There is a part of the brain (the cerebellum, I believe) that coordinates movements of the limbs in rhythmic patterns. In order to walk we need to move our legs in a cycle. If we want to carry something in both hands, the cerebellum coordinates the limbs. It’s the part of the brain that gets confused when you try to rub your belly with one hand, and pat your head with the other, or if you try to move your foot in clockwise circles and your hand in counterclockwise circles.
In babies, the cerebellum is under very active development and moving to music is exactly the sort of cognition that part of the brain performs. Babies love to dance because that’s how they learn muscle coordination and balance.
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