From what I'm seeing here, your boss most likely thinks that because you were wearing headphones, you weren't paying as much attention as you probably should have been to your work duties, and as a result, forgot to call the client. The punishment may be indirect, as obviously the headphone wearing didn't cause you you forget to call the client, but your boss likely thinks that that is one of the causes. Furthermore, it also seems the the punishment's message is actually sinking in, which seems to be the point of the punishment.
Another question you should ask yourself: would I accept the (in reality, petty) headphone punishment over something potentially more severe, such as pay docking or suspension?
If you really want to continue to dispute the punishment, I would, first and foremost, talk with your boss. Sit down with him/her and illustrate just how much music means to you when programming, and then ask when you can expect to be able to wear your headphones again. It may or may not work, and you could face a heavier punishment. If you really want to carry it further, speak with your boss's boss, though I would be wary of carrying an issue like this further on up the chain, as they may see it as a petty dispute that you should deal with on your own.