for them. Set to several tracks by the cerebral rock darlings Radiohead, the new piece is characteristically sexy and energetic but less aggressive than we’ve come to expect from Petronio. It also exerts an emotional distance that bestows an appealing formality on the sensual sweep of his slippery language. The women are cast as alluring, untouchable goddesses, the men as their inevitable pursuers, but the choreography is not so gender specific. Benjamin Cho’s costumes colour-code the 13 dancers into three groups, while tassles, fringes and a suggestion of wings add a sense of frivolity to the seductively wayward aura.

Brown’s own New York troupe may be visiting the Edinburgh Festival later this week, but Scottish Ballet has scored a major festival coup in acquiring For MG: The Movie, her 1991 creation for eight dancers. Brown’s language is even more the antithesis of ballet than Petronio’s, and in For MG the glowing simplicity of her gradually expanding vocabulary creates a spellbinding poetry. Contrasting springing movements with the utter stillness of a single dancer who remains motionless – his back to the audience – throughout, and using repetition like an intoxicant, she produces a work of compressed beauty. The commissioned score (by Alvin Curran) is a hypnotic foray into piano melody and found sounds; lighting is heavenly. The company danced it magnificently.

Page’s own Fearful Symmetries, made for the Royal Ballet in 1994, has everything going for it, including sensational designs by Antony McDonald, gorgeous music by John Adams (well played by the Scottish Ballet Orchestra under Nicholas Kok) and choreography that endlessly fascinates. Pumping up its classical sophistication – it was the only pointe shoe ballet on this bill – Page concocts a landscape of constantly evolving relationships centred around a single male dancer. Dynamic and moody like its surging music, Fearful Symmetries boasts style and substance in equal measure, and this excellent company performed it with a knowing sense of both.