[beefman]

You're referring to Vienna. It's broadly part of Europe and narrowly functions as its own city-state. Its intermediate allegiance may be less important.

It's long had outsized musical influence but was only the world leader in music during the classical period, roughly 1750-1820. This does not overlap Austria-Hungary. However, I don't know the economic output of the Habsburg monarchy relative to the rest of Europe, so it may still be an exception.