Dramatic irony is definitely shown through the narrator’s remonstrations to the audience that he is not mad—he is not insane. The audience knows, even though the narrator has yet to accept it, that he is indeed mad. There is irony in the stealth with which the narrator creeps around waiting for the eye to be open, when it is the stealth that keeps the old man asleep and unaware. There is situational irony on the night when he startles the old man, opens the lantern after an hour or more and sees the eye looking at him. This is ironic because it is the open eye that he has been waiting for, and yet the eye fills him with rage. We would expect manic joy at the least that the deed could now be done. And there is great irony in that “his acute sense of hearing” caused him to hear the beating of a heart which could no longer—and did no longer—beat.
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The central theme of Edgar Allan Poe's short story The Tell-Tale Heart is ironic. The opening paragraph features the story's narrator vigorously objecting to any suggestion that his mental state is anything less than perfect:
"TRUE!—nervous—very, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses—not destroyed—not dulled them. Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad? Hearken! and observe how healthily—how calmly I can tell you the whole story."
The irony lies in the story that follows, which inarguably depicts an individual driven over the edge by the recurring sight of the eye of the old man with whom he shares a home, an eye described as resembling "that of a vulture—a pale blue eye, with a film over it." Which leads to the next example of irony in Poe's story: the plot by the narrator to kill the old man despite the latter's entirely inoffensive nature. The narrator makes a point of emphasizing that he holds no ill will towards the old man -- "I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire" -- yet such is his madness that he wants to kill the old man. There is irony in his sentiments and in his actions, which do involve the old man's death.
A final bit of irony lies in the story's conclusion. Having argued for his sanity, the narrator continues to display behavioral characteristics more like to the insane. His guilt over his actions causes him to imagine that he is hearing the beating heart of the deceased who he buried under the floorboards, which causes him to cry out to the visiting police officers that he has killed his roommate.