I watched episode 4 season 5 of the West Wing. It is called 'Han'. Now the lead in this episode plays this song by Choplin I think.
The episode is named for the Korean cultural concept of lament, "Han", of which Bartlet tells C. J. "There is no literal English translation. It's a state of mind. Of soul, really. A sadness. A sadness so deep no tears will come. And yet still there's hope."