Hi Kay! It sounds like you are reading a very poetic piece of writing. In this case, the author might not mean that she is literally singing about a man, but that she is thinking about him. The author indicates that the man is not there, which means she cannot sing for him, she can only sing about him. I knew him not is a poetic way of saying I didn't know him. In regular everyday speech we would always say "I didn't know him."