謙譲語： More info on お目にかかる & お目もじする?

Question

From my understanding, 伺う is the humble version of 会う, which means to pay someone / some place a visit, and requires a recipient. However, on this website, the humble version of 会う is listed as お目にかかる & お目もじする instead of 伺う.

If I look at the form of each compound verb, the meaning is rather obvious for 御目に掛かる. I believe it literally means, "I place my (humble) presence to your eyes," which makes sense. On the other hand though, 御目文字 is plain puzzling to me. 三省堂's definition says:

〔お目にかかる意の文字詞。もと近世女性語〕お目にかかることをいう女性語

If I'm not mistaken, 近世 means *"early modern." By this definition, I assume that it was originally feminine language, but not anymore, is it? What about its kanji form, 御目文字(する), which would be ご-eye-word, I daresay. How does this kanji combination relate to 御目に掛かる? *The English words "modern" and "contemporary" have different usages in different fields of study. Sometimes they overlap, sometimes they don't.

Lastly, how are お目にかかる, お目もじする, and 伺う used differently? Do people write them in full-on kanji, or otherwise?

教えていただけませんでしょうか。お願いいたします！

Answer 1

My confusion mainly arose from my misconception that 会う and 訪問する were one and the same. Given enough thought, however, it becomes readily clear that while 訪問する may entail 会う, it does not necessarily suggest vice-versa.

Therefore, お目にかかる and お目もじする are indeed the humble form of 会う, whereas 伺う is that of 聞く, 尋ねる/問う, and 訪れる/訪問する. (goo辞書)

The term "お目もじ" had a combination of words which did not make sense to me, because it was actually formed through a process involved in a phenomenon called 文字詞{もじことば}. (Further details in the linked Wiki page. Obviously reserved for the truly hardcore. Not I.)

Going back to its definition by 三省堂, they say it is もと近世女性語. This is a combination of the prefix "もと" (meaning "formerly"), "近世" ("early modern," as opposed to contemporary), and "女性語" ("feminine language"). To me, this seems to state that while the term was originally feminine in early modern history, it is not anymore.

Regardless, goo辞書 has the following to say about this term:

お目にかかることをいう女性語。手紙文などに用いる。

Compared with the definition by 三省堂 which I quoted in my question, goo辞書 does not comment on its status in terms of time. It clearly states that it is feminine language, and used (perhaps usually) for letters and other (written) exchange.

As for how they are generally produced, a search on 少納言 seems to suggest that お目にかかる and お目もじ(する) are the preferred forms instead of writing them out entirely in kanji and 送り仮名 (i.e. 御目に掛かる & 御目文字する).

I hope this helps any unfortunate soul who may have the same doubts as I did.

Edit: Regarding お目もじ(する), a native speaker on HiNative commented that the gender distinction it used to have no longer applies nowadays. Whom to trust, goo辞書 or a living, breathing, native speaker? You be the judge.