Quite a few phrases in English are constructed like so:
How [adjective] a [noun]...?
This is the question form of the construction, which is often answered with the negative:
Not that [adjective] a [noun].
or the positive:
Quite [adjective] a [noun].
However, from time to time I'll hear the word 'of' inserted before the 'a', e.g.:
Not that [adjective] of a [noun].
This usually sounds wrong to me, with the exception of the case where the adjective 'much' is used. So, this sounds fine to my ear:
Not that much of a problem.
whereas this doesn't:
Not that loud of a noise.
Why is it that 'much' should be used with 'of', and other adjectives not? Is it because 'much' is seen as measuring a quantity (of something), whereas other adjectives that may be used in this construction are seen as measuring the quality of a whole thing?