I don't require it, but it defintely influences me.
I don't know if it influences the style in which I build at all, but I do find that if I have music on, I tend to get finished much faster, but I feel like the construction process was sort of... out of sync with myself, if that makes sense.
What I mean is, when I build something normally, I enjoy the construction process as much as the finished product and I constantly think about what I'm doing, how I'm doing and what I'll do next, however, this way, it may take me a while to finish. (That's not including distractions in real-life and the actual game.)
If I'm listening to music while I build, I don't tend to take a real notice of what I'm doing. Yes, I guess it flows more naturally and I do get the building done quicker, but it doesn't leave as much of an imprint in my mind, and I don't tend to connect with the building as much, nor do I quite like the finished product as much. This is probably because I get the most satisfaction out of my buildings both by, what other people think of it and how they use it, and then how much energy and thought I put into it. If I'm working with music, I generally disconnect from the thought I put into it, and subsequently enjoy it less.
If I did or didn't use music though, the finished product would be of the same standard and style, but I'd miss out, personally on the construction aspect that I enjoy.
Maybe that's just me, but Music will make me work faster, but can kill the enjoyment I get out of placing each brick. :s
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