Err. I can't say I know their titles. Just the most common one playing when they're just hanging out and chatting. It just has a slight chime to it between notes that keep my ears tickin every now and then. I honestly can't place it.
Open the musicroom and play through the songs. It still contains bugs but it should give you the name of the song you're looking for.
Soft Walk is the song where I hear the ringing sound. It's the oddest thing.