Culture is nothing more than the way we live our lives, and it can be informed by religion or not. If you are asking about a more monolithic entity like "civilization" then maybe we can say that Muslim civilization has declined, but that is nothing new. All civilizations rise and fall, including the Western civilization. It is somehow natural, and civilization is what we make it. Culture, on the other hand, is more local and regional, more amorphous and less linked to material objects like monuments and cities, which are what we usually use to judge civilization.
What makes a particular sound art "Islamic." I have to say that any comments I make on this are indebted to the late scholar of music, Lois Lamya al-Faruqi, who really helped to define an Islamic epistemology of music. Rather than using Western categories of analysis, she developed categories that were descriptive of the sound arts based on Islamic principles and proceeding from the Quran.