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The arrow of time is thought to be based on entropy — things inevitably tend to get less organized over time — and a song played backwards would be just as organized as the same song played forward. It (probably) won’t sound pleasant to human ears but it’s not actually a different song in a physics sense.
Musical notes are just noises our little brains find pleasant. Dogs and cats might not even find them pleasant, much less animals that won’t hang out with us. The entropy that defines the arrow of time operates of much bigger scales. Life has been defined as a fight against entropy but we, too, inevitably decay and become disorganized atoms.