One of the less publicized effects of Hurricane Katrina was that it washed bassist, composer, and conductor Matt Golombisky onto the shores of Chicago. In New Orleans, Golombisky had played in as many as a dozen bands at a time; here he’s not only kept up a similar pace but also runs a record label and organizes an annual festival, both of which bear the name Ears and Eyes.

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Of all the bands to which Golombisky contributes, the Tomorrow Music Orchestra (which plays Saturday at around 7:15 PM) best showcases him as both performer and instigator. The band started large but still reasonably sized in 2006, then quickly grew into the 18-piece behemoth that recorded last year’s invigorating Neon Jesus Garage. That’s about as big as your average jazz orchestra, but few other bands of that size have ever had such damnably weird instrumentation: the lineup on that disc includes bass, drums, guitar, oboe, two vibraphones, two alto saxophones (but no tenor), two flutists (not doubling on anything), a small brass choir (trumpet, trombone, and French horn), and a misshapen string quartet with two cellos and only one violin. Since the Neon Jesus Garage sessions, Golombisky has expanded the TMO by a third, adding another oboist, a second French horn player, a bass clarinetist, and an accordionist, among other players.

Two of the TMO’s star soloists—the husband-and-wife team of trumpeter James Davis and saxist Caroline Davis—work together and separately in several other bands on the Ears and Eyes label, and one of them, the James Davis Quintet, recently released what may well be the imprint’s most fully realized album. (Unfortunately the JDQ won’t play at this weekend’s fest.) Angles of Refraction has become my favorite disc of the past couple months, standing up to repeated listenings with a program divided evenly between up-tempo postbop and jazz flavored with balladic Americana. The Davises are a formidable pair: On alto, Caroline improvises with a balance of passion and polish that younger horn players often lack, sometimes using a rococo touch to curl around her husband’s trumpet lines. And James’s playing—with its pure tone, measured melodies, and judicious use of both notes and space—reminds me of the fresh breath Chet Baker blew through bebop in the early 50s.

Zing! plays the Ears and Eyes Festival at 4 PM Sunday, and later that night Dave Miller’s group Algernon goes on. Miller, one of those polymaths who can’t seem to find enough bands to fill his time, has built this unusual quintet into a sleek roadster, using Katie Wiegman’s vibraphone to lighten and brighten the sound of the two-stroke jazz-rock engine—Miller and Nick Fryer, both on guitar—that powers the band. Miller draws from jazz and rock (prog, psych, and post-) but also aspires to a kind of latter-day chamber music: tautly composed lines and detailed, surprisingly delicate arrangements butt up against raucous free improvisation and splashy electronics. On Familiar Espionage, Algernon’s forthcoming second album, the tunes (with titles like “Eraserhead” and “(Don’t Press the) Red Button”) have a definite post-rock feel, but Miller pushes them into jazzier territory—all the while avoiding anything that sounds like a traditional jazz solo.

Fri 12/7, 9 PM, Hearts for Sale, 2606 W. North, earsandeyesfestival.com, $5 suggested donation. A

Sat 12/8, 4 PM, Subterranean, 2011 W. North, 773-278-6600 or 866-468-3401, $15, $20 for a two-day pass, 18+.

Sun 12/9, 4 PM, Subterranean, 2011 W. North, 773-278-6600 or 866-468-3401, $15, $20 for a two-day pass, 18+.