Thank you for your question.
I'll give you the answer I've written before, by Ctrl+c Ctrl+v
Simply said, you can think of '의' as similar to 'of' in English.
But you can use a much more diverse way.
In a nutshell, It is used to indicate a [possession, Subject of action, object, property, function, apposition, relation, Degree, characteristic, result, etc]
e.g. 나의 옷 [possession] 우리의 각오[Subject of action] 다윈의 진화론[object] 금의 무게[property]
축하의 잔치[function] 100℃의 끓는 물[apposition] etc.
So, of course, you can say '한국의 음악'
Have a nice day~