This isn’t quite what you’ve asked, but I’ve found two things over the years:

• Familiarity matters. I remember that as a kid, I didn’t listen to music when doing homework. I couldn’t understand how people could manage. Later, I used music on headphones in a work environment to drown out noise that was more-distracting, and it wasn’t an issue once I got used to it, could write software without problems with music. I remember reading that some people say that they can’t concentrate when it’s too quiet, if they’re accustomed to being in a noisy environment, because the silence becomes a distraction.

• The type of noise matters. I don’t require white noise, but in terms of how-distracting something is, I’d say that my ranking is something like silence > white-noise-type stuff > “ambient” sounds like waves or wind > lyric-free music > music with lyrics > speech > half of a conversation.

  By “half of a conversation”, I mean a conversation in the background where I can only hear one end. This usually comes up when someone is talking on a cell phone in a public place in the background. I think that what’s going on here is something like that we’ve trained ourselves so that if someone says something and then there’s no response, it means that they’re talking to us, and so we’ll say “huh?” and look up. It’s good that that happens. Unfortunately, that’s also the effect one gets when one can only hear one side of a cell phone conversation. Just a constant series of attention-grabbing events for me. I’d rather have two people talking to each other near me than one person on a phone, even though it’s technically more speech.

  Generally, I prefer “lyric-free music or better” when doing something that requires concentration, but can live with music with lyrics.