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When Kronos Quartet founder David Harrington hears about the music that follows the world premiere on Saturday of his ensemble’s new piece, Mavericks/Monk, for Duke’s celebration of Thelonious Monk’s 90th birthday (see “Duke Performances“), he responds much as you’d expect: “Wow, I’d love to see all of that.”

The leader of the world’s most challenging and self-renewing string quartet since 1973, Harrington continues to ensure that his quartet remains vital. In the last three decades, Kronos has recorded works by American composers Terry Riley, Philip Glass, Steve Reich and John Adams, translated Harry Partch’s individualistic ideas into a more familiar format, and paid homage to Bill Evans and Monk with full-length tributes. Enthusiasts for stricture-bending, though, Kronos lent a sinister strain to Dave Matthews Band’s Before These Crowded Streets in 1998 and backed Tom Waits on “Diamond on Your Mind,” a song Solomon Burke put his stamp on after Kronos and Waits performed it live in 2003. Most recently, they’ve translated Jimi Hendrix and Sigur Ros with an online-only single. And now they’re returning to Monk, previously the subject of a 1985 Kronos collaboration with bassist Ron Carter and Monk producer Orrin Keepnews.

“In my opinion, Monk is an original American maverick creator, and I was thinking, ‘There are other maverick creators, some of whom we’ve worked with, some of whom we’ve played,’” says Harrington. “But I thought it would be wonderful to find a way of putting a number of these adventurous spirits together on one program.”

The Quartet will perform four interpretations of Monk’s “‘Round Midnight,” followed by works from other mavericks: Riley, Partch, Anton Webern, Raymond Scott, Tom Verlaine, John Zorn, and writers I.F. Stone and Allen Ginsberg. The concert concludes with Particle 423, a new piece by Stephen Prutsman that collects 423 samples of American music.

For that piece, Kronos will extend beyond its general set-upcello, viola, two violinsto add banjo, keyboards and percussion. Essentially, this program allows the Quartet to do what it’s always donefind new ways to stretch its reachwhile contextualizing Monk in the place of properly valiant giants.

“We’re bringing together people thatif the world would have been slightly different and time would have been slightly differentthey might have been friends,” says Harrington. “In any discussion of creativity, they belong in the same paragraph.”

David Harrington talks about his iPod Thursday, Sept. 13, at 7 p.m. in Nasher Museum of Art’s Auditorium. Admission is free. Kronos Quartet performs Awakening: A Musical Meditation on the Sixth Anniversary of 9/11 at Duke’s Page Auditorium Friday, Sept. 14, at 8 p.m. Tickets are $5-$46. The Quartet performs the world premiere of Mavericks/Monk: Kronos on Innovators at Duke’s Reynolds Industries Theater Saturday, Sept. 15, at 8 p.m. Tickets are $5-$42.