Pianist Aldo López-Gavilán arrived on the Vineyard Saturday and spent much of Sunday practicing in advance of concerts with Harlem Quartet on Monday and Tuesday as part of the Martha’s Vineyard Chamber Music Society summer series.

Harlem quartet in rehearsal: from left, Ilmar Gavilan, Melissa White, Felix Umansky, Jaime Amador. — Maria Thibodeau

Mr. López-Gavilán lives in Cuba but has traveled regularly to the United States since 2015 when diplomatic relations were restored. He makes regular appearances with the quartet.

Last month the pianist participated in Festival Napa Valley in July and played other smaller club gigs prior to the festival. His wife Daiana Garcia is conductor of the Havana Chamber Orchestra, which was also featured at Napa. They flew across the country to appear on the stage at Chautauqua in western New York on July 24. Then it was back to California, where Mr. López-Gavilán premiered his first piano concerto, Emporium, on July 29 at Lake Tahoe with the Classical Tahoe orchestra. All this is a lead-in to his two performances this week in Edgartown and Chilmark.

The pianist enjoys every opportunity to play with his brother Ilmar, a violinist and founding member of the quartet. They are from a musical family — their father Guido is a conductor and their late mother Teresita Junco was a pianist. In 1988 Ilmar, six years older, was sent at age 14 to what was still the Soviet Union to complete his musical education. During his four years in Russia, he returned to Cuba only once a year. After he began to live in Europe and the United States he returned more often. Aldo never had formal training in jazz, but on his visits his brother encouraged him as he taught himself composition and improvisation. “He knows his music,” he said of Ilmar.

“It’s easy to focus on a classical career in Cuba,” he continued, “but you can’t leave Cuba as just a classical player.” Financially, he said, it just doesn’t work. “So it’s common to find players in the national symphony [of Cuba] doing other projects.”

His classical influences are the 20th century composers — Europeans like Igor Stravinsky and Claude Debussy, and Americans like Aaron Copeland and George Gershwin. He said his own compositions cover a broad spectrum of styles. Much of what he writes is lush, beautiful and strongly rhythmic, but given his stated influences one would expect some dissonance. “I have a suite that is Modern,” the pianist grinned. His work is full of strange time signatures and impossible to dance to. “But it is nothing that you cannot comprehend,” he said. “If the mood and feeling that you try to transmit are in the right place, then it is a success.”

Pianist shares a moment of laughter with members of quartet. — Maria Thibodeau

Recently he collaborated with Susana Pous, the choreographer for DanzAbierta in Havana, on a production called Welcome. It was Mr. López-Gavilán’s first composition for dance. “They had ideas for movements, scenes and a script,” he said, “but the scenes had to change during the composition because of the length and speed of what I wrote.” He has written film scores as well and said they included a similar back and forth during the composition, but had the advantage of both the film and the music being recorded, while a dance score is for a series of live performances.

While compositions for film and dance must be played as they are on the page, Mr. López-Gavilán is renowned for his improvisation abilities. Jazz is famously spontaneous, but it is often forgotten that classical performances routinely include music from soloists that is not on the page. Mr. López-Gavilán said he is fond of Gershwin’s Rhapsody in Blue. “I always improvise in one part,” he said. “There is nothing in the score about where to improvise,” the pianist said of Gershwin, “but I’m sure he would approve.”

The Ludwig Meets Dizzy program at the Chilmark Community Center tonight begins at 8 p.m. at the Chilmark Community Center. It opens with Beethoven and moves on to Dizzy Gillespie and Billy Strayhorn.