Symbolism, Imagery, Allegory
They say the truth will set you free, but how about getting your art on? Art is therapy in The Woman in White—from painting to piano. Walter makes his living drawing, and everyone and his dog writes something down at some point in the novel. Laura has a very strong connection to music, and this connection gives us a good bit of insight into her character.
Sometimes, her fingers touched the notes with a lingering fondness, a soft, plaintive, dying tenderness, unutterably beautiful and mournful to hear—sometimes, they faltered and failed her, or hurried over the instrument mechanically, as if their task was a burden to them. (1.1.15.52)
The crucial thing here is how Laura seems to lose herself in her music. Music becomes a way for her to hide, but it also gives us a window into her emotions. For someone so passive, Laura's emotions are actually quite turbulent beneath the surface.
So music helps represent the inner self and the ways in which characters use art to cope with external pressures. Even Fosco seems to get lost in music, though his enjoyment is of a showy nature and highlights his super-pretentious personality.
At the more refined passages of the singing, at the more delicate phrases of the music, which passed unapplauded by others, his fat hands [...] softly patted each other, in token of the cultivated appreciation of a musical man. (3.3.5.4)
Characters internalize culture and art, which helps reflect their emotions and inner selves. We see this again when Laura takes up drawing as a form of art therapy.
"Yes," she said to herself, returning to her drawing. "I must try, because they are both so fond of me." She suddenly looked up again. "Don't be gone long! I can't get on with my drawing, Walter, when you are not here to help me." (3.1.3.27)
Drawing here acts as a sort of lifeline for Laura, who is struggling to put her mind back in order. Writing also serves as a form of therapeutic and creative expression for several characters: for Marian especially, it's a form of solace and an outlet for her chaotic thoughts.