After the renowned pianist Francesca Cunningham attempts suicide, she is examined by the psychologist Dr Larson. His technique involves removing a series of psychological 'veils' until he reaches the one concealing the patient's most private thoughts.
Under hypnosis, Francesca tells Larson her life story. She recalls being unfairly blamed for being late to school and being caned on her hands, leading to her failing a piano scholarship exam.
An orphan, she was sent to live with Nicholas, her second cousin and closest living relative. He was occasionally kindly towards her, but more often stern and forbidding. One of the servants, James, later told her that Nicholas's mother ran off with a singer, leaving him wary with women.
Nicholas made Francesca practice the piano for five hours a day, and arranged for her to attend the Royal College of Music. Initially devoted to her studies, she became increasingly drawn to American student Peter Gay, and they become engaged.
Nicholas refused to give his consent as her legal guardian to the marriage, and took her to Paris to groom her as a concert pianist, constantly exhorting her to look after her hands.
At Francesca's first concert appearance, her old schoolfriend Susan surprised her in her dressing room, unnerving her by reminding her of the caning incident. Francesca could not get this image out of her mind, and thought her hands were contorted and misshapen. She got through the performance, but collapsed at the end.
Her concert tour eventually reached the Royal Albert Hall, where her performance of Rachmaninov was a triumph. Afterwards, she ignored Nicholas in favour of Peter. They dance together at a club, and then...
Francesca refuses to tell Larson what happened. Larson changes the subject to Max Leyden, hired to paint Francesca's portrait. Painter and subject became increasingly drawn towards each other, and they plan to live together in Italy.
Francesca told Nicholas, warning him not to stop her. She played the slow movement of Beethoven's 'Pathétique' Sonata, while Nicholas told her that he devoted his life to her, and she wants to throw it all away for a man who won't even marry her. When she ignored his demands to break off the relationship, he smashed his cane on her fingers. Francesca ran out into Max's arms. They drove away, but were injured in a car accident.
Francesca woke up in the nursing home, certain that she will never play again. She told Max she wished she had died. Shortly afterwards, she attempted suicide, leading to her encounter with Dr Larson.
In a lecture to colleagues, Larson outlines the case history and emphasises Francesca's fear of damaging her hands, which he claims has produced a barrier in her mind preventing full recovery. He believes he can break through this barrier via music, persuading her to play the piano under hypnosis.
Larson puts on a record of the 'Pathétique' and encourages Francesca to play. She starts, but recalls the cane smashing on her fingers. She screams and falls silent.
Larson visits Max at his home, to ask why he has removed Francesca from his care. Max refuses to co-operate. Larson says that he will seek Nicholas's consent. Max says that he won't be her guardian much longer, as they're getting married next week. He confesses that he hasn't yet proposed to her.
Larson goes to see Nicholas, who agrees to help identify a piece of music. When played the 'Pathétique', Nicholas angrily smashes the record. Larson observes that he has dropped his cane.
Nicholas urges Francesca to complete Larson's treatment, saying that it's no use brooding over the past. She agrees to return.
Larson asks Peter what happened on the night she returned to London. Peter told her that he was married, and she walked out on him. Larson asks him to bring round a recording of the waltz they danced to.
Max, Peter and Nicholas meet at the latter's house. They hear the 'Pathétique'. Larson reveals that it's Francesca playing. He advises them to expect a new Francesca, who has come to terms with her past and is facing the future... and wants to be with the man she truly loves. Francesca descends the stairs, and chooses Nicholas.