It seems like there's some interesting cross-cultural stuff going on in the description of emotions in Homeric Greek compared to my US/English way of talking about these things. For "happy," the words I find are:
εὐτυχής
μακάριος
εὐδαίμων
For "sad:"
δυστυχής
But most of these words seem to have more to do with fortunate/unfortunate or blessed/not blessed than with the emotional states. Is this just a cultural mismatch in ways of conceptualizing life and feelings? For example, I could say that singing makes me happy. That doesn't have much to do with being fortunate -- even very unfortunate people can sing. Can anyone clarify the contrasts in meaning, tell me if these are right for the Homeric language, and tell me if I'm missing more relevant words?