I am the same, and the effect of music on the productivity of workers has been known for a long time. However, music which is primarily focused on lyrics or just listening to speech (eg. audio books) can be quite disruptive, and in most cases I find that this reduces my productivity. I think this is because when I'm writing software I'm probably also using the same language areas of the brain which are triggered when listening to speech.

Also, it's well established that speech and singing are handled by different brain areas, so do not necessarily conflict.