For its 10th anniversary, the Brentano String Quartet wanted to put together something that would exhibit its commitment to music both past and present as well as it knack for inventive programming. So it invited a group of composers to write short companion pieces to accompany fugues from J.S. Bach’s unfinished masterpiece The Art of the Fugue. The result is "Bach Perspectives: Ten Composers React to The Art of the Fugue," which the Brentano brings to Jordan Hall next Friday.

The project took three years to bring off, according to Mark Steinberg, the Brentano’s first-violinist. "It’s really a celebration of three things: Bach, composers and composing today, and our 10th anniversary," he says over the phone from New York. "We know that The Art of the Fugue has always been important to composers, who have studied it and learned from it and been influenced by it. What we wanted to do was to allow Bach to be heard through the ears of some of the great composers around today."

Influential it certainly has been. This collection of "contrapuncti" stands as a summa of the art of contrapuntal music. Since Bach didn’t specify any instrumentation on the score — indeed, he left no indications about its performance at all — The Art of the Fugue is often taken as a textbook rather than a musical piece per se. Each of the 10 composers the quartet assembled — they include Nicholas Maw, Sofia Gubaidulina, Charles Wuorinen, and Wynton Marsalis — responded to the invitation with works that spoke to his or her particular inheritance of Bach’s influence.

Steinberg says that the commission was meant to be as open-ended as possible. "We asked each composer to pick a specific fugue and write a companion piece to it. We didn’t want to constrain anyone. We wanted to allow them to give full rein to their imagination. A piece could be played before, during, or after the Bach." And sometimes all three: Steven Mackey’s Lude functions as prelude, interlude, and postlude, interlacing itself among the textures of Bach’s Contrapunctus XI.

Most of the contemporary composers work some aspect of their chosen fugue into their own piece. The only exception is Nicholas Maw’s Intrada, which precedes the Art’s first Contrapunctus at the opening of the program. "His work sets up an atmosphere," Steinberg explains. "It swirls around energetically, then winds down and morphs into a single pitch — D — which is the first pitch of the opening fugue. The Bach just emerges from his piece. It sets it up in a really special way."

Besides being a great composer, Bach is, of course, a great educator, and the Brentano has found the immersion experience to be intensely edifying, in ways specific to the musical activities of the foursome. "In terms of playing quartets, Bach is a fantastic teacher," says Steinberg. "How do you match lines horizontally while still keeping track of the music’s harmonic changes, all while balancing each chord perfectly? It’s a huge challenge; we’re still sorting out the things he’s taught us and will probably be sorting them out forever. There’s nothing that we could play that would hone our ears better than this."

The Brentano Quartet presents "Bach Perspectives" April 4 at 8 p.m. at Jordan Hall, courtesy of the FleetBoston Celebrity Series. Tickets are $30 to $40; call (617) 482-6661.

RETURNING FACES. It will be a busy weekend as the music season begins to head into the pre-summer homestretch. German conductor Ingo Metzmacher returns to the BSO with one of the most creative programs we’ve seen all year: the premiere of Elliott Carter’s Boston Concerto along with Ives’s Three Places in New England, some of Mahler’s Wunderhorn songs (with baritone Matthias Goerne), and the suite from Bartók’s still-dazzling Miraculous Mandarin. That’s April 3, 4, and 5 at 8 p.m.; tickets are $25 to $90. Call (617) 266-1200. Musicians from Marlboro make one of their annual pilgrimages to the Isabella Gardner Museum on April 6 at 1:30 p.m., playing string quartets by Haydn and Bartók plus Mozart’s Divertimento for Winds and Strings K.334. Tickets are $18 and include museum admission; call (866) 468-7619. And the Slovenian pianist Dubravka Tomsĭc, truly a musician’s musician, makes a welcome return to Boston in a Symphony Hall recital of Haydn, Beethoven, and Chopin. That’s at 3 p.m. on April 6; tickets from the Celebrity Series are $35 to $55.