There’s a good Minute Physics video on it you can find [here](https://www.youtube.com/watch?v=1Hqm0dYKUx4).
To summarize it, starting from a certain key, every other key in the octave is a whole multiple of the same frequency. Because they’re whole frequency multiples, they stay in harmony with each other. All of your sound waves start and end at the same time, meaning you get a constant sound.
If you play notes that are not frequency multiples of each other, you end up with sound waves that waiver over time, with the peaks of the sine wave happening at different times making the sound warble over time.
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