The mix of an American vernacular string master with a jazz-pop pianist now is its own genre, apparently. It started with Ricky Skaggs and Bruce Hornsby, and Chick Corea and Bela Fleck, both from 2007 (Corea and Fleck, with their healthy fanbases, continued on to a live album and DVD).

It seemed to me that in these productions, the piano dominated. It, after all, sets up the harmony, the bass, the rhythmic pulse. String instruments like the banjo, even played as brilliantly as Fleck, do not sustain notes; gravitas is hard to achieve in these conditions.

There may be more equipoise with Thile and Mehldau. The latter is at the top of the jazz piano heap, an innovator not as famous as his elders Jarrett, Corea and Hancock, but just as influential to younger players. It’s insightful to hear him play in a more “inside” fashion; there’s not a false note from him on the whole project (unnecessarily spread out over two discs—but that’s the record biz these days).

Thile is the mandolin component of a gang of American string super-cats: Fleck, bassist Edgar Meyer, dobroist Jerry Douglas, fiddler Mark O’Connor, and even cellist Yo-Yo Ma, who is always used to great effect in these various collaborations.

Thile shreds the mandolin, and is a formidable writer: His Punch Brothers may have created the most advanced bluegrass-Americana-whatchamacallit ever. But he’s more than that: He’s a freakishly good singer. His vocal roots are in the country-bluegrass tradition, but he can stretch to cover huge new territory—so when he plays, it can be a substantive complement to Mehldau’s underpinning gist of the matter, or it can sound like icing. When he sings, however, he commands the moment. If you don’t find time for this set, download their virtuoso, rollicking cover of Dylan’s “Don’t Think Twice It’s Alright.” It will make you think more than twice about what’s possible with these guys.