Longing
Baines is the character that represents this theme most fully in the film as his longing for Ada begins once he hears her play her piano for the first time. Ada has ignited something inside of Baines that he has not felt in a long time if possibly ever. But it is a longing that is deep and comes from a place where he truly understands her. He is able to know her through her music and by opening up about the way her music makes him feel it draws her closer to him as he is truly listening to her voice which comes through the keys of her piano and not by the words from her voice.
Desire
This film is very much about the desires of one's heart. Stewart desires to have a family and create a life with Ada as her husband. Ada desires to be loved in a way that needs no words. And Baines desires to have passion and connection in his heart for a woman. All of their desires though do not match up as Stewart's desire is not expressed in any meaningful way to Ada in which she desires to reciprocate. He in fact pushes her towards a relationship with Baines by offering her services to him in order to learn to play. But it is Baines desire for her that is the underlying reason for him wanting the piano. In the end, it is the unmet desires that cause the greatest change as Stewart's dreams are crushed by the desires of Baines and Ada.
A Voice to Speak
The reason for Ada's inability to speak is unknown. Even she does not know the reason for her muteness. This is a major theme of the film as Ada's voice comes from her piano. It is where she expresses her deepest feelings. Places where words cannot describe are touched by the keys of her piano. As Ada's journey unfolds in the picture she begins to be understood by Baines. He hears her music and is connected deeply to her. It's as if he knows her intimately without words. But it is only when Ada is willing to let go of her piano and let it be buried in the sea that she is able to begin to speak. She finally allows the part of her that only will allow her to open up through her piano to die, and by doing so it allows her voice to come alive as she now seeks a connection with words to the world around her.