The ancient, codified forms of Indian classical dance. The in-the-moment, unpredictable sounds of modern jazz. What could they possibly say to each other?

So much that “Song of the Jasmine,” a new collaboration between Minneapolis’ Ragamala Dance and New York-based jazz saxophonist and composer Rudresh Mahanthappa, could be one of the year’s must-see performing arts events.

Co-commissioned by four arts organizations including Walker Art Center, “Song of the Jasmine” has been booked for an 11-city national tour starting in August, without anyone having seen it all the way through. We’ll be first when the evening-length work has its world premiere in the Walker’s McGuire Theater, Thursday through Sunday.

The seeds were sown in 2007, when the Walker presented Mahanthappa’s world jazz group Kinsmen. Ragamala’s Aparna Rama­swamy was in the audience and liked what she heard, and the way Mahanthappa brought Indian ragas and instrumentation into his music. Both are second-generation Indian-Americans, and she thought it would be interesting to work with him.

Walker performing arts curator Philip Bither offered to help. He was a fan of Mahan­thappa and had history with Ragamala.

“Many years of working with Ragamala on various projects, all of which involved some kind of collaboration, gave me utter faith they would find their way on this one,” Bither said. He was clear about the relationship between the two creative sides: “They’re equals and were commissioned as equals.”

Right there is one reason this collaboration could have been a mess. Dancers perform to music, but the music is there to support the dance. Both Ragamala — Aparna and her mother, Ranee, co-artistic directors and choreographers — and Mahanthappa wanted to move their own art forward, not simply get along.

“What we didn’t want was a shallow cross-cultural collaboration,” Aparna explained. “We are all artists who have created a lot of work with great depth. We didn’t want to meet on easy ground.”

Early on, they had to confront the question of which would come first, the music or the dance. “We wanted both to happen simultaneously,” Mahanthappa said. “It doesn’t usually work that way. It’s one or the other.”

He had never composed for choreographers; Ragamala had never danced to jazz, which includes an element foreign to most dancers: improvisation.

“Dances are generally not improvised,” Mahanthappa said. “This project is a big push in that direction for Ragamala, something they wanted to explore.”

Aparna and Ranee began working on the choreography, Mahanthappa on the music. Both sides sent MIDI files, videos and e-mails back and forth, and there were many late-night texts and conversations. Starting last December, everyone convened for three intense periods of multiple rehearsals at Ragamala’s south Minneapolis studio. Final rehearsals started last week at the Walker.

The musicians — Mahanthappa and jazz guitarist Rez Abassi, Raman Kalyan on South Indian flute, violinist Anjna Swaminathan and Rajna Swaminathan on mridangam (South Indian drum) — all live on the East Coast and have flown in from New York, Baltimore, Virginia and Washington, D.C.

At an early rehearsal in December, some of the music had been composed and parts of the dance choreographed. Things were loose and tentative, with frequent stops and starts as the musicians and dancers negotiated tempos and transitions. The dancers’ bare feet slapped the floor and Mahanthappa’s alto saxophone soared in a fiery, instantly memorable melody.

“It’s going to be different every time,” Ranee explained during a break. “We’re getting to know each other.”

In fact, each performance will be different from night to night, and from venue to venue as Ragamala and Mahanthappa go on tour, because improvisation is part of the dance as well as the music. At a rehearsal in mid-April, there were long passages of crisply choreographed and executed group movements, and parts where the dancers moved independently while staying aware of and responsive to one another. That’s improvisation.

“Song of the Jasmine” is guided by the poems of sixth-century Tamil Bhakti poet Andal, a woman who wrote about desire so strong that illusion seems real, and the agony and ecstasy of longing to unite with the divine.

“Those emotions are what we are painting on the stage,” Aparna said.

Jazz is music that communicates and evokes emotions, and Mahanthappa wanted joy to be first. “It’s not in the dance tradition to start with a bang,” he said. “Usually it starts slowly and amps up. In my music, my sensibility, 99.9 percent of the time my set starts with a bang. I wanted to bring that element in. They [Ragamala] were game for it.” And so “Song of the Jasmine” begins in a blaze of joy, shimmering blue silk and 80 suspended bronze bells.

Aparna describes the collaboration as “a wonderful process. … You never know until you jump in. What I found is that we can stay true to so many of the elements of our form, our aesthetic, and the creative process that satisfies our souls, but also employ all of these new strategies for creativity.”

For Mahanthappa, “this whole project has been really inspiring. It has cracked open my sense of how music is placed in the world. It has changed the way I see how music can be used, conveyed and interpreted.

“What [Ragamala] is doing rhythmically as choreographers is astounding. Their sense of rhythm with their feet is as good as any drummer. It makes me think of Max Roach and Jack DeJohnette. … It makes me want to play.”