It is a nice idea.

Sometimes I also thought on putting an author note detailing a few songs the reader should listen to to get a better experience.

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I think it's a big mistake, people will have to make a separate tab to play the music, breaking the flow of the story.

And people might listen to their own music while reading, like I personally listen to classical music while I read.

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Hmm, if that's the case then go ahead!

It may break the narrative though, just giving a warning.

I don't think it's a good idea. Like VX said, it would break the flow of the story. Also, some people listen to music anyway, so they don't really need more music. I also think that some people who are distracted easily might find background music as more of a distraction.

I am definely going to implement the author note thingy on my next story.
With a warning, of course.