The first thing to notice is what the reader sees/hears. Consider the similarity of the words heart, hear, hearken, heartbeat, and hearing. The repetition of such words adds to the increasing tension. It is the narrator's warped senses of hearing and sight that lead to him to murder and to admit the deed. In the first paragraph, the narrator comes right out with it: hearing is all important.
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?
The narrator is certainly a madman. In the second paragraph, the narrator describes the old man with whom he has no conflict except for his "pale blue eye" which reminded him of a vulture. Note that the narrator can not bear to look at the old man's eye; as if he can not bear for the old man to look at him. In other words, he can not bear to look at the old man looking at him because it throws the gaze back on himself: the eye mirrors the "I" (narrator).
He intends to kill the old man to rid himself of having to look at the old man's eye. The insane narrator prides himself on the power of his senses. "Never before that night had I felt the extent of my own powers--of my sagacity." He early says that he's heard all things in heaven, earth, and hell. He adds that he believes the old man has begun to feel his (narrator's) presence in the room, like an increasing terror. Adding to this "sense" of growing terror are the sounds in the room which seem like a countdown to that terror, "hearkening to the death watches in the wall." As the narrator's senses become more acute, his madness increases: like a ticking time bomb. Note the combination of sight and sound in the phrase "death watches" which are heard but also indicating a sense of being "watched."
Poe, through the mad narrator, is careful to describe the impending terror gradually, first by using sight. The narrator has crept into the room for the eighth night in a row. He decides to open the lantern a bit and as he does, the light shines on the old man's open eye; thus, gradually and slowly revealing the source of the narrator's own fury. Poe uses the sights and sounds to gradually increase the tension.
The narrator is convinced that he is not mad; rather, his senses are so acute, that he can not help himself. Just as he was fixed upon the old man's eye, he becomes fixated upon the sound of the old man's heartbeat and this increased his fury. As the tension increases, so does the sound of the old man's heartbeat (as heard by the narrator). It becomes so loud to the narrator that he fears a neighbor will hear it. It is as if Poe has provided a soundtrack for this horror story. The sound gets louder as the tension and the madman's fury increase. The madman's senses overwhelm him. The heartbeat gets louder and louder, a crescendo, until he can bear it no longer and then kills the old man. Finally, the narrator's madness is truly revealed. His madness in this story was based upon his belief that his senses were overtly acute. After dismembering the body and hiding the parts under the planks, he continues to hear the beating heart. This is impossible and the officers of course hear nothing. Once again, the volume of the beating increases until the narrator can take it no more and he admits the murder.