The narrator seems to be quite disconnected from Sonny at the beginning of "Sonny's Blues." He doesn't even know that his brother has been arrested for taking (and possibly dealing) heroine until he reads the newspaper. When the narrator tells stories about Sonny's adolescence, he mentions that he was never particularly fond of Sonny's vision to become a jazz musician, and that seems to further support the observation that there is some distance between Sonny and the narrator.
The end of the story provides a completely different picture of their relationship. The narrator agrees to go to a nightclub with Sonny and watches him perform there with his friends. On page 136, he almost seems proud to be Sonny's brother:
"And it turned out that everyone at the bar knew Sonny, or almost everyone (...). I was introduced to them and they were all very polite to me. Here, I was in Sonny's world. Or, rather: his kingdom. Here, it was not even a question that his veins bore royal blood."
During the beginning and middle of the story, the narrator associates jazz with drugs because he thinks that some musicians have to be high in order to play. He does not consider performing jazz music as a respectable career and does not think that it will give Sonny a stable job. However, once the narrator gives him a chance, he realizes that other people respect Sonny and his jazz music. Perhaps this makes him reconsider his harsh judgement of Sonny's choice to become a musician.
Watching Sonny interact with the other musicians helps the narrator realize that Sonny is happy with those people. The joy that Sonny feels when he plays jazz music is contagious. After the performance, the narrator seems much happier. He thinks about his parents, uncle, and daughter and shows some emotion. He also seems to finally be accepting of the fact that his brother is a jazz musician.
The last scene of the story shows how jazz music bridges the gap between Sonny and the narrator even though in previous scenes, it seemed to help create the gap.
