The emotional atmosphere of a story is generally referred to as its mood, the emotion(s) that it is intended to create within the reader. By beginning the story with a discussion of a funeral, the mood is inflected by melancholy and mournfulness, but the revelation (in the first paragraph) that no one has seen the inside of Miss Emily's home in ten years also makes the mood somewhat mysterious. This air of mystery pervades the story as we learn of the strange smell that emanates from Emily's home, as we see her purchase poison with some reluctance to say for what purpose she plans to use it, as she shuts the community out of her home and life for a decade.

The mood is also sympathetic, especially when we learn that Emily's father drove away her suitors and then died, leaving her all alone; when we learn that she was so reluctant to admit that he'd died because she was afraid to be alone; when we learn that her family sort of turns on her when she is courted by Homer Barron and then again when he appears to leave her alone as well. The way these details are presented seems designed to elicit our sympathy for Miss Emily's pitiable state.

At the same time, we have a little nagging feeling that not all is right with Emily, that something tragic has happened to the loudly single Homer Barron, and so the mood is a bit menacing as well.

The dominant atmosphere throughout the short story "A Rose for Emily" is one of curious melancholy. Emily Grierson is a mysterious individual who hails from a prestigious family and is considered a recluse. The story begins with Emily's funeral, and her sad story is told from the perspective of the town of Jefferson. The town reveals Emily's oppressive upbringing and hints at her mental disorder. The reader becomes curious as Faulkner reveals the terrible odor permeating from her home, Emily's purchase of arsenic, and Homer Barron's disappearance. These elements leave the reader in suspense and add to the story's curious atmosphere. Faulkner's short story is also full of Gothic elements that provide a melancholy atmosphere. Emily Grierson's life and death are tragic and fill the reader with sadness. 

The general atmosphere of the story “A Rose for Emily” is pleasant indifference.

The narrator of the story describes the town’s attitude toward Miss Emily, the daughter of the town patriarch.  Although there is some general curiosity, the town really isn’t interested in her or sorry she died.  She is a recluse and an eccentric, and her behavior is generally selfish.

When Miss Emily Grierson died, our whole town went to her funeral: the men through a sort of respectful affection for a fallen monument, the women mostly out of curiosity to see the inside of her house, which no one…had seen in at least ten years.

This opening sentence demonstrates the no one really cared about Emily, and this is the general atmosphere throughout the story.  They are curious, and not mean-spirited, but generally indifferent.