Guitarist Julian Lage (say “Lahzh”) was a jazz prodigy who became the subject of a documentary at eight, performed at the Grammy awards at thirteen, and joined the faculty at Stanford at fifteen. If you show that kind of early mastery you can burn out, or worse, but like onetime bluegrass prodigy Chris Thile, Lage found new challenges in getting American musical traditions to talk to one another. He still leads a jazz band and plays with various ensembles, but he’s also performed with avant-rock guitarist Nels Cline, and over the last few years his most productive collaboration has been with bluegrass guitarist Chris Eldridge—who in some of his bands (including Thile’s Punch Brothers) goes by the name Critter.

 Jazz and bluegrass grew from geographies almost as different as can be imagined, but they’ve come closer in the past than you might think. Eldridge grew up in a family oriented toward what used to be called progressive bluegrass, whose players borrowed jazz moves: his father is banjoist Ben Eldridge of the famed Washington, D.C., band the Seldom Scene. Nevertheless, to put jazz and bluegrass together and let them relax enough to breathe isn’t a common thing. Lage and Eldridge have had to come up with original ways to do it.

 Lage is the dominant player, often pushing Eldridge past where he has gone before, but Eldridge’s bluegrass provides the majority of the material. Though some songs resist categorization, most fall into three basic types. They play quite a few old-time tunes and songs, with Eldridge laying out the basic stuff of the music, and Lage bouncing off it in scarily compact little dissections and then handing it back. They pay homage to old-time guitar great Norman Blake in a luminous version of “Ginseng Sullivan,” with Eldridge on vocals. Eldridge also sings when they do jazz standards like “Someone to Watch Over Me” (an interesting tune for a male vocal, to be sure). He takes the vocal line disarmingly straight, and Lage weaves arabesques around him.

 Another type of piece might be called chamber grass or chamber folk, and it’s here that the minds of Lage and Eldridge meet most closely. At times they are able to keep track of each other while both improvise, something very few players are able to do. “Bone Collector,” the leadoff tune from their upcoming album Mount Royal, is an intricate little symphony for two guitars, with the brilliant tones of Lage’s 1939 000-18 Martin ringing out in an impossibly long crescendo at the end. The Lage/Eldridge show at the Ark on Monday, February 27, promises striking virtuosity of the rarest kind—that which doesn’t grow from established procedures.