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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2015-02-03T19:13:56.600
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grammar
What's the difference between 大きいケーキ and 大きなケーキ?
(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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2015-02-03T19:50:47.270
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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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2015-02-04T01:46:20.413
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Here is an extensive article about this topic.

[「大きい声」と「大きな声」](http://www.urayasu.meikai.ac.jp/japanese/meikainihongo/7/sasaki.pdf)

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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