Rights managed music is music, whose producers are members of a collecting society (GEMA, Suisa, AKM, etc.).
According to copyright laws, musicians are entitled to charge license fees for the use of their music. Every piece of music is copyrighted, which means all business owners have to pay a license fee (in Germany to the GEMA) if they want to play music or have a radio in their premises.
The exclusive rights of use for Royalty-free music are purchased directly from the producers as they are no member of any collecting society.
Which means that music is only rights managed, when the producer (composer, song writer, etc.) is a member of a collecting society (GEMA in Germany).
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