Okay, so most of times we encounter singing in Pure it's melancholy, suggesting that singing is used as some sort of coping mechanism or excretion of grief. It's not like Pharrell's song… but's it is important. There are two main scenes where there is singing involved. The first one is with the old woman singing in her house:
Finally, the old woman lifts her head and says, "He broke her heart." And then she closes her eyes and starts singing loudly—shrill, anguished notes, as if she's trying to drown out everything around her. (19.101)
And the second one is when Pressia sings at the very end of the book:
Pressia's voice doesn't surprise Partridge. It's as if he's been waiting to hear it for many years. It lilts with sadness, and it takes Partridge a moment to place the tune. (59.106)
Whether it's happy or sad, singing is a way we can release our emotions. For the old woman, her singing (more like screaming) was used to block out the cruel world around her. But for Pressia, her singing is a kind of cathartic release. All of her pent up sadness and suffering is bunched up into the sweet lullaby. Even a melancholy tune can have an uplifting mood, and Pressia sings from her heart to free the sorrow back into the world.