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Israeli jazz musicians Anat and Avishai Cohen make a great brother-sister act. Then again, sometimes they don’t.

When the siblings perform Oct. 9 at Congregation Sherith Israel as part of the 28th San Francisco Jazz Festival, they will not be playing together, as they often do. Instead, they will lead their own separate bands.

“It’s a very cool that they invited me with my band [the Anat Cohen Quartet], and he with his [Triveni, a trio] — to each have our vision,” says Anat. “We’re individuals.”

While the trumpet-playing Avishai has leaned toward African and funk styles, Anat has developed a passion for South American jazz and folkloric traditions, especially upbeat choro music from Brazil, which features her clarinet as a prime solo instrument. She also plays the saxophone.

But she loves all kinds of jazz subgenres, from be-bop to Big Band. She loves klezmer, too, though she swears she would never play it in public. “I can fool around a little bit,” Anat says, “but I have too much respect for it to play it.”

Anat’s reverence for music shows in her recordings and live performances, though she contends that the borders of jazz have shifted over the years.

“What makes someone a jazz musician in 2010?” she says. “Is it if you play songs from the ’20s, ’30s or ’40s? Today it’s less the American songbook 32-bar structure. Musicians today understand anything is possible at any given moment.”

The Cohens, along with a third sibling, saxophonist Yuval Cohen, grew up playing jazz together in their native Tel Aviv. The three siblings later attended Boston’s Berklee College of Music. Anat and Avishai now live in New York, while Yuval still makes his home in Israel.

Anat credits her parents, both music lovers, with instilling their kids with a passion for music, even to the point of making careers out if it.

“They really let us follow our hearts,” she says of her parents. “The fact that three of us were in [music] and went to a conservatory three times a week, until 9 p.m., it became our life. We were definitely supportive of each other. I never felt a competition between us.”

She began classical clarinet studies at age 12, but the music of Louis Armstrong, more than anything else, turned her on to jazz. Cohen later attended a Tel Aviv arts high school, where she added tenor sax to her arsenal of reed instruments.

She went on to play sax in the Israeli air force band, before moving to Boston for intensive study. After Berklee, she moved to New York, where she found work with various Afro-Cuban and Brazilian ensembles. She made her recording debut in 2005, and has since released three more solo CDs. She also recorded an album with her brothers.

Anat does get back to Israel for visits. She says since she left in 1996, the Israeli jazz scene has expanded well beyond the “couple of bars” she remembered patronizing in her younger days.

Though she’s lived in the United States for many years, she remains a proud Israeli. That’s why she is troubled by musicians such as Elvis Costello and Carlos Santana canceling Israeli tours, as well as the boycotting of Israeli concerts.

“Boycotting individuals who are trying to bring good to the world is ridiculous,” she says. “Ignorant people confuse government policies and individuals. There are things that happen [in Israel] I’m not happy with, and I do worry I will get to a place and they will blame me for what happens in Israel.”

Meanwhile, Anat, like her brothers, continues to tour the world. Though as a musician, sometimes traveling is not so simple. She says more than once, she has been detained from boarding a flight while carrying more than one instrument.

“If I want to bring a tenor sax, soprano sax and clarinet, it’s risky,” she says. “Homeland Security might say no.”

The Anat Cohen Quartet and Avishai Cohen’s Triveni will perform at 8 p.m. Oct. 9 at Congregation Sherith Israel, 2266 California St., S.F. $25-$50. Information: (866) 920-5299 or www.sfjazz.org.