The first is a less traditional piece *gasp*. It's actually from the impressionistic composer, Fracis (Francis)Poulenc, and while not appropriate for the Mass, it is appropriate for sort of laying the ground before meditation. The character of various moods in this piece point to a lot of what is happening all at once at the time of our Lord's crucifixion --- not only in the sense of the tragedy, but it's universal significance. This is what makes this piece unique and most worthwhile.
This video only has highlights of the song, but even for a taste, here it is:
Next, we have Zoltan Kodaly's Stabat Mater. He is also a modern composer, but his style is suitable still for the Mass.
This video is not worth watching but only listening to, so I recommend you close your eyes:
It seems that even the video editor seems to have been of the same opinion (see comments above), as 2/3rds of the way through this video, the image goes blank.
