Ask bassist Or Bareket how he identifies and he might tell you “musician.” It’s a simple, true response to a question that otherwise requires a complex answer.

Part of a wave of exceptional Israeli musicians who have supplied a steady thrum of creative energy to the New York jazz scene since the 1990s, Bareket has emerged in the past decade as a standout composer and bandleader with a vision that’s strikingly international, even by the Big Apple’s polyglot standards.

Back in San Francisco’s Black Cat with his quartet for an eight-show run May 11 to 13, he’s focusing on music from his third album, “Sahar,” which was released in May on the German label Enja. The title means “moon” in Hebrew and “just before dawn” in Arabic, though according to the album’s website, “sahar” can also be translated as a “state that feels suspended in infinity, outside the waking experience of the passage of time.”

Whatever the definition, “Sahar” represents a major leap in the evolution of a body of work that encompasses folkloric rhythms and forms from the Mediterranean, South American and North African cultures to which he’s heir, filtered through his deep knowledge of modern jazz idioms.

The 38-year-old Bareket attributes his cosmopolitan vision directly to his upbringing. Born in Jerusalem and raised in Buenos Aires and Tel Aviv, he was exposed to sounds from all his familial lines. His Argentine-born mother grew up in a family of Iraqi Jewish and Ashkenazi origins, while his Israeli-born father hails from a family with Moroccan Jewish and Ashkenazi roots.

“I grew up with distinct musical folklore, a little bit of everything,” he said in an interview. “My family moved to Buenos Aires when I was a baby, and I was there for early childhood. We moved back to Israel in the early 1990s when I was 6 or 7 years old.”

In Tel Aviv, he found himself betwixt and between groups at an elementary school run by American Reform Jews who’d made aliyah.

“It was located in a neighborhood with a lot of Mizrahi, Yemeni, Persian and Moroccan Jews,” he said. “There was an even mix between the Americans and the local kids, and I didn’t necessarily identify with any group. I had an Argentine accent, and my appearance was ambiguous. It was a blessing and a curse.”

His parents grew up at a time when Mizrahi origins were considered anything but cool in Israel. The culture he absorbed from them came in hints, abstruse clues and reluctant accounts. He regrets the situation but understands the desire to blend in, he said.

“My maternal grandmother came to Israel from Baghdad on the back of a truck at 5 or 6,” he said. “She was completely assimilated and didn’t speak Arabic. On my first album there’s a song dedicated to her in an Iraqi rhythm. I wish it was a rhythm taught to me by my grandmother.”

The Or Bareket Quartet that will play the Black Cat reflects the cosmopolitan swirl that keeps the New York scene simmering, with Dominican-American Alfredo Colon on alto sax and EWI, or electronic wind instrument; pianist Jeremy Corren, who gained widespread notice on two of vibraphonist Joel Ross’ Blue Note albums; and Oakland-reared drummer Savannah Harris, who’s also performing with vocal star Cécile McLorin Salvant at the SFJAZZ Center from May 5 to 7.

Bareket is in a good deal of demand himself. The commanding bass player won the International Society of Bassists’ jazz competition the year after he moved to New York in 2011. He has performed with many of the most celebrated jazz improvisers, including guitarist Peter Bernstein, Brazilian bandolin maestro Hamilton de Holanda, saxophonist Chris Potter, drummer Billy Hart and the late pianist Don Friedman.

Bareket’s jazz-fan father turned him onto the music, and he grew up listening to Keith Jarrett, Pat Metheny, Duke Ellington and Miles Davis. Around the age of 15 he remembers realizing that the bass was a distinct instrument unto itself.

“I hadn’t seen a lot of live music,” he said. “I asked my dad about it and he bought me Jaco Pastorius’ first album. After a few bars of that first track ‘Donna Lee,’ I had a rare moment of clarity. I knew this is what I’m going to do.”

He focused solely on electric bass until his younger brother, Eden Bareket — today a respected New York baritone saxophonist — told him, “You’re not playing a real bass. If you really want to play jazz, you have to pick up the upright.”

It happened that an old upright bass belonging to his late uncle, who had died during the Six-Day War in 1967, was kept at his grandparents’ house. It was an “old, busted plywood bass that was like a shrine to my uncle in one corner of the living room,” he said. “I had never considered playing it, but my father and brother said, ‘Just ask.’”

His grandparents agreed to let him use the bass. “I had it restored,” he said. “I brought it to New York and still have it today. My grandparents consider it on permanent loan.”

Or Bareket Quartet

May 11-13, Black Cat Jazz Club, 400 Eddy St., S.F. 7:30 p.m. and 9 p.m. sets on May 11 ($25-$35); 7:30 p.m., 9 p.m. and 10:30 p.m. sets on May 12 and 13 ($35-$45).