I wonder if you just mean background music. That's music you like to have on when you are doing something, because it makes a tedious job or exercise more relaxing. I suspect not, because you seem to need the rhythmic impectus. I've never heard Angeleyes' two suggestions in BE. I think we'd say something like I play rock as background music.
The terms I suggested weren't actual names of what we'd call it, but they were types of music using two different adjectives as examples to describe it.
I'm with you on background music as a term to use in general.
In bosun's original question, he used lilting in such a way as to describe a type of music, not as a specific name.