The issue of ownership can become a very complicated issue when it is applied to music. One way to examine the situation is to see where the money actually goes that a person would pay to experience a piece of music.
At the most basic level there are two parties that are always involved with the creation of music and can claim some degree of ownership over a musical performance regardless of how the music is experienced. There is the artist who wrote a given piece of music, and there is also the performer who performs a given piece. These two people can be the same person, but they do not have to be. In the case where they are not the same person, both individuals can claim a large share of ownership of a given performance. Without the composer, there would not be a musical piece to play for an audience, and without the performer the audience would never be able to experience music.
In the modern commercial music landscape there is also a third party which can lay claim to a portion of this ownership pie. That third party is the record company itself which often claims ownership of muscial pieces through copyright law. It is the record company which owns the distribution rights of a given musical piece. In a sense, they buy the rights from the artists through record contracts to control who can and cannot experience a piece of music. It is a similar type of role that a museum would have with a painting or sculpture. Just as a museum buys a piece of art and charges people to view it, a record company buys the rights to distribute a peice of music and charges people to listen to it.
With the emergence of MP3's over the last few years, the commercial landscape is beginning to radically change, and record companies are struggling with finding ways to maintain their ownership rights over the creation of their artist's music.