Thing I wish I had understood in school: a wave is a periodic, differentiable system. A periodic system is a loop. Differentiable means the states are approximately continuous (you can fit a curve to them). A smooth wave has a differentiable derivative.
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The representation of periodic sound involves multiple dimensions of periodic generators that can be visualized as stable geometric surfaces. If there exist rotational operators between dimensions, we perceive them as space. Independent dimensions: we perceive them as color.
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