"Fatigue" can be solved with lighter rotations, for example. It depends on the cause: overplay, never liked it a whole lot, my ex liked it so now I don't, etc., etc. Burn is permanent, various levels of fatigue are not. And it is often hard to find the cause of fatigue, so it comes back to "how much do you want to hear that song today".
Unless you do perceptual questions along with the score, "burn" is useless.
On on-line testing, I have implemented tests where if the score was below the mid-scale point a person was asked, "if you don't want to hear it now, did you ever enjoy it?" A "Yes" gets a list of reasons why it might not be liked any more. Think "Gagnam Style" as an example of "It was fun for a while but now I hate it".