If the purpose is to have the meaning "unlimitedly", Since 無制限 is an adjectival noun we should use に to turn it into an adverb instead of で if I'm not mistaken... ?
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The grammar may be correct; で is accepted 連用形 for adjectival nouns - a quick Google turns up quite a few sites that use で and seem to be written by native Japanese speakers - "時間無制限で", for example. It may be used on a case-by-case basis depending on the adjective in question (I myself have only seen で used with 中止法 or in conjunction with particles like は or も)– kikuJun 6, 2018 at 19:13
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4Remember that translations usually adapt somethings to sound more natural to the target language, I think this で means "by" or "in a x way". "You can download music in this site in an unlimited way". Now, i'm not sure why the original sentence was written with で instead of に– Felipe Chaves de OliveiraJun 6, 2018 at 19:24
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1Hint: 無制限 can be either a na-adjective or a noun.– user4092Jun 6, 2018 at 20:47
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Now that I've put some thought into it, I guess it's just a matter of one being more common in a given situation, in english it's true that saying "You can download music unlimitedly" might be more common, and while you can say that in mother tongue as well, we usually literally say "You can download music in an unlimited manner(way)." So I assume that the same occurs in japanese, neither is wrong, but one might be more common.– Felipe Chaves de OliveiraJun 7, 2018 at 18:19
1 Answer
It seems you may be overanalyzing the phrase a little bit. Grammatically speaking,
「無制限{むせいげん}で」
is just a
"Noun + Particle"
That is to say that 「無制限で」 is not really formed by conjugation. The phrase certainly functions adverbially, but it is not an adverb per se. You may be letting the English translation "unlimitedly" fool you even though that is a valid translation.
The function of the particle 「で」 here is to describe the situation/condition in which an action is performed. That is indeed a fairly standard use of 「で」.
One of my mottoes uses the same 「で」. It is 「腹{はら}ペコでスーパーへ行{い}くな!」, which means "Don't go to the supermarket hungry!". (That is because I would tend to purchase too many things if I went to one hungry.)