When you own a copyright, you have exclusive control over an original creation. If you so choose, you may copy the work and sell it. Music rights allow you to perform the work for a Los Angeles audience and make derivatives, or new versions, inspired by the original piece.
Inspiration is not limited to copyright owners. Other musicians may feel compelled to create and express something new and different with elements of your work. Whether or not that constitutes copyright infringement depends on whether the derivative passes muster under fair use.