Dance is the most ephemeral of the lively arts, existing after the curtain goes down only in what we can recall of it. There’s no handy score for the viewer to consult, and video goes just so far to capture choreography.

Dance companies are ephemeral, too. The curtain can descend on them as easily as on the dancers themselves.

That is what is about to happen — by design — to a company that is an icon of modernism and the avant garde in art, music and dance, the Merce Cunningham Dance Company. Cunningham died at 90 in 2009, and now his eponymous company, devoted to his work, is traveling the world on a two-year “Legacy Tour” before shutting down Dec. 31, 2011 with final New York appearances.

The tour brings the company to Power Center Friday and Saturday for two performances under University Musical Society auspices, framed by residency activities of every stripe.

Companies like New York City Ballet — a creative laboratory for the works of George Balanchine and Jerome Robbins in their lifetimes — or like the Martha Graham, Jose Limon, or Alvin Ailey companies — repositories for great works of their founders — have gone on after their prime movers’ demise. Why not the Cunningham company? And what will we see on this last chance to dance with Merce’s elegant, complex creations? Company Executive Director Trevor Carlson, with the company for many years and a longtime associate of Cunningham, took time out recently to talk about these and other topics.

Q. What will we be seeing here in Ann Arbor?

A. We have 18 pieces in the repertory for the tour. One has fallen out already in the last year, two have not yet premiered, and there’s a kind of shuffling of works in repertory that the dancers can keep on their bodies.. Seven of the works had to be revived, and “Squaregame,” from 1976, which we’re doing in Ann Arbor, was among them.

We’re pairing it with “Split Sides,” from 2003.

We wanted, as much as we could, to represent different decades from Merce’s repertory. Musically, the works have an equal diversity. “Square Game has music by an early collaborator who remains with us, Takehisa Tosugi, who is our music director. “Split Sides” has music by Radiohead and Sigur Ros. Both are really quite playful in a way. “Squaregame” is a bit like a game, and “Split Sides” began like a game, with a rolling of the die to determine the order of the evening. It so happened that the presenter, in this case, was interested in both of these works, and we felt they worked well together. I’ve not seen the combination, but I think it’s a nice mix.

Q. How did the company go about reconstructing “Squaregame”?

A. There were some dancers who were in the piece who were able to coach, and we used video and those dancers’ memories. It was done in workshop in Merce’s lifetime and Merce used a number of sections from that work in Events, so some of the company members were familiar with those sections.

Q. How did the decision to close the company after Merce’s death evolve?

A. I’ve worked with the company for 12 or 13 years in different positions, including company manager. I’ve been executive director for, I don’t know, six years, and I had a very close relationship with Merce, which is partly what made me seem suitable for the position of executive director, and I felt comfortable to address the issue of what would happen when he wasn’t here anymore. I wanted to address it together with him, to know where his thoughts were; he’s never been one who has been so clear as to make a declaration of sorts, but rather to talk options and practicalities. It seemed that we might do something different than others had done, that one of the options might be a formal closure. When I returned that as a question to Merce, he said, well, yes.

Q. What happened then?

A. I went looking for other examples and found they don’t exist. There is not any other artist-driven organization that maintains the artist at the center and has planned a formal closure once the artist is no longer there. Some have closed, but often out of distress. So we developed this without an example to follow.

All of us involved have been comfortable and confident with the way it’s been organized. The scariest part has been the prospect of explaining the formalized closure publicly. And fielding the questions and concerns. In point of fact, we’ve gotten a great amount of praise from within our community but also from outside.

Q. Why do you think this hasn’t happened elsewhere?

A. Well, our situation is very different from New York City Ballet, which has dances by different choreographers, or the Ailey or Limon companies, which took on other choreographers’ works in the creator’s lifetime. And we were not interested in a being a dance company that functioned as a museum.

We do hope that what we’re doing could a lesson for others, an example. It is appropriate for who Merce was and what purpose the company served in his lifetime. It’s not the answer for all artist-driven organizations, so it’s not sort of a soapbox for what others should have done or should be considering.

Q. What will happen to Merce’s dances after the company dissolves?

A. Works will be licensed to companies and schools — that’s one of the things that created confusion in my mind when I thought we must keep this going. Merce set up another organization to hold copyrights, the Merce Cunningham Trust, and we’ll hand assets over to that. Right now, we have something like 41 open contracts, and there are quite a few companies who are performing Merce’s works.

Q. And what about the dancers who are currently with the company?

A. They will continue to the end of the Legacy Tour. And then it’s a transition, a kind of birth, a Life After Merce. We have a bit of a handicap here, all of us, myself included, in that we are an organization built around and driven by the creation of new work, and it is time for us to transition to something different: not creating or supporting creation, but rather making a body of work available for scholarly use or performance. It’s an organizational restructuring. Merce established the trust - it was birthed in 2000 and it’s in its adolescence now at this point. Maybe as we close a parent organization, we give this young organization a chance to transition to adulthood and to be something different than what we have been.

Q. And the school? And the archives?

A. The Merce Cunningham Dance Foundation, which I’m the executive director of, oversees the school, company and archive. With the closure of our foundation, all the other aspects cease under our direction. It’s clear that Merce didn’t want his company performing the work of other choreographers. Going on a world tour with dancers he chose and trained was a clear and appropriate thing to do. So this closure of the company within the foundation was something that was understood.

The archive has been purchased by the New York Public Library and has a home.

The school has functioned to support the needs of Merce’s dance company and Merce’s creative life. Individuals associated with the school are interested in finding their way to make the school independent, but the question of the studio is still something unanswered, but it will cease under our leadership and umbrella. The legacy plan was a three-year plan, and that’s not incidental; it is an opportunity for the trust and all the others impacted to have a three-year opportunity to see what they want to do in the future, to assess what they want to do, to make adjustments before we formally close.

Q. This must all be incredibly difficult.

A. It would be much sadder to watch someone else deal with this of necessity and sadder without having discussed it with Merce. And what we’re doing is appropriate for Merce, and for the company. The company is an incredible group of dances, and they look fantastic. I can’t take credit for how they look, so I can say that. I just make sure they get the support they need.

Myriad residency activities, free and open to the public, are part of the visit. For a complete list, visit ums.org