Watch Chris Thile & Brad Mehldau Perform 'The Old Shade Tree' Live

Among the qualities that make Brad Mehldau and Chris Thile a not-quite-unlikely pairing — virtuosity, curiosity, a natural drive to bridge divisions of style — the one that may run deepest is a sense of resonant, articulate melancholy.

Thile, the singer-songwriter and mandolin wizard who now hosts Prairie Home Companion, comes to this bittersweet air from the bluegrass tradition, where the high lonesome sound is firm bedrock. Even within the shiny parameters of Nickel Creek, he could convey a welter of heartache beneath his ebullience. The same holds in Punch Brothers, which has made hair-trigger group cohesion not only an art, but also a spectator sport.

For Mehldau, the jazz pianist and composer, a current of sweet sorrow flows through many different areas of musical interest: Billie Holiday caressing a desolate ballad, Radiohead turning introspection aglow. Mehldau has even explored this yearning in formal terms, variously evoking "sehnsucht" (a German word; see Schubert) or "saudade" (Portuguese; look to Jobim).

On Chris Thile & Brad Mehldau, due out Friday, the two artists find common ground at a range of coordinates, including a songbook standard, a Celtic ballad and a song by David Rawlings and Gillian Welch.

But their emotional languages most fluently converge in the realm of singer-songwriter Elliott Smith, a mutual touchstone. And it's not just that Thile and Mehldau cover one of Smith's most familiar songs, "Independence Day," inscribing its minor chord progression with graceful filigree.

There's also a deep Smithian sensibility in "The Old Shade Tree," the album's opening track, and the lone original that bears a shared songwriting credit. Set at a purposeful medium tempo, the song begins with an almost regal harmonic character and gradually accrues tension, if not torment. Thile sings at first in a high, vulnerable register, edging into his falsetto, but when he delivers the most cathartic line — it involves an ax, though that word goes unsaid — he brings a hardness into his tone.

This performance took place at the Bowery Ballroom near the end of 2015, just before Thile and Mehldau went into a studio to make the album. The closeups of Thile's face capture his uncorked intensity as he sings.

I guess none of you thought of its roots

As the living dead trapped underground

Or of the blizzard to come and the hero I'd be

Planting bonfires all around town

A shade tree is usually a symbol of stability and succor. Here it's a manifestation of angst and torment, something to be subversively thwarted. The sadness in that act is girded with steel.

Chris Thile & Brad Mehldau comes out January 27 on Nonesuch.

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