Bach had his unfinished fugue. Schubert had his "Quartettsatz": one-fourth of a traditional string quartet, had the piece been completed. These unfinished works provide intriguing glimpses into the compositional workshop. Pairing fragmented music by such revered composers as Haydn and Shostakovich: even Mozart: with 21st-century composers in a musical dialogue is the foundation of the Brentano String Quartet's latest project, Fragments: Connecting Past and Present, co-commissioned by Carnegie Hall.

What inspired Fragments?

Being haunted by fragmentary pieces and reconnecting with them led to the idea behind this project. I enjoy the idea of spying on a composer as he works. Somehow these unfinished pieces make me feel as if I can catch a glimpse of the thought process, or a small whi& of the scent of creation. As performers, we can live with the music that is there and think about what else it may have been, but only composers would be able to share inspiring thoughts about these works directly with others. I had the idea to find other unfinished works and get the dialogue going.

What do you think the 21stcentury composers learned from examining unfinished works by their predecessors?

Probably quite a bit and also nothing out of the ordinary. In saying that, I only mean that composers are perpetually in dialogue with the past and all inherit a lot from their predecessors. Whether they borrow and build upon or rebel against, it is not possible to write music completely free from the shadow of any earlier composer. On the other hand, this was an unusual opportunity to comment directly on specific works. I wouldn't pretend to guess what the composers may have learned, but they have responded in a variety of ways. Some of the composers used snippets of the original fragments as building blocks or quotes in their pieces. Some transformed elements from the original works to become new melodies and musical thoughts. Some buried quotations from the earlier works in unexpected places so that they support the unfolding of the music as a kind of sca&olding. And some have chosen to imbibe in some sense the musical spirit of the earlier composer's language and then simply write a new piece in which that spirit is allowed to infect their own.

As a performer, what have you gained from this process of linking unfinished works from the past with new works from the present?

The easy answer is that we have gained new, wonderful pieces. This has been truly thrilling for us, and we feel so fortunate to have these new works and to have what has turned out to be a rather beautifully balanced program when they're put together. We've also gained the opportunity to share some of this fascinating and touching music with our audiences by having a context in which it makes sense to program these incomplete works. In terms of our understanding of the musical language of both the earlier and the newer works, this is not something I am able to articulate. And yet I think we are all aware that there are resonances between the older and newer works that infiltrate and color our music making as we play them side by side.