In "The Cask of Amontillado" by Edgar Allan Poe, what types of tone are used?

The narrator’s tone is self-congratulatory, humorous, and reflective.

The narrator of the story is Montresor, a mentally unstable man who has decided he needs to murder a man.  Montresor makes an interesting narrator because, as a madman, he is not afraid to say what he thinks.  Most of the time, Montresor’s tone is self-congratulatory, meaning he believes he is doing something great and is smarter than everyone else.  He is bragging about a murder he...

The narrator’s tone is self-congratulatory, humorous, and reflective.

The narrator of the story is Montresor, a mentally unstable man who has decided he needs to murder a man.  Montresor makes an interesting narrator because, as a madman, he is not afraid to say what he thinks.  Most of the time, Montresor’s tone is self-congratulatory, meaning he believes he is doing something great and is smarter than everyone else.  He is bragging about a murder he accomplished.

The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge… At length I would be avenged; this was a point definitely, settled --but the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish but punish with impunity. 

The man did something to Montresor, and Montresor intends to do something about it and get away with his revenge.  This is self-aggrandizing and self-congratulatory talk.  Montresor feels superior to Fortunato.

Sometimes, the tone is humorous.  For example, when Montresor jests about the word “mason” and Fortunato’s connection to the special society of the Masons, it is actually pretty funny.  Montresor is not a Mason, and does not know the signs, so Montresor tells Fortunato he is a mason, meaning he is a bricklayer.

"You? Impossible! A mason?"

"A mason," I replied.

"A sign," he said, "a sign."

"It is this," I answered, producing from beneath the folds of my roquelaire a trowel.

"You jest," he exclaimed, recoiling a few paces. "But let us proceed to the Amontillado."

Montresor actually is a mason, at least for the moment.  He is planning to brick Fortunato up in the wall and leave him there.  That is his grand plan for getting revenge on the man for whatever wrong he committed.  Montresor had to explain the trowel somehow.  Montresor’s family motto "Nemo me impune lacessit" also adds humor. It means "no one attacks me with impunity."  In other words, when Montresor mentions his family motto, he is broadcasting his vengeful nature.  Fortunato is either too drunk or dense because he doesn’t seem to get it.  He isn’t suspicious and he doesn’t try to leave.

At the end of the story, Montresor becomes reflective.  He almost seems remorseful, but he might be using sarcasm.  When he is considering how he felt all those years ago,

My heart grew sick; it was the dampness of the catacombs that made it so. I hastened to make an end of my labour. I forced the last stone into its position; I plastered it up… For the half of a century no mortal has disturbed them. In pace requiescat! 

Montresor tells us that he was sickened, but it was not by his actions.  It could be remorse. He also ends with “Rest In Peace.”  Again, this could be sarcasm, or a genuine feeling of remorse.  He is telling this story fifty years later, so his reflection may have resulted in actual grief.