Ask Wayne McGregor or Christian Spuck what Vivaldi’s Four Seasons and Shakespeare’s sonnets have in common and they’ll both seize on the fact that we all think we know these works so well, we don’t really bother to pay them close attention any more. The double bill by Ballett Zurich that arrives on the Edinburgh International Festival (EIF) stage tonight throws down a richly imagined gauntlet to that unwarranted complacency. McGregor’s Kairos is set to Vivaldi Recomposed – a Four Seasons suite re-imagined by experimental composer Max Richter – while Spuck, director of Ballett Zurich since 2012, has put the mystery surrounding four of Shakespeare’s poems at the heart of his one-act ballet, Sonett. And no, he’s not creating an Elizabethan time capsule by having lute music underpinning his choreography: he’s elected to use Philip Glass’s Symphony No 8 instead.

Spuck will joke that “I used up all the Purcell I loved in The Return of Ulysses!” – a hit during EIF 2009 when it was performed by the Royal Ballet of Flanders. In fact, it’s doubtful if he would have used Purcell’s wistful plaints for Sonett. Or indeed any music that had a period feel to it. “I wanted to make a mystery, not some kind of nostalgia,” he says. “So it was a conscious decision to use music from a completely different time. The Glass piece gives us space for a speaker – we have an actor delivering the text – and it also gives real drive and good tempi for the dancers to convey those doubts and questions I think we have about the poems.” Ever since Spuck encountered Shakespeare’s sonnets at the age of 21 – albeit in German translations – he has been gripped not only by the imagery but also by the sense of secrets and codes that whisper from between the lines. The intrigue that surrounds Shakespeare’s Dark Lady is like a magnet to his creative impulses.

He still finds the centuries-old puzzle exciting. “Who is she? We’ve never known for sure. Did she really exist, or does Shakespeare invent her as a way of expressing feelings that can’t be admitted to some-one else? And we have to ask: is that some-one a woman, or a man? Is “dark” a negative description? Is there menace? There are certainly secrets. And already, you have a drama about the sonnets, even before one line has been spoken – and I love drama!” Those who saw The Return of Ulysses at EIF 2009 will agree that he does, remembering Spuck’s ability to use movement – stillness, spatial relations, touch and the absence of touch – to draw us inside the emotional conflicts that beset Penelope as she fended off suitors during Ulysses’s prolonged absence. The dancer who embodied Penelope – Eva Dewaele – is now Spuck’s Dark Lady.

Encased in the vast sweeps of Emma Ryott’s magnificent costume design, Dewaele, in Spuck’s words “disrupts the ballet a little bit. And for some audiences, I think her presence – and that of our speaker, Mireille Mossé – will be an irritant. But you know, for me that’s not such a bad thing. I love beauty on-stage, but it has to have depth. If it's so nice, so pretty, so superficial, that it is really only ornamental – for me, I’m afraid it gets stuck. Goes nowhere, doesn’t touch me or move me. And I want audiences, even for a short work like Sonett, to be touched by what they see and to think about what is still hidden, and fascinating, about the writing of these poems that still speak of love and pain to us. If I have to irritate audiences a little to make them think about that – well...” There is a mischievous chuckle, a reminder that Spuck has a very ready sense of humour, even when he is talking about the serious aspects of making new work and expanding the horizons of his dancers at Ballett Zurich.

It’s easy to see why Wayne McGregor gets along so well with Spuck: they both have that meld of serious intent, distinctive choreographic styles and just a hint of the quirky jester that adds up to innovative vision in dance-making. They first met when the British-born McGregor was making work for Stuttgart Ballet, where Spuck was choreographer-in-residence. They stayed friends even after going their separate ways, and when Spuck took over the reins at Zurich – drawing up lists of interesting choreographers he wanted his dancers to work with – he extended a hopeful invitation to McGregor. “It was just a lovely coincidence, “ says McGregor. “that Christian contacted me at a point where there was a gap in my schedule – and a piece I was longing to make.” He explains that another friend, and frequent collaborator, the composer Max Richter had just finished his Vivaldi Recomposed. “Here’s a really beautiful thing...He gave me a copy to listen to before it was released, and I loved it. I almost couldn’t believe it when Max said he wouldn’t release it if I wanted to make a piece to it... I mean – what a truly amazing friend, saying that and meaning it.” It was only sometime later, when Zurich became a working possibility that McGregor was able to take Richter’s music into the studio and create Kairos.

“It’s an extremely difficult piece to play,” says McGregor, “but it’s really great to choreograph to! As soon as you put it on, it gives you this great, propulsive energy. And one of the many great things about the Zurich dancers is they’ve got amazing virtuosity at speed. The women will give you pointe-work that is so fast – really stabbing, articulate, quite aggressive pointe-work that fits really well with that very driven, staccato music that Max has brought together. Christian has found a tremendous balance in his company – dancers who are open and curious, with an appetite for creativity, but also dancers who are fine-tuned instruments and who can match your expectations. And Max’s music.”

Vivaldi’s Four Seasons are, he agrees, casualties of the muzak machine. “You hear the opening bars and think “I know this” and you stop listening. Max has been able to re-focus our attention on the beauty of it, but in a very subtle and contemporary way that’s truly visceral – nothing like the hokey kind of re-mix you hear in lifts.” Another cherished collaborator, artist Idris Khan has created designs that, according to McGregor, float in the ideas of time and memory that shade into the choreography of Kairos – a Greek word he translates as “in the moment”, although in McGregor’s reckoning, that moment could be an amalgum of moments across time with the past co-existing with the present and even the future. That seems a perfect summation of what this Ballett Zurich double bill represents in itself: music and poetry from the past allied to new aesthetics that point to fresh directions for dance in the future.

Ballett Zurich are at the Edinburgh Playhouse from tonight (Thurs 27) to Sat 29 August.