The O’Farrill clan may claim the distinction as the first family of Afro- Cuban jazz. It helped invent the hybrid genre in the 1940s, when Chico O’Farrill came to New York from Havana, and they have worked to reinvigorate the music despite barriers in both Cuba and the United States.

“We’re kind of people caught between two worlds,” said Arturo O’Farrill, a pianist and Chico’s 50-year-old son. As such, he added, it’s his obligation to encourage “an evolving relationship between two countries that should never have been separated culturally” and to “pay a debt forward” in his father’s name.

The musical story of the family begins with Chico, who was studying in Georgia in the mid-1930s when he fell in love with jazz. A decade later, after playing trumpet in Cuban orchestras, he moved to New York, where he quickly became a top composer and arranger, working with Benny Goodman, Dizzy Gillespie, Stan Kenton, Charlie Parker, Stan Getz, Count Basie and Machito, among others.

“ Chico O’Farrill is the greatest Afro-Cuban jazz figure of all time,” Leonardo Acosta, the author of “Cubano Be Cubano Bop: One Hundred Years of Jazz in Cuba,” said by phone from Havana. “His way of using the orchestra as an instrument, his ability as an arranger and composer and his skill in converting Cuban music into jazz and vice versa gives his work a kind of chemistry that no one else, neither Cuban nor American, has. ”

At first Arturo gravitated toward experimental jazz groups; for a while he played keyboards in J. Walter Negro and the Loose Jointz, which blended hip-hop, funk and disco elements.

“As a young man Arturo was not all that keen on the music of his father, whose shadow he was trying to escape,” said the Cuban saxophonist Paquito D’Rivera .

The turning point, Arturo O’Farrill said, came in the early 1990s, when his father resumed recording under his own name after a long drought. Arturo began by playing piano on some of those sessions and eventually wrote arrangements for and conducted the orchestra that backed his father.

In 1995 Arturo and his father began sharing conducting duties for Chico’s Afro-Cuban Jazz Orchestra in weekly performances at the Manhattan jazz club Birdland, which continued after Chico’s death in 2001. Arturo also founded and directed the Afro-Latin Jazz Orchestra, which in 2009 won a Grammy for the CD “Song for Chico.”

“I was able to let go of many ghosts of the past,” Arturo said when asked about his shift in musical direction. “My father was a brilliant man, and the honorable thing to do was help him get his art out. ”

Arturo’s sons, who have just released a CD of Latin-inflected jazz called “Giant Peach,” are carrying on the tradition. Zack, 19, is a drummer, and Adam, 16, a trumpet player; the O’Farrills are participating in the ¡Si Cuba! arts festival in New York. Both sons have made trips to Cuba with their father.

Those visits have been filmed for “Oye Cuba! A Journey Home,” a documentary about the O’Farrills that is expected to be released next year.

“Younger musicians there have lost a sense of the history of this music, and my perception is that part of this goes to the struggle that Cuba has had with jazz, and the attempts over the years to expunge it from their schools” as a manifestation of imperialist bohemianism, said Diane Sylvester, the director.

Mr. O’Farrill’s creativity seems to have been energized by the Cuba trips.

“It inspires him,” she said, “and on a personal level it helps him process the deepest question of all: Who is my family?”