The current copyright law is unsustainable. Pretty much every melody you can think of is copyrighted and as an artist you can be anxious that anything you make can be claimed by someone else. Copyright laws need urgent change as they are not fit for purpose...
In this case that's not the problem. Beethoven isn't copyrighted, but public.
How will sonic fingerprinting be able to decide whether it is that copyrighted work, or whether it is somwonw playing it live? It just won't