Mammalian brains have a crossed over nervous system. This means that the left side of the brain controls the activities of the body’s right side etc This is thought to be an adaptation that allows for each side of the brain to be specialized resulting in greater capacity and reduced conflict. It is known that the right and left halves of the brain register sounds differently because of differences in the brain cells in each side. Most right handed people process language on the left side of their brains. Since music has got lots of spoken words in it, if listened to through the right ear, most of it is getting presented to your left brain which is where your language center is making it preferable to listen via that route.
If you are looking for the artistic or imaginary aspect of the music however, then your left ear is what you should use as the right side of the brain is responsible for this. “Music awareness”-whatever that means is also a function of the right side.
So, what is it in the music are you listening to?