A cautionary tale of the "if this goes on..." ilk. The government, which includes all humanity, sets down a law that copyright and royalties apply to any musical theme, and with the aid of computers manages to keep track of them. Although at first this is seen as a boon to composers, as the centuries pass it becomes a burden as good, original music becomes impossible to create. For example, one composer who thinks he has created a delightful tune discovers to his pain that it is a recreation of a popular piece some decades earlier. Eventually the law is overturned and the databases erased in order to give humanity the freedom to create again.
The story was in the English language, and included in an anthology, perhaps in the 70s to 90s, though I can't be certain of this.