Kronos Quartet founder David Harrington proudly boasts that his ensemble never repeats a set list -- including the two at Walker Art Center Friday and Saturday. That's partly because of the enormous number of commissions the string quartet has generated in its 37 years and partly because Harrington's taste is relentlessly eclectic.

"I love that we have had more than 700 pieces written for us," violinist Harrington said from his San Francisco home.

At the Walker, Kronos will play pieces composed for the group by indie rock heroes Damon Albarn (of Blur and Gorillaz) and the National's Bryce Dessner as well as material from Iraqi, Iranian and Palestinian musicians.

Recently, Harrington has been working with Vietnamese musician Van-Anh Vo, whose main instrument is like a 16-string zither, called the dan tranh.

"I started Kronos during the Vietnam War, and have always wanted to create a bridge between American and Vietnamese musical cultures. She can help me and Kronos do that," Harrington said. "It is probably going to take a year or so to come up with something, but it will be an exploration of Vietnamese culture and life."

This sort of global perspective has long been a feature of the Kronos oeuvre. The theme of Friday's performance at the Walker will be "Music Without Borders," and the concert will include material from the group's 2009 release, "Floodplain," which has an explicit international scope, and, as with most Kronos albums, includes both new commissions and original arrangements of traditional compositions.

Among the "Floodplain" selections on Friday's set list will be "Oh Mother, the Handsome Man Tortures Me," an Iraqi song written in the 1970s featuring a sinuous, sinewy melody with martial rhythm; and "Tashweesh," a three-minute electronica-oriented tune originally done in collaboration with the Palestinian collective Ramallah Underground. There will also be pieces by Canadian Derek Charke, a rendition of new-music pioneer Terry Riley's "Ecstasy," a commissioned number titled "Oasis" by Kronos favorite Franghiz Ali-Zadeh from Azerbaijan, and "Threnody for Those Who Remain," by Iranian Sahba Aminikia, a mournful piece about the death of his father and the protests after last year's elections in Iran.

The theme on Saturday is "Sonic Edge: Indie, Rock, Jazz, Beyond," featuring commissioned works by artists including Albarn and Dessner. "Bryce and I had a wonderful conversation about family and history," Harrington said. "Kronos was going to be playing at the very city in Poland where he was from and where his grandmother still lived at the time. I thought it would be great to have him make some imaginative contact with his family and so he wrote 'Aheym,' which means 'homeward.' It's very driving and passionate."

The lone noncommissioned work will be a version of "Flow" by performance-art goddess Laurie Anderson, who is near the top of Harrington's extensive list of future collaborators.

"We want to give our audience as much of an idea of the expanse of our work as possible, especially if we haven't been there for a while and we haven't been to Minneapolis for eight years," Harrington said. "Every new concert is a new opportunity and has a new context."