Kris Davis Capricorn Climber (Saturday) The pianist Kris Davis has been generating nothing but interesting music in recent months, and has a new band, Capricorn Climber, that seeks out the unexpected corners within established musical relationships. Her partners, all adept with spontaneous texture, are the tenor saxophonist Ingrid Laubrock, the violist Mat Maneri, the bassist Eivind Opsvik and the drummer Tom Rainey. At 9 and 10:30 p.m., Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $10 cover, with $10 minimum.
Marc Johnson and Eliane Elias (Friday and Saturday) Mr. Johnson, a bassist of deeply sonorous style, and Ms. Elias, a pianist with a transparent touch and a fondness for subtle harmonic shading, recently released a lovely album together, “Swept Away” (ECM), with the saxophonist Joe Lovano and the drummer Joey Baron. For this engagement, the headliners, a husband-and-wife team, work with the veteran drummer Victor Lewis. At 8 and 10 p.m., Iridium Jazz Club, 1650 Broadway, at 51st Street, (212) 582-2121, theiridium.com; $35 cover, with a $10 minimum. (Chinen)
Giuseppi Logan Quartet (Thursday) Mr. Logan is an alto saxophonist whose promising start, on the mid-1960s free-jazz scene, was curtailed by a mysterious silence. (In one prominent accounting of the era he was said to have vanished; in fact he was homeless, having suffered the ravages of drug dependency.) His comeback has been lovingly chronicled, and championed by younger musicians like Matt Lavelle — who has organized this concert, and who will play fluegelhorn and alto clarinet in the band, alongside the bassist François Grillot and the drummer David Miller. (Also on the bill, playing a 9:30 p.m. set, is the cellist Gil Selinger.) At 8 p.m., Firehouse Space, 246 Frost Street, Williamsburg, Brooklyn, (917) 709-7799, thefirehousespace.org; $10. (Chinen)
Mario Pavone’s Arc Trio (Friday) Mr. Pavone, a bassist-composer of experience and vision, presents a new body of music composed for this trio, with two exceptionally intuitive partners: the pianist Craig Taborn and the drummer Gerald Cleaver. At 9 and 10:30 p.m., Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $15 cover, with a $10 minimum. (Chinen)
Jesse Stacken / Matt Pavolka / Vinnie Sperrazza (Thursday) Mr. Stacken, a pianist, joins Mr. Pavolka, a bassist, and Mr. Sperrazza, a drummer, in exploratory interplay. The trio plays at 10 p.m., and an earlier set, at 8:30, will consist of a far-ranging solo performance by the baritone saxophonist Jonah Parzen-Johnson. At 10 p.m., IBeam, 168 Seventh Street, Gowanus, Brooklyn, ibeambrooklyn.com; jessestacken.com; $10 suggested donation. (Chinen)
David Virelles and Continuum (Friday through Sunday) A freethinking young Cuban pianist, Mr. Virelles released one of last year’s best and most intriguing albums: “Continuum” (Pi), an ever-shifting amalgam of ancient folklore and avant-garde protocol. Mr. Virelles presents this project at the Village Vanguard, where he has worked in bands led by the saxophonists Chris Potter and Mark Turner. He’ll have the same rhythm section as on the album: the bassist Ben Street, the percussionist-poet Román Díaz, the venerable drummer Andrew Cyrille. At 9 and 11 p.m., Village Vanguard, 178 Seventh Avenue South, at 11th Street, West Village, (212) 255-4037, villagevanguard.com; $25 cover, with a one-drink minimum.