Ralph Alessi’s Modular Theater (Saturday) Collective improvisation is the mode and mission of Modular Theater, a slippery ensemble led by Mr. Alessi, an exacting trumpeter, and featuring Loren Stillman on alto saxophone, Drew Gress on bass and Mark Ferber on drums. 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. (Nate Chinen)
Brooklyn Babylon (Wednesday through Nov. 12) An intriguing multimedia collaboration between the graphic artist Danijel Zezelj and the jazz composer Darcy James Argue, “Brooklyn Babylon” concerns itself with issues of development and dystopia in a certain borough at an uncertain future date. The piece, part of the Next Wave Festival at the Brooklyn Academy of Music, will involve projected animation, live-action painting and an original score executed by Mr. Argue’s 18-piece band, the Secret Society. At 7:30 p.m., Harvey Theater, Brooklyn Academy of Music, 651 Fulton Street, Fort Greene, Brooklyn, (718) 636-4100, bam.org; $20, $14 for season tickets. (Chinen)
Marilyn Crispell (Friday) Ms. Crispell, a pianist equally celebrated for aggressive atonality and delicate lyricism, makes one of her infrequent club appearances, on intimate terms. Her first set, at 9 p.m., will be a solo recital; for the second set, at 10:30 p.m., she’ll be joined by the bassist Mark Helias, a longtime collaborator. At Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $15 cover per set, with a $10 minimum. (Chinen)
Cryptogramphone at the Stone (Friday through Sunday, Tuesday through Nov. 13) Cryptogramophone, a stylishly progressive Los Angeles label run by the violinist Jeff Gauthier, has taken over the Stone for the next couple of weeks, airing out its left-of-center aesthetic one show at a time. Among the coming week’s highlights are Trio M, an enlightened collective (Friday at 8 p.m.); Mr. Gauthier’s chief band, the Goatette (Saturday at 8 p.m.); a quintet led by the alto saxophonist Tim Berne, playing new music (Saturday at 10 p.m.); and Tiny Resistors, a chamber jazz-rock group led by the bassist Todd Sickafoose, augmented by a string quartet (Thursday at 10 p.m.). At 8 and 10 p.m., the Stone, Avenue C and Second Street, East Village, thestonenyc.com; $10 cover per set. (Chinen)
Peter Evans Quartet (Sunday) The trumpeter Peter Evans has a mind-boggling recent album, “Ghosts” (More Is More), that pursues complex derivations of standard form. He works here with the same slashing band as on the album, with the pianist Carlos Homs, the bassist Tom Blancarte and the drummer Jim Black; in their freely improvised second set they’ll be joined by John Butcher, a British saxophonist known for his extended technique. At 8:30 and 10 p.m., Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $10 cover, with a $10 minimum. (Chinen)
Paradoxical Frog (Thursday) So much possibility rumbles from this improvising collective — with Kris Davis on piano, Ingrid Laubrock on tenor saxophone and Tyshawn Sorey on drums, and all three contributing tunes — that on its superb self-titled debut, released last year on Clean Feed, you don’t have time to fixate on its free-jazz pedigree or wonder who’s running the show. Which is as it should be. At 8:30 p.m., Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $10 cover, with a $10 minimum. (Chinen)