Based on Aristotle's definition, an argument can be made that this story is a tragedy.
1.Tragedy depicts the downfall of a noble hero. Usher was once a great family as the now decayed mansion attests.
2.The tragic hero is often subjected to the will of fate. Roderick and his sister are the only surviving Ushers as the family bloodline has become too thin. Because of the genetic degenration of the family, Madeline suffers from catalepsy and Roderick has a "nervous affliction" which effects oversensitivity, especially to sounds. As they are debilitated, the Ushers are fated to remain in their home under the care of a physician.
3. He/She makes a tragic mistake because of a personal fraility, a flaw in reason or in nature. A victim of his nervous affliction and overwrought nature, Roderick is tortured by noises; the stress upon his mind causes him to have "an inconsistency" in behavior. With "trepidation" the "hypochondriac" is tortured by the fear of loss of his sister who has been pronounced dead. In reality she has had a seizure and is not really deceased.
4.The tragic hero achieves some revelation or recognition about human fate or destiny. This is a "change from ignorance to awareness of a bond of love or hate." Not allowing an autopsy for her leaves Madeline able to rise and embrace Roderick in a death grip as one; a consequence he has not recognized.
While this story does have some comedic elements, including dialogue, characterization, and other devices, overall it is to be perceived as an ironic tragedy.
The Fall of the House of Usher, within its plot, is foreshadowed by the physical cracking or splitting of the home itself. The "house," meaning the family, also splits by story's end, and becomes divided into two separate warring parties. We are led to believe that this story is tragic in nature, because by story's end, a kind of death has occurred within the Usher family -- the death of the family itself.