For the past several years, the Brentano String Quartet, Resident String Quartet at Princeton University, has kicked off the fall music season in Princeton with a free concert in Richardson Auditorium. Mid-September can be a time when families are getting adjusted to the school year or getting children organized at college, but enough people took a break from early fall activities last Friday night to almost fill Richardson as violinists Mark Steinberg and Serena Canon, violist Misha Amory and cellist Nina Lee  presented their annual concert. This Quartet could easily get away with just playing the classics, but Friday night’s concert proved that these musicians have been thinking imaginatively. The concert was part of a multi-venue commissioning project to assign an unfinished fragment or work of music to a contemporary composer to write a companion piece.

The fragments themselves are works of art. Behind many great masterpieces are the composer’s sketchbooks and unfinished thoughts, and in these days of computerized composition programs, these fragments are gems as one can hear a composer’s thought processes until something interrupted the work or pulled the composer in another direction. Particularly in the case of the Franz Schubert and J.S. Bach fragments, one wondered what was going on in the life and mind of the composer that these pieces ended in the middle of a solo phrase. This was the challenge to the contemporary composer — to pick up where the 18th or 19th-century master had left off and forge a new path for the music.

Charles Wuorinen drew his inspiration for his Marian Tropes from the 15th century sacred music of Josquin and Dufay. Staying true to the early Renaissance contrapuntal and harmonic styles, Mr. Wuorinen interwove open interval sonorities and tapered Josquin cadences into a tonal work with echoing phrases and a drone which might have been heard at the time from a sackbut or low stringed instrument. The occasional jarring glissando or discord reminded the audience that this is the 21st century, and the four members of the Brentano Quartet smoothly passed what would have been vocal lines among their instruments.

Franz Schubert lived such a short time and composed so much seemingly flawless music that an unfinished work of his is like a diamond just needing a bit of polish. It is unclear why Schubert never finished what is now called a Quartettsatz in C Minor, and American composer Bruce Adolphe maintained the lyrical thought of Schubert’s complete “Allegro assai”and fragmented “Andante.” The great Schubertian tune of the first movement was conveyed by Mr. Steinberg as first violinist, and picked up by cellist Ms. Lee in Adolphe’s Fra(nz)g-mentation.  Adolphe incorporated a jagged rhythmic drive into the quick tempo borrowed from Schubert’s first movement, and the musicians easily found the lyricism and musical gentility of Schubert’s style.

The fragment treatment which contrasted most dramatically with its original material was Sofia Gubaidulina’s Reflections on the Theme B-A-C-H, based on Bach’s unfinished “Contrapunctus XVIII” from The Art of the Fugue. Whereas Bach’s peaceful “Contrapunctus” was nicely blended in the Brentano Quartet, with an especially elegant melodic line from second violinist Ms. Canin, Ms. Gubaidulina’s arrangement provided a great deal of variety in dynamics with sharp instrumental lines and driving rhythms, conveying the composer’s well-known unconventional approach to sound.

All of the composers commissioned by the Brentano String Quartet for this “Fragments” project found great challenge in examining unfinished musical art from previous centuries and bringing them into the 21st century. John Harbison, who composes in almost every genre, found humor and sauciness in his “Finale” to Haydn’s unfinished Quartet in D Minor. Amidst the rhythmic drive of the Harbison piece, the members of the Brentano Quartet showed that they were independent players, yet cognizant of one another and always working together. The final Mozart fragment and its follow-up Mozart Effects by jazz composer Vijay Iyer flowed right into each other, with an almost indiscernible end of the old and beginning of the new. It was fitting that the Brentano Quartet ended this inventive musical concert with a work of Mozart, whose final unfinished Requiem has spawned some of the most significant musical mystery discussions of the past two centuries.