Penso che gli avverbi あ ら か じ め, 前 も っ て e 事前 に vogliono dire lo stesso. Sono sempre intercambiabili al 99%.
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I respect Ayumi-san's answer but I have a different opinion from a different angle. It is only a difference of opinion.
I think the adverbs あらかじめ, 前もって, and 事前に means all the same. They are 99% always interchangeable. The difference in usage of these words is, after all, a matter of rhetoric.
Sorry, Ayumi-san, let me use your sentence.
The following is my opinion
- I checked all the sentences with "OK", which means I think all the sentences are grammatical and make sense. In other words, I don't care if it is a good writting or not, only care if it is grammatical and making sense or not
- あらかじめ and 前もって are genuine Japanese word(訓読み). 事前(に) is a word consisted of Kanji（音読み）. That is why 事前に look like formal.
- You can say あらかじめ予約する is incorrect (or redundant) because, when you make "a reservation", it is always "in advance（あらかじめ）"; you never make a reservation a posteriori; so you don't have to say "in advance（あらかじめ）"; it is redundant.
Yes, it is redundant but I think it is allowed as a kind of emphasis. If you insist you never allow redundancy, you shouldn't allow "前もって予約する“ nor "事前に予約する“ either.
- 予め（あらかじめ）予約する is, although grammatical, looks like really redudant．So it is better to write あらかじめ予約する . It is only a difference of how you write.
- I think あらかじめ is least used among the three. It is probably because あらかじめ was first used to read Chinese documents in Japanese 1500 years ago, like 予 と書いて あらかじめ と読む、or 須 と書いて、すべからく と読む．It is rather a big word.
P.S: if you want to pass some examination of Japanese, I recommend you should follow Ayumi-san's opinion.