Arturo Sandoval has a special relationship with Dizzy Gillespie.

The Cuban-born maestro, who appears with his six-piece band at Herbst Theatre on Saturday in a SFJAZZ 30th anniversary celebration, says, “Dizzy loved Cuban music, and when we met, we understood each other very well.”

Sandoval — a composer, bandleader and scholar as well as virtuoso jazz trumpeter — plays powerful Cuban jazz and bebop, about which he says, “You do not need to try to figure it out. Just listen to the expression.”  

Saturday’s show salutes bebop hero Gillespie, featuring music from “Dear Diz (Every Day I Think of You),” Sandoval’s recent Grammy Award-winning album in the Latin jazz category.    

In an interview from Los Angeles, where he lives, Sandoval said  what he loves most about the trumpet is that it lets him express his feelings.

But Gillespie’s music is not for faint-of-heart players, or amateurs, Sandoval says: “You have to be a serious, dedicated musician, who practices a lot.”

The description fits Sandoval, a founding member (with Chucho Valdés and Paquito D’Rivera) of Irakere, an innovative 1970s Cuban band that gained international attention. Later, Sandoval worked with his mentor Gillespie, playing trumpet in the United Nations Orchestra.

Saturday’s concert, with Sandoval on trumpet and percussion, Zane Musa on saxophone, Mahesh Balasooriya on piano, John Belzaguy on  bass, Johnny Friday on drums and Samuel Torres percussion, closes SFJAZZ’s excellent 2011-12 Latin jazz programming, among the best in of its type in The City’s history.

In January, the organization opens its new, state-of-the-art SFJAZZ Center at Fell and Franklin streets in Hayes Valley.