Quartet San Francisco’s July 15 concert at the Old Whaling Church in Edgartown was resounding proof that classical music is not what it used to be — it’s better and more accessible than ever, and as exciting as at any time in its history.

Opening the Martha’s Vineyard Chamber Music Society summer season, the quartet played only 20th and 21st-century music for a delighted audience of society members and other fans.

“We love and respect the traditional string quartet material,” first violinist and arranger Jeremy Cohen told the audience. But this group’s mission is to play the “music of our collective lifetimes,” he said.

While the quartet has visited the Vineyard before, this was its first time performing the current program, which is heavy on American composers and includes Mr. Cohen’s arrangements of such enduring standards as Stairway to the Stars, Sweet Georgia Brown and Duke Ellington’s Caravan, co-written by Ellington trombonist Juan Tizol.

Mr. Cohen also introduced Vineyard listeners to the music of Chicago violinist Eddie South, who studied at a conservatory in Prague because American music schools would not accept a black student.

The chamber music society concerts alternate during the summer season between the Old Whaling Church and the Chilmark Community Center. — Ray Ewing

Mr. South’s signature song, Black Gypsy, shows the influence of his European sojourn, which included a stint playing with Stephane Grappelli and Django Reinhardt in 1930s France, Mr. Cohen said.

A medley of songs from Leonard Bernstein’s West Side Story saw Mr. Cohen, violinist Joseph Christianson and violist Chad Kaltinger bowing the voices of the different Jets who sing Gee, Officer Krupke in the musical.

Mr. Cohen said he watched the musical clips from the film of West Side story countless times while writing his arrangements for the string quartet.

“I’m seeking the character of the whole story,” including lyrics and choreography, he said.

Antonín Dvořák’s Humoresque was written in 1894, but it was 20th-century violinist Joe Venuti who swung it into the jazzy version the quartet played Monday night.

Astor Piazzolla, the late Argentinian composer, bandleader and bandoneon player, “is a rock star almost the way Leonard Bernstein is,” Mr. Cohen said, before the quartet played Piazzolla’s musical manifesto Nuevo Tango.

Jean-Luc Ponty, who emerged in the 1970s as the first electric violinist working prominently in rock and jazz, is another of Mr. Cohen’s favorites. The quartet played two Ponty originals, Bowing Bowing (written for Grappelli) and New Country.

The show opened with Mr. Cohen’s 2015 suite, Three Bridges for String Quartet, a sparkling musical travelogue of places the quartet has performed: San Francisco, in an allegro full of jazzy energy; Buenos Aires, with a pensive, tango-inflected adagio, and Shanghai, in a bustling presto.

“We’re inspired by the places we go,” Mr. Cohen said.

The acoustic environment of the Whaling Church is ideal for unamplified music, with string quartets perhaps the best-sounding ensembles for the space. Playing with flawless technique and infectious verve, the neatly, but unassumingly dressed QSF drew a standing ovation at the end of their show, which concluded with another Joe Venuti number as an encore: Wild Dog, complete with barking.

Mr. Cohen performed on a violin that formerly belonged to the concertmaster for MGM Studios. “It played every solo from The Wizard of Oz to Dr. Zhivago,” he said.

Cellist Andrés Vera stood up along with the rest of the quartet as he played a shiny modern cello attached to his body with a shoulder frame and strap.

At the end of the night, Mr. Cohen promised the quartet would return to the Vineyard, and noted that Mr. Vera will be back this fall to teach music students in Island schools as he has done in the past.

Monday’s concert opened the 49th summer concert series of the Martha’s Vineyard Chamber Music Society. The series continues July 23 at the Chilmark Community Center with the All-Star Piano Quartet: violinist Alyssa Park, cellist Timothy Loo and violist Scott Woolweaver, along with society founder and artistic director Delores Stevens on piano.

The program of Beethoven, Debussy and Brahms will be Ms. Stevens’ final performance as artistic director, according to chamber music society executive director Louisa Gould.

The series returns to the Whaling Church August 5 with the Harlem String Quartet playing music by Debussy, Brahms, Guido López-Gavilán and William Bolcom, and concludes in Chilmark with the Verona Quartet in a program of Beethoven, Ravel and Karol Szymanowski. 

For more information, visit mvcms.org.