We all know that uncountable noun does not take an article. But then, if there's an adjective modifying an uncountable noun what should happen?
An article before adjective + uncountable noun? OR
No article before adjective + uncountable noun?
My research:
I found some examples of having article + adjective + uncountable noun such as...
A soothing music.
A deadly pollution.
A hot tea.
A hard work. And the like.
The short answer is no. The adjective does not change the syntax.
The long answer is that nouns can convert class from mass to count or vice versa. There's an old joke that if you have a really powerful machine that turns anything into powder ("a universal grinder") then you can make any noun from a count noun into a mass noun -- "that's a lot of man on the floor."
To go the other way, you don't even really need a machine -- whenever you are comparing multiple instances of a mass noun, you convert it to a count noun: "the sands of Texas are whiter than the sands of Florida."
As a result, you will find many instances of nouns that are usually mass nouns being converted to count nouns.
For your examples, I find "a soothing music" hard to parse, "a deadly pollution" makes sense (we are imagining several instances of pollution, this one a deadly one), "a hot tea" is fine (with food items that are mass nouns, we convert them a lot when we are ordering them at a restaurant, e.g. I'll have a tea), "a hard work" sounds terrible to me when describing the mass noun "work" (which means labor) but there is also a count noun "work" (a creation arising from a lot of labor, like the works of Beethoven) and here it makes sense to describe one as "hard."
But the point is that the adjective has nothing to do with it. It's just that the mass noun has been converted to count, and there happens to be an adjective.
I already chose oerkelens' answer but I found something useful while reading Swan's Book. I think it's very helpful and thus answering here.
With certain uncountable nouns – especially nouns referring to human emotions and mental activity – we often use a/an when we are limiting their meaning in some way (and we generally limit it by putting adjectives). Here are the examples -
We need a secretary with a first-class knowledge of German (NOT...
with first class knowledge of German).
She has always had a deep distrust of strangers.
My parents wanted me to have a good education (NOT ....to have good education).
(Adapted from Practical English Usage, section 149.4)
No, the adjective plays no role here. What does, is context.
While music, pollution, tea and work can all be used as mass nouns (and regularly are) as in these examples:
They played lovely music at that concert.
There is heavy pollution in this city.
When you have a cold, I recommend drinking hot tea.
Hard work will make you forget your worries.
When you are referring to a specific instance of the concept, yuo do use an article, which can be either definite:
The loud music they played here hurts my ears.
The heavy pollution in this city is bad for my health.
The hot tea you gave me burned my lips.
The hard work you did was in vain.
Or indefinite:
In the restaurant they played such a lovely music!
The old diesel engines cause a deadly pollution in this city.
It is cold outside! I could do with a hot tea!
That is a great work of art!
(Yes, that last example is cheating... I couldn't come up with a better example :) )
