Hi DJ,
Without looking it up, I've always thought that "empathy" is what you feel in your gut when you grasp someone's situation, like Bill Clinton's corny (possibly insincere) line, "I feel your pain."
Sympathy, on the other hand, is an intellectual grasp of another person's situation.
Nonetheless, we wouldn't send someone an "empathy card." "I wish to express my sympathy" means "I wish to offer my condolences" for some sad misfortune. You might go on to express that you feel their loss too, which in my opinion would really be empathy.
But in the pure sense, sympathy and empathy can describe your understanding of, or grasp of, or reaction to someone else's great joy, as well as great sorrow, or even intellectual position on some issue.
To sympathize with someone's views is to understand or appreciate them, while to empathize would be to agree with them.
"That's my take." I may be wrong.
"Sympathetic vibration" is an interesting scientific and musical analogy in which the sound waves set up when
A vibrates cause
B to vibrate "in sympathy" because
B naturally vibrates at the same frequency as
A. (The violin shatters the wine glass.) (letters not referring to musical notes)
- A.