Bob Dylan once suggested that his 1975 album “Blood on the Tracks,” which critics took as an autobiographical sketch of his much-publicized divorce from his wife, Sara, was actually based on Chekhov. Chris Thile makes no such claims for “Punch” (Nonesuch), the new album from his group, the Punch Brothers. But he doesn’t ask that audiences take the project’s focal suite, “The Blind Leaving the Blind,” about a failed relationship, too literally — even though the feelings are very much present.

“There was definitely some purging going on,” Mr. Thile said recently. After his marriage dissolved in 2003, the mandolin player began pouring his energies into a new passion, assembling a band with his childhood friend, the violinist Gabe Witcher. The outfit, which also features Chris Eldridge on guitar, Greg Garrison on bass, and Noam Pikelny on banjo, was first dubbed the Tensions Mountain Boys. The turn of phrase was a bluegrass pun right out of the irreverent Mr. Thile’s jokebook. Yet the music on “How To Grow a Woman From the Ground,” the group’s 2006 debut (released under Mr. Thile’s name), uncovered a onetime child prodigy pushing the limits of traditional form, even further than he had with his longtime neo-bluegrass trio, Nickel Creek, which played its farewell gig last November at Nashville’s Ryman Auditorium.

“I come from the school of thought that says never let the truth get in the way of a good story,” Mr. Thile said. “I drew on what I went through. A lot. But it’s definitely a lot less personal than it seems.” To get to the marrow, listeners have to focus on the generous instrumental passages the album indulges, or visit the Allen Room at Jazz at Lincoln Center tomorrow night, where Mr. Thile will perform with the Punch Brothers — and celebrate his 27th birthday — as part of the American Songbook series.

As Mr. Thile, a native of California who began performing professionally when he was 12, has often acknowledged, he was getting pretty burned out on Nickel Creek. His frustrated muse was boxing him about the ears. To paraphrase Mark Twain, whose use of a popular 19th-century jingle in a short story inspired the new band’s name, it was time for Mr. Thile to light out for the territories.

“The whole Punch Brothers experience has been one of infinite possibilities,” he said, dropping a reference to what he calls the “constant vigilance” demanded by the gang’s current inaugural tour. The musician was sharing an often jocular conference call with Mr. Witcher, with whom he has been playing since both were seemingly barely out of kindergarten. “Any one of us can suggest any direction and expect that the other guys will be able to go there. Not only that, but be excited about going there. Everybody in the band has practiced a lot and has a really open mind. I can’t check out at any point in the show.”

“Punch,” which will be released next Tuesday, showcases a bristling enthusiasm for fleet daredevilry on all manner of stringed instruments, at once emulating a model of tradition and catapulting the group forward into the unknown. The pieces were written with a sweeping allowance for improvisation, which skews the sound toward a kind of contemporary classical feeling. Although, since it often is cut with bittersweet vocals and a feathery delicacy of tone, the songs have little of the astringent chill of 21st-century chamber music. Maybe you can call it “post-Americana.” The Punch brethren have another way to express it.

“It’s almost music,” Mr. Witcher said.

“It is absolutely almost music,” Mr. Thile added. “No matter what you’re doing, you’re going to try and figure out what it is. You need words to describe music. If someone says it’s kind of like a bluegrass band, I’d say, ‘Well, okay, we look like a bluegrass band.'”

According to Jon Nakagawa, the producer of contemporary programming for Lincoln Center, those ambiguities are well-suited to the current season of the American Songbook series.

“We like to say that the great tradition of American popular songwriting goes from Stephen Foster to [Magnetic Fields front man] Stephin Merritt,” he said. “Chris’s songwriting is very much in that tradition. The Punch Brothers’ sound is very forward-thinking. It has that edge.”

Mr. Thile, whose long run with Nickel Creek helped to reconcile Radiohead with Ralph Stanley — something he still does, as his rendition of the Brit-pop heroes’ “Morning Bell” abides in the Punch Brothers’ set list — insists he’s not seeking to confuse genres. “We didn’t set out to do something no one could categorize,” he said. “That would be a crummy music-making goal. We still love to play bluegrass, but I don’t think any of us could honestly come up with a straight-up bluegrass tune at this point.”

The Punch Brothers perform tomorrow at Jazz at Lincoln Center (Broadway at 60th Street, 212-721-6500).