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姪 "niece" is often pronounced [[me.i]] rather than [[meː]] (see e.g. this comment in chat). I think the reason for this is that there is a morpheme boundary in 姪, presumably
姪 = 女【め】 + イ = female イ
Unfortunately, 姪 is not listed in any of the answers in the question "Kanji for native Japanese concepts: Kun'yomi spanning multiple morphemes" (or it might be hidden in another word and I haven't noticed).
What is the meaning of イ and what is the etymology of 姪 and 甥?
Shogakukan's 大国語辞典 shows that 姪【めい】 has a historical hiragana spelling of めひ, not めい, showing that the modern mei reading is not on'yomi but rather kun'yomi. This different derivation is probably also why the pronunciation is different: [mei] with a more distinct [i], and not [meː]. The term for "nephew", 甥【おい】, has a historical hiragana spelling of をひ. As you note, め is an old morpheme indicating "female", and を is an old morpheme indicating "male". We now have a clear follow-on morpheme ひ.
This ひ is of uncertain derivation. The closest vaguely relevant match that I can currently find is prefix 曾【ひ】, often glossed as "great" in terms like 曾【ひ】お祖母【ばあ】さん "great-grandmother", 曾【ひ】孫【まご】 "great-grandchild", etc. Shogakukan's given definition for 曾【ひ】 is:
血縁関係を表す語について、それよりさらに一代離れた関係にあることを示す。
For terms expressing a blood relation, this indicates a relation separated by one more generation.
I wonder if there might have been an older meaning, still referring to relative distance from oneself, but not necessarily of a different generation; and an older usage, not as a prefix but as a noun. I'll keep looking.
