Did I say 'half'? I really did think half at one point, but since we already have hemi and semi, I didn't think that could possibly be right. What gives?
Well, hemi, semi and demi do all mean half. They probably all relate back to one of those Protoindoeuropean roots, but they are filtered through, respectively, Greek, Latin and Old French. Demimonde, interestingly comes from and old Alexandre Dumas fil comedy, in which the demimonde is "half the world". It is "the link between good and bad society ... the world of compromised women, a social limbo, the inmates of which ... are perpetually struggling to emerge into the paradise of honest and respectable ladies". One of these denizens is called a demimondaine.
A demitasse is, fairly straightforwardly, a halfsized cup.
But things are never simple. It turns out that demiurge, the impetus for this blog post, does not come from "demi" at all. It comes from "demos", the common people, and "ergos", work. The demiourgos was a public worker in Greece, and this was sometimes used as a title for a magistrate. Kind of like a public servant in our parlance, I expect. In Platonic thought, the maker of the world was such a magisterial being, a subordinate to the Supreme Being and not always working for the good. (Look around--are you surprised?)
I did discover a term I had never heard of before: the hemidemisemiquaver, or a 64th note. You've heard of a quarter note, right? Think about it...