prepositions - How to understand "of" in "She is a woman of enviable beauty."

I found It's hard to understand the word of in some sentence which I gotten when I was checking the word of from an online dictionary.

A sort of explanation about of the dictionary given are shown below:

You use of to indicate a characteristic or quality that someone or something has.

And the dictionary also showed some examples:

the worth of their music.

According to the explanation given above,I suppose this sentence would means their music has a quality of worth.

the creaminess of her skin

I suppose this sentence would means her skin has a quality of creaminess.

So far the explanation works properly.

But,

She is a woman of enviable beauty.

I can't understand this one ,because I can't suppose it means the enviable beauty has a quality of a woman. It looks weird if I simply using the explanation to understand it.

And I also can not understand this one.

A matter of overwhelming importance

Source:http://www.iciba.com/of

the worth of their music means their music has a quality of worth. But a woman of enviable beauty means Enviable beauty's qualities are had by a woman.In other word,it means a woman has a quality of enviable beauty.so noun1 of noun2 seems sometimes means noun1 has a quality of noun2 ,and sometimes means noun2 has a quality of noun1 .

Are noun1 and noun2 exchangeable?

Taking an example:

Do the worth of their music and their music of the worth have the same meaning.

Thanks.

.

Answer

I think this is partly due to the confusing examples the dictionary gives. The reason behind this seems to be that, when listing senses, the dictionary only focuses on the meaning, not the grammatical use of the word.

I think it's useful if you stick to this: in a noun phrase like this one, whatever comes before of is what we want to talk about.

Let's have a look at the first two examples:

The worth of their music

We want to talk about the worth, which comes before of, not the music. Although using of here lets us know that "their music has the worth," we are not talking about the music itself.

The worth of their music has decreased in the last few years

What has decreased here is the worth, not the music.

Likewise,

The creaminess of her skin

talks about the creaminess, which is a quality of her skin, but not the skin itself.

Now, for the other examples

A woman of enviable beauty

Remember, we want to talk about the thing that comes before of, so here we want to talk about a woman, not the enviable beauty. It just tells us the quality, i.e. the beauty, of the woman.

The same goes for

A matter of overwhelming importance.

Here, what is talked about is a matter, not its importance.

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Note: I know I actually cheated when writing this answer, because these are, at least in my opinion, examples of two different uses of of (one is a complement, another a modifier.) For a more technical explanation on this matter, see Huddleston & Pullum (2002), page 439 and 446.

However, I believe it is important to keep things simple, and describing it this way, while not perfectly accurate, works most of the time for learners. If anybody wishes to write a more technically accurate answer, that would be great as well.