The Bad Plus is an odd bird. The three members of this trio individually lean on specific languages of jazz improvisation, but collectively the band hesitates to get close to any single tradition. It likes to build a crescendo past the point of comfort, or move extremely slowly, or structure a kind of pop song with irresolutions and gravitational tempo shifts and wild staggers, or pump stiff grandiosity into something simple and scratchy. It plays, a little perversely, with putting on a hard shell. It exaggerates with a straight face and builds self-contained events within themselves rather than partial re-enactments of an open-ended story, which is what most jazz is.

The band has made all this its own tradition, but it has also been working on a sub-tradition, in its second decade, by collaborating with various fourth members: the saxophonist Joshua Redman, the guitarist Kurt Rosenwinkel and, most recently, the guitarist Bill Frisell. On Friday at Jazz at Lincoln Center’s Allen Room, the Bad Plus played with Mr. Frisell for the second time — the first was at the Newport Jazz Festival last summer — and in deference to him became something other than its usual self. It melted a little, becoming more open and mysterious. It shifted toward the kind of atmospheres Mr. Frisell likes: long tones and echoes, rambles and rustles, smoky and atomized music. It was also moving toward a taste that Bad Plus and Mr. Frisell share: the compositions and sound of the drummer Paul Motian.

Motian died in 2011, as many in the jazz world will remember. Mr. Frisell played with him for almost 30 years in a trio with Joe Lovano. The Bad Plus loved him, too: one odd bird recognizes another. (Ethan Iverson, the trio’s pianist, has written a learned liner-note essay, full of exclamation points and arcana, for a new six-CD Motian box set to be released next week on ECM.) And so Friday’s concert became, in part, about Motian and his world, as much as last year’s Newport set had been. And in other parts the set was about the onstage event itself in its most objective terms: one language encountering another.

The group played Hank Williams’s “I’m So Lonesome I Could Cry,” which Mr. Frisell recorded in 2005 with Motian and the bassist Ron Carter. Mr. Frisell improvised slowly and sensuously, immersing himself in the song’s harmony, and Mr. Iverson worked against that feeling, building up tension through staccato dissonances. They also played Ornette Coleman’s “Lonely Woman” and Lee Konitz’s “Subconscious-Lee,” both of which in this context felt Motian-ized, although it might really have been the other way around — a case of those composers having long ago shaped what we understand to be Motian’s originality.