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I learned ancient greek at University. This is how we've been taught.

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For Chi we learned, that it could be pronounced both /kʰ/ and /ç/. Tough I never met any professor during those 7 years, who pronounced /kʰ/.

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For ει we've been explicitly taught, that it's /ei/. This was pointed out quite clearly 'cause in my language you'd usually pronounce "ei" as /aɪ̯/. Never heard any professor pronouncing it differently.

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I just checked my books on ancient greek and all of them confirm this.

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So either there is a difference in the pronounciation of ancient greek in the different modern languges, or Wikipedia is wrong.