SWING THAT AX Mary Halvorson and her big, loud guitar hit Barbès for an alubm-release show this week.

Photograph: Peter Gannushkin

Mary Halvorson’s suitcase is, momentarily, unpacked, and her calendar almost empty. Such leisurely spells are rare. The guitarist has spent much of the past year hopscotching around the globe in a variety of ensembles, most notably a sprawling 12-piece outfit led by the visionary composer Anthony Braxton—a former teacher of Halvorson’s and many of her peers, who have been shaking up the city’s creative music circles.

“I got to go to some amazing places that I’d always wanted to see,” Halvorson says, bracing herself against a chilly breeze outside a coffeehouse near her apartment in Fort Greene, where she’s lived since 2002. “Like Moscow, Mexico City, Buenos Aires.” Between travels, Halvorson, 28, recorded her first trio album in the studios of New Haven label Firehouse 12. Tunes from Dragon’s Head are on the set list for her show at Barbès on Wednesday 12. And while Halvorson has a serious capacity for improvisatory shred, the album reveals a growing fascination with more traditional jazz elements, shimmering amid the angular shards of notes.

“I’ve been more focused on jazz,” says Halvorson, who plays a 1970 Guild Artist Award guitar because it was the biggest, loudest model she could find. “Changes, arpeggios, scales. This is sort of to learn the guitar better, as a technical exercise. But it’s also because I’ve been getting back into that music: a lot of classic stuff, stuff I listened to in high school and college until I killed it.” Asked for examples, Halvorson almost turns sheepish, confessing: “Like Kind of Blue. That track ‘Flamenco Sketches,’ I just rediscovered it. I’m zoning in on things. Drummers—I’m listening to a lot of Art Blakey and Elvin Jones.”

That passion comes most noticeably to the surface on the opening to “Totally Opaque,” in which drummer Ches Smith and bassist John Hébert call to mind the almost subliminal grace of the classic Miles Davis session. Meanwhile, Halvorson lets a simple, repetitive progression of notes hang suspensefully in the air before she begins to articulate her extended, pointillistic lines, finally circling back to the initial form.

The musician doesn’t want it to sound obvious, though. “I write intuitively,” she says. “I’m not an intellectual. If I was writing a grant I’d have a hard time putting it into words. I don’t want to think that a certain song is a combination of my love of Deerhoof and my resparked love of Miles Davis. Maybe I have been listening to those records and it seeps in, but I really try not to be conscious of it.”

Reconciling such forces makes for magnetic tension in performance. “Mary and I share an affinity for dense, abrasive harmony,” says bassist Trevor Dunn, a prolific collaborator of John Zorn and Melvins, who enlisted Halvorson to play guitar in his accurately named Trio Convulsant. “She’s not afraid to explore the awkward while maintaining a sense of melody, balancing the fragile with the overwhelming.”

Halvorson, who is collaborating with her close friend, violist Jessica Pavone, on a new collection of vocal pieces for release on Thirsty Ear, is the kind of musician other musicians love to have on their bandstands. She’s recently been working with pianist Myra Melford and saxophonist Tim Berne, widely admired figures who were beginning to make their names when Halvorson was a toddler. It’s her trio project, though, that dominates her focus. The album’s title Dragon’s Head, which alludes to the north node of the moon in astrology, reflects this. “It has to do with karma, and what you’re supposed to be achieving in your lifetime,” she says. “It’s not an easy path, but a path you work towards developing. I like that concept.”

An ardent student of the stars, Halvorson dismisses pop astrology as fluff, while noting that John Coltrane waited for a perfect astrological moment to record A Love Supreme. Aside from a passing reference on her album, don’t expect her—a Libra, by the way—to follow Mary Lou Williams’s example and record a Zodiac Suite, or select bandmates based on their planetary alignments. “That would be funny,” she says. “Hopefully I’m not that crazy.”

The Mary Halvorson Trio plays Barbès Wed 12. Dragon’s Head is out now.