A musical composition is a separate thing from a sound recording and a separate copyright applies to each. For simplicity here, lets assume the two copyrights are held by the composer and performer respectively although, of course, they can sell or assign their copyrights to others.
A performer making a sound recording will need a licence from the composer and that licence generally defines how any profits from the recording will be distributed. Maybe the composer grants the licence on the basis that any profits are shared 50/50. Alternatively, the performer could pay a fixed sum of money for the licence and then keep all the profits for themselves. It’s for the composer to set the terms.
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