The widespread (I would say universal) custom is to not listen to music the entire duration of the Three Weeks, up until the day after Tisha B'Av at halachic noontime. This includes all music, recorded or live, with or without musical accompaniment, with the exception to chazzanut.*
However, is one permitted to listen to a sad song during the Tisha B'Av? What about if the song specifically talked about the Churban Beis HaMikdash and the longing for the Geulah?
I think (and I have no source for this) that the reason we do not listen to music during the Three Weeks is because it might make us feel happy or begin to dance.
In addition to all this, what about if the song has nothing to do with the Churban or other Tisha B'Av themes, but is just a sad-sounding song in general, with slow rhythms and such?
*According to many opinions this is true.