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Critheïs. According to the article in PW, in Greek the spelling Κριϑηΐς is the usual form, although Κρηϑηϊς is common enough to be noteworthy. One of the only widely-available English translations of the Life of Homer is here, and it's quite readable. It uses Critheïs, which would be fairly standard for English through much of the 20th century. I think it's also preferable because 1, 'c' is the standard Latinization for Greek names beginning with kappa (German sources are going to use 'K', naturally); 2, the main vowel in the usual Greek spelling is iota, not eta, and 3. the diaeresis appears in the original and is used in English transliterations of Greek names to indicate syllabification; without it, the name appears to be two syllables, with a diphthong 'ei', but with it, it's clearly three. While any number of forms could be encountered in literature, Critheïs is particularly likely since it's used in popular translations (I don't think the Life of Homer is that widely read these days, so it probably doesn't have a ton of recent translations, and few are likely to be more well-known). P Aculeius (talk) 19:17, 23 May 2018 (UTC)[reply]
I've moved it to the favoured title of "Critheïs" and made redirects from all the alternatives which have been mentioned, with a hatnote on the moth article to which Cretheis redirects. Job done! PamD20:19, 23 May 2018 (UTC)[reply]
Thanks, will see if I can come up with some more source material soon. There were a lot of notes in PW, but locating them may take some work! P Aculeius (talk) 20:47, 23 May 2018 (UTC)[reply]