Jazz guitarist Mary Halvorson explores territory where there are no rules

“Orange head secretes a lie above you,” sings guest vocalist Robert Wyatt on “Bigger Flames,” the fifth song on Brookline native Mary Halvorson’s just-released album “Artlessly Falling.”

The album — which Halvorson, 40, recorded with her Code Girl sextet in December, a couple of months after being awarded a MacArthur Foundation “genius grant” — features the guitarist/composer’s own surreal, impressionistic poetry, much of it obscure enough to seem like it’s in code.

“Well now it’s your house, set neatly on fire,” Wyatt continues a few stanzas further into the same song, “its blistering heart bloats high above you.”

That’s as close as “Bigger Flames” comes to directly divulging its point. The song’s opening line contains a strong hint, though: “Orange head secretes a lie”? Are we talking about Donald Trump?

“Yup,” confirms Halvorson, laughing, speaking by phone from her home in Brooklyn a few days before the election. “They’re all pretty impressionistic. But that one, to me, was more or less about the environmental crisis, and the state of the world being what it is.”

Halvorson’s path to where she could enlist a legend like Wyatt to sing her lyrics is an intriguing one.

She took up guitar at age 11 upon discovering Jimi Hendrix. After high school, Halvorson went to Wesleyan University intending to study biology or psychology. There she met two particularly impactful influences who caused her to abandon those plans.

“I got the music bug pretty bad,” she says, “and at a certain point I just couldn’t go back.”

She took private lessons from the experimental guitarist Joe Morris, who lived not far from campus. And she took every class available with the prolific composer and saxophonist Anthony Braxton, a much-beloved Wesleyan professor of music.

“He was just so interesting to be around,” says Halvorson of Braxton. “He made music seem fun. He made it seem like there were no rules. I should say, ‘He brought to my attention that there are no rules,’ which I kind of hadn’t realized. So just having that kind of encouragement, and that kind of license to just explore, I think was really what I needed at the time, and also what really sucked me in.”

Braxton helped inculcate Halvorson’s love of experimentation and disregard for musical genres, beginning with a class she took freshman year, whose title she remembers as “Materials and Principles of Jazz Improvisation.”

“What was so cool about his classes is that he loved all types of music,” says Halvorson. "And the genre didn’t really matter. . . . He also had a class called ‘The Music of Sun Ra and Stockhausen.’ "

Halvorson graduated from Wesleyan in 2002, moved to New York, and began recording and touring. The first of her own 10 albums was released in 2008. She has also appeared on upwards of 50 others, including four with the collaborative trio Thumbscrew, the most recent of which, “The Anthony Braxton Project,” was released this past summer.

Halvorson’s renown has grown considerably of late. In 2017 she headlined at the Village Vanguard for the first time and won four categories in that year’s DownBeat Critics Poll, including the first of her four consecutive wins as best guitarist.

Her first Code Girl release, an eponymous double album, was the result of her wanting to incorporate words into her music. Halvorson herself wrote the free verse poems that served as the album’s lyrics, recorded by a quintet featuring Amirtha Kidambi on vocals, Ambrose Akinmusire on trumpet, and Thumbscrew colleagues Michael Formanek and Tomas Fujiwara on bass and drums, respectively.

“Code Girl,” released in 2018, earned Halvorson yet more critical acclaim and the attention of the MacArthur Foundation. By the time she was notified she had won her genius grant last year, Halvorson was already writing words and music for a follow-up. Code Girl had expanded to a sextet, with Adam O’Farrill replacing Akinmusire on trumpet and María Grand added on tenor saxophone and vocals, and Wyatt had agreed to sing on it.

Halvorson had become obsessed with Wyatt’s music via his 1974 solo album “Rock Bottom,” Wyatt’s first after the 1973 accident that had rendered him a paraplegic, and worked her way back to his earlier recordings with the band Soft Machine.

“I found out the way it is with Robert Wyatt is that people either have no idea who he is or they’re obsessed with him,” she says, laughing. "I knew these two guys that ran a club in New York, and every time I went in Robert Wyatt would be playing, and so we started talking about it. They knew I was a big fan, and one of them said, ‘Hey, you know every year we mail him a package. He’s a big jazz fan, and we mail him a bunch of jazz vinyl. Would you like to include something?’ "

She jumped at the chance. “To my surprise, I got a postcard from Robert Wyatt. So he actually listened to the record and wrote me this really nice note. I couldn’t believe it.”

That led to a sporadic correspondence. Halvorson would often mail Wyatt new records she put out. So they already had a connection when she approached him about appearing on “Artlessly Falling.”

“I really wanted to have a male singer on the record, and so he was my first choice,” explains Halvorson. “He wrote back right away and was like, ‘Yeah, I’d love to.’ "

While the first Code Girl album’s lyrics consisted entirely of free verse, “Artlessly Falling” involved stricter poetic forms.

“Last-Minute Smears” is a found poem constructed from words drawn directly from Supreme Court Justice Brett Kavanaugh’s testimony to the Senate. Fujiwara accompanies its vocal passages with a militaristic cadence, and uses beer cans for effects elsewhere on the track.

“That was all my idea,” says Fujiwara. “So yeah, [the military drum rolls] was something I played around with. Obviously the beer cans. At one point I had some textures that sounded like a gavel.”

Fujiwara and O’Farrill are featured alongside Wyatt on the opening track, “Lemon Trees,” a double tanka drawing words and inspiration from the Lawrence Osborne novels “Beautiful Animals” and “The Forgiven.”

“Walls and Roses” is a pantoum, with Wyatt and Grand alternating wispy vocals on the song’s four stanzas and Halvorson unleashing furious bursts of effects-laden guitar chops in between. Its words, like “Bigger Flames” and its orange head secreting lies, keep its meaning coded, inviting listeners to formulate their own interpretations.

“That’s why I don’t make the lyrics super explicit,” says Halvorson. “I like that people can take different meanings from it. So, for instance, even if that song to me wasn’t about Trump, or wasn’t about the environment, if you took that from it, that would be cool with me. I like that idea that everybody can hear or see things so differently.”