One answer: It depends on my mood.

Let's just focus on the time when I'm working, as you mentioned "productive songs".

Some days, I'm extremely annoyed by music, I find it repetitive and it drives me away from my imaginative mindset.
Some others, I'm thrilled by it and feel like when I type it follows the beat of the song.

I tend to go with the more artistic kind of music and not the pop/popular one.
I stay away from songs that seem like no thoughts have been put into them. I only associate myself with things reflect me and listening to those pop songs would mean that I'm one of those sheeples that listens to consumer made music that have no depth.

You only hear the music when your heart begins to break.

Yep, depends on the mood.