The student of German had said there was a single word in Greek for this concept. I didn't know it, but as soon as I could I looked it up and today's word is the result. The equivalent of epichairekakia in Latin is malevolentia (like the English word 'malevolence'), according to blogger Michael Gilleland. He says that the Greek word is a compound formed from the preposition epi 'upon/over' + the Greek words for 'rejoice' and 'evil' (chairo and kakia). More interesting to me than the etymology are the instances he mentions of its use as a positive. Gilleland says Aristotle thought epichairekakia prevented pity and Sophocles presents Athena asking if laughing at one's enemy is not the sweetest laughter.

Comments
Epichairekakia thanks for the word. For years I’ve been haphazardly working on a paper about the morals of the Olympian. “Epichairekakia” is a perfect description of behavior I’ve found disturbing above them. They had no qualms about gloating, bragging and delighting in the misery the of others. As several critcs of Homer point out, the Olympians were not role models. But, I guess they and the Ancient Greeks are not us and we have to accept different standards for their behavior.
Yes, the Olympians often laughed at mortals, but some of them also had their share of misfortunes. Athena was almost raped by Hesphastus (Vulcan), Apollo had a lot of sad experiences with women, and Hera was always miserable with Zeus’ antics.
I just learned the word Schadenfreude a few days ago and now I’ll add Epichairekakia to my list as soon as I learn to pronounce it. Thanks for the new word.