Edgartown’s neoclassical Old Whaling Church was filled with classical music Saturday night as the Martha’s Vineyard Chamber Music Society presented the final concert of its 47th season, featuring the Martha’s Vineyard Piano Quartet.

This is the fifth November that the all-star ensemble has brought its recording-quality musicianship to the church’s minimal stage. Pianist Delores Stevens was a co-founder of the chamber music society in 1971 and currently serves as its artistic director. Violinist Stephanie Chase, a former child prodigy and Tchaikovsky Competition winner, is a widely acclaimed performer, recording artist and teacher.

Cellist Scott Kluksdahl and violist Scott Woolweaver are also highly distinguished exponents of their instruments, with international performing careers and faculty positions with American universities.

The ensemble’s program was a banquet of 17th and 18th-century solo, trio and quartet music by J.S. Bach, Luigi Boccherini, Franz Schubert and Johannes Brahms, each preceded by a few words from the performers about the composer and his work.

Ms. Chase introduced Bach’s Partita in B Minor for violin solo, BWV 1002, by noting that although the concert program listed four dance-inspired movements — Allemande, Courante, Sarabande and Tempo di Bourrée — the work, from circa 1720, in fact has twice that many.

“Each movement has its ‘double,’” she said, a French term. The stately German-inspired Allemande, the pulsing Courante, the triple-meter Sarabande and the rustic, clog-clomping Bourrée each was followed by Bach’s double, extending themes in the dance, she explained.

Ms. Chase’s solo performance was fluid and nimble, yet so robust and compelling that even the eight iron strokes of the town clock, sounding the hour directly above the hall, were more felt than heard by her audience in the pews.

Mr. Woolweaver and Mr. Kluksdahl then joined Ms. Chase for Luigi Boccherini’s sprightly Trio in B-flat Major, Op. 47, #3, which Mr. Woolweaver called “a little palate cleanser after that sumptuous first course.”

An Italian cellist and prolific composer known for “airy, light, even adorable” works, Boccherini moved to Spain as a young man and thus developed his talent away from the classical-music establishment in Vienna, Mr. Woolweaver said. “We think his music warrants discovery.”

Following the two-movement Boccherini trio, written in the 1760s, Ms. Stevens came to the stage to introduce Franz Schubert’s Adagio and Rondo Concertante, F Major, D 487 as a “quite unusual” example of the 19th-century composer’s work.

“Schubert is known for his gorgeous songs,” she told the audience. “But when he was 19, he fell in love with a soprano, and she had a brother who was a pianist.”

Schubert’s challenge was clear: “How do you impress your girlfriend who’s a singer?” Ms. Stevens asked. The Austrian composer’s solution was to write a showpiece for her piano-playing brother. This quartet’s performance showed how dazzled she must have been by the result, a stunning piece with many moods and an undeniable early Romantic strain.

Sadly, according to historians, Schubert would not be given permission to marry his soprano. The Adagio and Rondo Concertante, composed before he had reached his 20th birthday, did not receive a public performance until decades after his death. It remains one of his very few works for piano and strings; another is his famed Trout Quintet, from three years later.

The ensemble went full Romantic after intermission, with the Piano Quartet, Op. 5, G-minor by Johannes Brahms. Written between 1856 and 1861, Ms. Stevens said, “it’s been a standard for chamber music for so long now.”

The Brahms got anything but standard treatment from the quartet, with every member playing as if the work had been commissioned just for them. At the end of its rousing final movement, the Gypsy-influenced Rondo alla Zingarese, the well-dressed Old Whaling Church listeners were on their feet in an ovation.

A reception downstairs followed the concert. Nancy Rogers was Ms. Stevens’s page turner. The Martha’s Vineyard Chamber Music Society opens its 48th season with a concert May 27, 2018.

For more information, visit the society’s website: mvcms.org.