The Seattle Repertory Jazz Orchestra (SRJO) plays three concerts this weekend with the incomparable Cuban drummer Ignacio Berroa, part of a banner season that has included a Golden Ear Award from the local organization Earshot Jazz and a gala that raised a record $90,000.

The SRJO sprang to life 24 years ago as a vehicle for vintage classics but lately has been challenging itself with dynamic, unfamiliar material.

“We’ve been introducing audiences to more and more music that they’ve never heard before,” said SRJO co-director Michael Brockman. “The turning point was the concert with Anat Cohen.”

Indeed, the band’s 2015 show with Cohen yanked the SRJO into the international present, where jazz actually lives, a trajectory reinforced last fall by its concert with composer Maria Schneider.

This week, Berroa will challenge the group with a riot of complex rhythms, though the drummer stressed in a phone interview from his home in Miami last month that the concert will be as much about big-band jazz as Cuban beats.

“I’m a strange Cuban,” said the 65-year-old drummer. “I’m a proud Cuban guy who loves to play straight-ahead jazz.”

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Berroa was Dizzy Gillespie’s go-to drummer — not a “percussionist” but the drummer who sits behind the band — from 1981 until Gillespie’s death in 1993. He is no stranger to Seattle. Fans may fondly remember seeing him with Gillespie at the old New Orleans Restaurant, in Pioneer Square, back in 1989, or more recently at Jazz Alley, with Chick Corea. Berroa’s local connections also include a 1983 recording, “Into Somewhere,” with the late local saxophone hero Don Lanphere.

Gillespie once described Berroa as “the only Latin drummer in the world in the history of American music that intimately knows both worlds: his native Afro-Cuban music as well as jazz.” That means Berroa is entirely fluent in Cuban polyrhythms like abakuá, guaguanco, cha cha cha and so forth, but also plays straight-ahead, big-band swing.

That’s no mean feat, especially when you consider that when Berroa grew up in Cuba, neither jazz nor traditional Cuban music were politically correct — the former because it was the “music of the enemy” (the United States), the latter because it grew out of the Yoruba religion.

Berroa absorbed traditional music from his family — his father and grandfather were both professionals — and learned jazz from hotly traded cassette tapes, radio broadcasts and live performances by Cuban jazz drumming star Guillermo Barreto.

“One of the reasons I left Cuba was because I wanted to pursue my jazz career,” explained Berroa, who fled his homeland in the 1980 Mariel boat lift and moved to New York.

Ironically, Cuban cultural policy loosened up almost immediately thereafter, and Berroa soon found himself playing at the Havana Jazz Festival. But opportunities were still more abundant in the U.S.

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Over the past decade-plus, Berroa has emerged as a leader with, among other recordings, his 2006 Blue Note debut, “Codes,” and a dazzling, must-have 2017 trio album, “Straight Ahead From Havana” (Codes Drum Music).

The set list for the SRJO shows is not yet set in stone, but expect to hear Afro-Cuban classics such as “Manteca,” “A Night in Tunisia” and “Cuban Be Cubana Bop,” all associated with Gillespie; Count Basie’s “Splanky”; a composition by saxophonist Bob Mintzer, “Run For Your Life”; and Berroa’s lovely tune for his granddaughter, “Laura’s Waltz.”

Also expect to hear a drummer driving a big band with the panache and power of a Basie alum like Sonny Payne, as well as a soloist who can navigate a rhythmic hurricane and land on his feet.

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Cubana Be Cubana Bop: Ignacio Berroa and the Seattle Repertory Jazz Orchestra, 7:30 p.m. Saturday, April 13, at Illsley Ball Nordstrom Recital Hall, Benaroya Hall, 200 University St, Seattle; 2 p.m. Sunday, April 14, at Kirkland Performance Center, 350 Kirkland Ave., Kirkland; and 7:30 p.m. Monday, April 15, at Edmonds Center for the Arts, 410 Fourth Ave. N., Edmonds; $10-$50; 206-523-6159, srjo.org