Ted Cassidy (Lurch) was an accomplished organist. However, when he "played" the Harpsichord, he was only miming the actions. When Lurch is playing while Gomez and Morticia are fencing the music doesn't match the movements of his hands.
Although it was kept a secret for years, the part of thing was performed by Ted Cassidy. He sometimes had to travel to the studio to do it, even if Lurch wasn't in the episode. A stagehand performed the part if both Lurch and Thing appeared in the same shot.