Emily Molnar and Nicole Lizée had their first meeting at the café by domestic security in Montreal's airport. After exchanging video links and recordings of their work, the artistic director of Ballet BC and the Lachine, Que.-based composer tried to squeeze the most out of Molnar's short stopover in Quebec. They talked about books, film and new visual art, discussing recent obsessions and ideas that were on their minds.

"We both make work by building worlds within worlds – we break stuff down until we find new opportunities," Molnar explains.

The Molnar-Lizée partnership is one of three choreographer-composer pairings that form the basis of ENCOUNT3RS, a landmark triple bill that opens at the National Arts Centre in Ottawa on Thursday night. It's rare to see three prominent Canadian ballet companies onstage together and this major project, in honour of Canada 150, does just that, uniting Ballet BC, Alberta Ballet and the National Ballet of Canada on the same program. Thirty-minute ballets have been commissioned from key choreographers from each company, pairing them with a Canadian composer of their choice. "I was so compelled by the intricacy and imagination of Nicole's work," Molnar says. "She pushes the potential of what an orchestra can do as a collective."

Jean Grand-Maître, artistic director of Alberta Ballet, is collaborating with Newfoundland-based composer Andrew Staniland, and Guillaume Côté, choreographic associate at the National Ballet, is working with the Toronto-based Kevin Lau.

The idea for ENCOUNT3RS dates to 2013, when English conductor Alexander Shelley was appointed music director of the National Arts Centre Orchestra. With Canada's sesquicentennial around the corner, Cathy Levy, who is director of NAC's dance programming, started to dream of a major collaboration.

"The question was: How do we make something monumental together?" she explains.

For Levy, it was crucial that this "something" be an actual investment in the country's contemporary-dance repertoire, rather than a mere celebration of it. She calls ENCOUNT3RS a "legacy project" in the sense that each of the ballets and music compositions will live on beyond their run at the NAC – all three will be remounted at their respective company either later this year or in the 2018-19 season.

For Ballet BC, a company that doesn't have the luxury of its own orchestra, remounting is made possible by a professional recording that NACO will make of each composition. Levy thinks the music can potentially stand alone in the future, too. "It is a rare logistical challenge to bring three ballet companies together for an evening and we didn't want this to be three shows and we're done. For us, it was very important that the artists own the work."

ENCOUNT3RS is also a way of trying to tackle an ongoing problem in contemporary dance: Mixed programs and non-classical work are a challenge at the box office. "It is about taking risks," Levy adds. "It's 2017 and this is about saying these artists are current contemporary makers of this form – and we want to celebrate that."

The commission offers each choreographer a particular kind of artistic opportunity. For Grand-Maître, who's known for his portrait ballets about Canadian singer-songwriters and normally has to worry about programming that balances the Alberta Ballet season, the project was a refreshing clean slate. "It's been a very long time since I've had a commission that's 'do what you want'," he tells me. He chose to work with the Juno Award-winning Staniland because of what he perceived as a lot of humanity in his music. "I'm wary of contemporary music where they're trying to reinvent the form, and innovation stands in for feeling."

Their Caelestis draws on the choreographer and composer's shared interest in the number phi and the related concept of the golden ratio. Staniland wanted to look at the way phi could be reflected in harmonic sequencing, while Grand-Maître wanted to apply the concept to the tension between the natural and technological world. He describes the ballet as a reimagining of Adam and Eve in a new technoindustrial landscape. "My choreography tends to be exaggerated. I like the dramatic flesh. The body becoming sublime – that's something I kept saying to my dancers in the studio."

Levy, who's seen Caelestis in rehearsal, says, "I think Jean's head has exploded in the most beautiful way."

After meeting in Montreal, Molnar and Lizée decided to build a ballet around the theme of dreaming. Lizée liked the idea of a person having an alter-ego while she's asleep, while Molnar liked the concept of lives not lived. "If you put your life on hold, where would you go?" she muses. They started to build a vocabulary that was based on the image of concentric dreams. "The stage is the eye of an observer who's dreaming," Molnar explains, adding that the protagonist in Keep Driving, I'm Dreaming is always shifting and that the ballet unfolds in a "surreal, abstract landscape, without beginning or end, and using the imagery of different relationships."

Out of the three choreographers, the process has been the most surprising for Côté. He requested to work with Lau after their collaboration on the National Ballet's large-scale adaptation of Le Petit Prince, which had its world premiere last June. Dark Angels started out with the concept of assimilation and ritual, looking at the individual versus the collective from a primal, animalistic point of view. "Kevin came back with an incredibly powerful and tense score," Côté tells me. "What we'd done in the past had been more melodic and this was suddenly, intensely powerful and rhythmical. I got very excited."

With a cast of 10 (mostly principal) dancers from the National, Côté felt he had to push himself into uncharted creative territory to do the music justice. "I was up against somewhere where I had to decide whether I keep creating in the vocabulary I always use – or do I try something new? And I tried something new. Working from the point of discomfort was necessary." Later he adds, " Dark Angels will definitely be something I remember, because it was definitely outside my comfort zone."

All three choreographers are thrilled to have their companies share a stage with their colleagues from across the country. Despite the sprawling distance between coasts, Canada's ballet community is small and the NAC studios have become host to a reunion of former classmates and collaborators. There's also an outpouring of gratitude for the creative leadership of Shelley, whom Levy describes as "the seventh artist" in the project; he was an ongoing source of input and inspiration for composers and choreographers alike and a real force in bringing ENCOUNT3RS from concept to stage.

"This is exactly what a National Arts Centre should do," Grand-Maître says.

ENCOUNT3RS runs April 20-22 at the National Arts Centre in Ottawa.