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I'm studying for Japanese exam of the second year and teacher corrected this sentence-mistake:

音楽 を 聞いた あとで、大きい ケーキ を たべました。

was corrected to 

音楽 を 聞いた あとで、大きな ケーキ を たべました。

What is the difference?

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Here is an extensive article about this topic.

「大きい声」と「大きな声」

Very short summary:

  • 大きい and 大きな are interchangeable in most cases.

  • On average, 大きな is 8 times more frequently used than 大きい which directly modifies the following noun.

  • 大きい sometimes means "elder/older". 大きな doesn't.

    一番大きい兄さん (the eldest brother) vs. 一番大きな兄さん (elder brother with the largest body)

  • 大きな/小さな sometimes expresses the sense of intimacy with the modified noun, while 大きい/小さい doesn't.

    小さな胸 (someone's little heart) vs. 小さい胸 (small breast)
    (the difference may be not as big as the English translation suggests)

  • Some set phrases only accept 大きな.

  • Statistical analysis revealed many famous novelists almost exclusively use 大きな in their works, while a few novelists mainly use 大きい.

  • And the author failed to find the meaningful difference in usage between 大きな声 and 大きい声, after investigating 440 real examples.


Personally, I see no meaningful semantic difference between 大きいケーキ and 大きなケーキ. However, I do feel 大きなケーキ is more common. Sticking to 大きな when it refers to the physical size of something seems to be a safe strategy, and that may be the sole reason your teacher corrected your sentence.

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(Going entirely based off my intuition here, so I could be wrong...)

I think both 「大きいケーキ」 and 「大きなケーキ」 are grammatical in that context, but the latter fits much better.

The difference to me seems to be that 「大きな〜」 is the natural choice for a judgment, while 「大きい〜」 is the natural choice for a description.

Compare

大きい車は、ほとんどの人に役に立たない。
"Large cars are not useful for most people."
(大きな also works here, IMO.)

vs

今、すごく大きな車が正面衝突した!
"A big car just crashed!"
(大きい doesn't seem to feel right to me in this sentence.)

In your case, you are sort of "telling a story", so suddenly being very objective about the size of the cake doesn't really make sense, it's your subjective impression about it that matters, hence 「大きなケーキ」.

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Example one, 大きいケーキ is a generalized observation about cakes. Example two, 大きなケーキ is a direct relationship between size and cake. Thus the English equivalency would be in 1) a big cake, and in 2) the cake I ate was huge.

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Difference of how to use

"大きいケーキ" > "ケーキが大きい" OK
"大きなケーキ" > "ケーキが大きな" NG

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