While I was leafing through my German dictionary looking for a definition, I came across the lemma "ei".
It listed not only the meaning I was familiar with (an interjection of surprise, as in "Ei, wo kommst du denn her?" or "Ei, ei, was seh ich da [= Œuf œuf, que lac-je là]?"), but also another one: "ei(, ei) machen", to caress or stroke, used to children, or "ei", the sound one makes when doing so.
I knew that phrase but had never seen it written, and had always assumed that it would be written "ai machen"—presumably based on 愛 "love", which is "ai" in Romanised Japanese and "ài" in Pinyin-Romanised (Mandarin) Chinese. (And FWIW, the phrase is simply "ei machen" for me; the doubled "ei, ei machen" sounds odd to my ears.)
So it's not "ai", then, is it? Huh. Oh well :)
