Finding Your Character's Voices

This is inspired by a fellow writer's words to me, upon reading the first edited draft of The Prince of Cups. I'm going to quote part of what he said here, so that we're all on the same page.

What I find fascinating is that your characters are so different from mine, yet they're very real. Just as you're a very different person from me even though we get along well.

It's not just because they are born from separate heads, though of course that's a lot of it, but because our character's voices a...