mis-

The story

1. Proto-Indo-European*mey-?
2. Proto-Indo-European*meyth₂-
3. Proto-Germanic*missaz
4. Proto-Germanic*missa-
5. Proto-West Germanic*missa-
6. Old Englishmis-
7. Middle Englishmys-
8. English todaymis-

From Middle English mys-, mis-, from Old English mis- (“mis-”), from Proto-West Germanic *missa-, from Proto-Germanic *missa- (“wrongly, badly, mis-”), from the adjective *missaz (whence also miss), from Proto-Indo-European *mitˢtós (“mutual, reciprocal”), from *meyt(h₂)- (“to replace, switch, exchange, swap”), extended from the root *mey- (“to change”). Cognate with Scots mis- (“mis-”), Dutch mis- (“mis-”), German miss-, mis- (“mis-”), Danish mis- (“mis-”), Swedish miss- (“mis-”), Icelandic mis- (“mis-”). Compare also French més-, mé- (“mis-”), from Old French mes- (“mis-”), from Frankish *mis-, *missa- (“mis-”), from the same Proto-Germanic source above.