In the short story, the central setting place is a clean and well-lit café. It is quiet there, as the reader may assume from several indirect phrases. There is no music because it is the best place to wipe off the helpless thoughts that bring the characters to despair. They need a quiet place to be themselves and have a rest from their loneliness.
There is no explicit indication of whether the music played in the café where the action takes place. The only time it is mentioned in the text are the following sentences: “You do not want music. Certainly you do not want music.” It is a part of the older waiter’s inner dialogue at the end of the story. He ponders over the best clean and well-lighted place to spend an evening. Then he concludes that a “bodega” (Spanish for “a bar”) is much worse than the café he works at.
Bars usually play loud music at night. For the older waiter, it is a negative feature. Music does not let you hear the sounds of nature, such as the wind in the trees or the heels of a passer-by clicking. Nor does it allow your thoughts to fly away while you are watching the shadows in the trees.
Sounds play a prominent role in the short story. “The old man liked to sit late because he was deaf and now… it was quiet and he felt the difference.” From this phrase, it becomes clear that there is no music in the café. When you want to get rid of the thoughts buzzing as flies inside your head, “you do not want music.” Hemingway could have added the word “quiet” to the short story’s title.