What is it called when you want to feel sad or enjoy feeling sad such as with sad movies?

We sometimes seek out sad movies (or books) not in spite of the sadness but because of it. When a movie makes me burst into tears whether tears of sadness or joy or ideally both at different points of the movie I know it's a good movie.

What is this emotion called? Is there a name for it? It's sadness but it's not ordinary sadness since usually we seek to avoid sadness but this sort of sadness is sought out and we enjoy feeling it. We don't like what is happening to the characters, but we like that the movie moves us to feel sadness so strongly.