I used to have a lot of trouble listening to music and doing homework or programming at the same time. It was distracting and I had trouble thinking while the music was going. Sometimes I'd have it on for tedious parts of a task and then when I got to a part that took a lot of careful thinking, I'd turn it down until I got to another boring part. I probably wasted a lot of time just flipping the music on and off. I also noticed that music with words was much more distracting than music without words, so sometimes I'd just listen to light orchestral music instead of the rock and folk I usually listen to.
In any case, what I noticed eventually is that if I listen to music through a headphone on my right ear only, I find it easier to tune out, and less distracting than when I use both ears, or just my left ear. In fact, I find having music in only the left ear to be rather obnoxious.
Why the right ear? It's hard to know, and with a sample size of one, and an investigation that is hardly double blind (or even single blind), it's not at all likely that I'll ever figure it out for sure. But it strikes me as an interesting phenomenon and there's no harm in speculating so here are some ideas:
It could be that the particular ear is not relevant, and the reason I favor one ear over the other is random. I don't remember quite when this habit started (sometime in the last 3 years I think), or why I originally chose to use only my right ear and not the left. It's possible that it was random, that I thought the music was too loud or distracting so I took one headphone off and it seemed better, so the next time I took the same one off even though it wouldn't have made a difference. However, I vaguely remember that even at the beginning the reason I chose the right ear is that the music was only unpleasant in my left ear, hence there was negative feedback encouraging me to remove the headphone from my left ear, but not from the right.
It may be that my right ear just happens to be slightly less sensitive than my right ear. This isn't at all obvious in everyday life, but perhaps there is some 5% or 20% difference in sensitivity peculiar to me.
My favorite, hypothesis, however is that it has something to do with the division of labor in the brain (and hopefully I don't fall victim to too many pop-neuroscience misconceptions here). I'm right handed, so when I type, use the mouse, or write or draw, as I would while working, my left hemisphere has to work harder than my right hemisphere. The left hemisphere contains the center for language, and it was the words in songs that I found most distracting, so maybe the one level of indirection is enough to prevent the music from unduly interfering with my internal dialog. Stretching a bit more, a lot of what I do is highly analytical (like computer programming, or math and science homework), so if the left brain is the center of logic then I may be relying on it more than on the right brain (when doing so called right-brain centric activities, especially drawing, but also writing poetry, I often listen to music from speakers or with both headphones, so there may be some connection there too).
Google turns up a few other reports of things like this on this, but it's all anecdotal (although I haven't yet tried to search the scientific literature, maybe there is something there, not sure how much of it I'd understand though).
What about you, oh vast teeming readership, do you think this is a real phenomenon? Or is it just stochastic noise (pun intended!) and confirmation bias?