Daniel Carter marks his territory by aiming his trumpet at the ground in a virtual circle, and then lunges toward the ceiling with shrill intensity. Moments later, he broods on a clarinet and whines on a tenor sax. Then he gnaws at a flute like it’s a stick of beef jerky, tearing at it with youthful enthusiasm. The 57-year-old performs for a regular CBGB crowd that gravitates downstairs for a piece of the avant-action every Sunday night, but Carter’s not confined to the Bowery.

He’s also at the Brecht Forum (122 West 27th Street), a Marxist center in Chelsea with folding chairs, ceiling fans, wooden floors, and other relics from the ritualized loft days, when the jazz, admission, and sex were often free. Relaxed, he cradles the clarinet and paddles through the middle registers. He then jumps to the tenor, testing one idea that he likes, another that he doesn’t, a third that likes him, and a fourth that prompts further exploration. With eyes shut, fingers ready, and ears to the room, he incorporates a faucet’s drip, listener’s cough, and foot’s tap into his improvisational patterns.

But he’s mellow, not melodramatic. You can hear his trills and triads, or tune them out completely and concentrate on your math homework, which, of course, he won’t help you with. “School and me did not mix too well,” he says, “and that probably extends to my music,” which, he explains, “is about freedom; the space within traditions to blow meaningful shapes that you truly believe in.”

After growing up in New Jersey, moving to Massachusetts, and serving army time in Italy, where he set up turntables and amplifiers in the barracks, Carter moved to New York City in 1970 and began performing weekly, from sunup to sundown, with everyone from Sun Ra, Cecil Taylor, and William Parker to David Murray, Oliver Lake, and Sam Rivers. He then joined several hardcore punk bands, nurturing an emotional drive that led him, by the mid ’80s, to play on street corners, subway platforms, and “wherever cops and storekeepers wouldn’t move you,” he says. Since then, he’s been heard with Medeski, Martin and Wood, Yo La Tengo, DJ Logic, Spring Heel Jack, Dee Pop, Reuben Radding, and Matt Lavelle, as well as on his own albums, including his most recent Aum Fidelity release, Luminescence, an incisive, instructive set of soft editorials and tender tantrums.

But he’s not the kind of musician who’s open to ideas without developing any of his own. His hypnotic, breathy solos absorb everything from Abbey Lincoln’s “World Is Falling Down” to John Coltrane’s “Naima,” quoting a collection of treasured tunes that lend salt to his whiskey-sour wounds and, at the same time, heal them.