A BODY WITHOUT ORGANS (Sunday) This metaphysically named series, held every other Sunday in Greenpoint, Brooklyn, reflects the rugged ideals of its organizer, the drummer Mike Pride. In a late set here, at 10:30 p.m., Mr. Pride digs in with the German clarinetist Uli Kempendorf and the Norwegian bassist Eivind Opsvik. An earlier set, at 9:30, will feature a group led by the drummer Jeff Davis, with Mr. Opsvik, the multireedist Oscar Noriega and the guitarist Jonathan Goldberger. At CoCo 66, 66 Greenpoint Avenue, Brooklyn, (718) 389-7392, coco66.com; cover, $6. 20090312
FONDA-STEVENS GROUP (Monday) This long-running free-jazz outfit, led by the bassist Joe Fonda and the pianist Michael Jefry Stevens, previews material from a new album, “Memphis” (Playscape); the other members in the group are the trumpeter Herb Robertson and the drummer Harvey Sorgen. At 8:30 p.m., Roulette, 20 Greene Street, near Canal Street, SoHo, (212) 219-8242, roulette.org; $15; $10 for students, 60+ and those under 30. 20090312
THE LANGUAGE OF (Friday) The baritone saxophonist Charles Evans and the trumpeter Peter Evans jointly lead this freethinking young post-bop ensemble, which released an album a few years ago pointedly titled “No Relation.” Before the group’s featured slot here, at 10 p.m., Charles Evans will play a 9 p.m. duo set with the pianist Neil Shah, a longtime musical acquaintance. At I-Beam Music, 168 Seventh Street, Gowanus, Brooklyn, ibeambrooklyn.com; suggested donation, $10. 20090312
TONY MALABY QUARTET (Friday and Saturday) Tony Malaby, a tenor saxophonist equally capable of focused tension and wild abandon, enlists experienced partners in this quartet: the trumpeter Ralph Alessi, the bassist John Hebert and the drummer Billy Drummond. At 9 and 10:30 p.m., Cornelia Street Café, 29 Cornelia Street, West Village, (212) 989-9319, corneliastreetcafe.com; cover, $10, with a one-drink minimum. 20090312
TOM RAINEY, INGRID LAUBROCK, MARY HALVORSON (Wednesday) Mr. Rainey, a starkly suggestive drummer, teams up here with Ms. Laubrock, a German-born, British-based tenor and soprano saxophonist, and Ms. Halvorson, a guitarist with a sharp-splintered but flexible attack. Their core purpose is a subversive but graceful whole-group abstraction. At 8 and 10 p.m., Barbès, 376 Ninth Street, at Sixth Avenue, Park Slope, Brooklyn, (347) 422-0248, barbesbrooklyn.com; cover, $10. 20090312
THE REFUGE TRIO (Tuesday) Throughout its recent self-titled release on the Winter & Winter label, this ensemble — Theo Bleckmann on vocals, Gary Versace on Hammond B-3 organ, and John Hollenbeck on drums — makes shrewdly atmospheric use of a distinctive textural palette. The group was named after a Joni Mitchell song, but its repertory extends to originals (by all three members), jazz standards (Monk, Coltrane) and farther-out fare (Allan Holdsworth). At 7:30 and 9:30 p.m., Jazz Standard, 116 East 27th Street, Manhattan, (212) 576-2232, jazzstandard.net; cover, $20. 20090312
THE THROES/FLOW TRIO (Monday) The Throes are a free-jazz outfit spearheaded by two inventive horn players, the trumpeter Nate Wooley and the cornetist Taylor Ho Bynum. Flow Trio, a bit more established, features Louie Belogenis on tenor saxophone, Joe Morris on bass, and Charles Downs on drums; the group has a stark but rewarding new album, “Rejuvenation” (ESP-Disk). At 7 and 8:30 p.m., the Local 269, 269 East Houston Street, at Suffolk Street, Lower East Side, rucma.org; $10; $7 for students.