I’m not able to do my work with music, or even noise-canceling headphones. I’ve tried, and it doesn’t work.

I know that I’m unusual, in that sense, but there you have it.

I do listen to music, on my morning walks, though. That’s the only time, during the day, when I do.

I prefer to work in silence. But by that I mean actual silence. However, I live in a city where there's construction going on I can hear through my window. If I have to work from the office, there'll be colleagues yapping around (helps with creativity or whatever the sugarcoating is for the open office). Bonus points for one of the offices being next to a different construction site.

In these situations, I tend to prefer having some kind of "ambient" music on, instrumental only, so I can be isolated from the distracting environment. Noise cancelling doesn't work well enough against voices, although I do enjoy the reduction of random ambient noise (A/C hum and the like).

You're not unusual. Constant need for something in your ear is a very new phenomena and for some reason a lot of people have gotten in the habit of isolating themselves from the world around them and stopped being in presence of the reality. Sad.

Have you tried brain.fm?