Contumely is insolent or insulting language or treatment. Most of us first came across this word in Hamlet’s soliloquy, “Th’ oppressor’s wrong, the proud man’s contumely”, and were puzzled by it, as it’s hardly a word in common use. I would have laid bets that it’s now obsolete, except that a search found this sentence from an issue of a British newspaper, the Daily Mail, of November last year: “Yet it is hard to see how the monarchy may be delivered from contempt and contumely until the immediate crisis is faced down.”
The word came into English from Old French contumelie, which in turn derives from Latin contumelia. That seems most likely to be a combination of con-, with, plus tumere, to swell. The link is that the swelling up was with misplaced or ill-judged pride, leading to arrogant behaviour.
There’s no agreement about how to pronounce contumely. Some people say it as three syllables, /ˈkɒntjuːmlɪ/ , some as four, /ˈkɒntjuːmɪlɪ/; most stress it on the first syllable, but some prefer the second, especially when they say it as four syllables, /kɒnˈtjuːmɪlɪ/. That’s not really a problem for most of us, since we’re hardly likely to want to say it unless we’re playing Hamlet; in that case, the scansion of Shakespeare’s blank verse requires three syllables with the stress on the first.