It's not about keyword density anymore. It's about actually writing about the topic of the keyword... such that you mention some of the other words or phrases that Google expects when people talk about that kind of keyword.
For example:
If I take an article about a random celebrity and start putting the keyword "coffee maker" in it, then I've failed at on-page optimization because there is no connection between the word "coffee maker" and the rest of the article. I could adjust the density up and down and play with the positioning, but it wouldn't matter.
If I'm actually talking about coffee makers, though, I don't have to worry about keyword density. (Some say that having too much of the keyword will lead to a stuffing penalty, and they might be right. Solution: stop worrying about keyword density.)
Basically, keyword density doesn't matter.