There are lots of possible answers, depending on what specifically you’re most interested in understanding.
From a “what are they, really?” perspective: All notes are just sound waves with different wavelengths. As you go higher up a scale, the wavelengths get smaller, sometimes in ways of simple fractional relationships. For a simple example: the same note an octave higher is exactly half as long a sound wave. This puts the notes in such perfect sync that they sound almost the same.
Other notes along the way, though, may be 3/4ths as long, etc. These notes played together will create a BIT of disconnect (tension) because they don’t sync up perfectly. But they’ll sync up well enough to create a pleasing mix of “not quite the same but they sound like they still fit together”. So this relationship will create notes that are in the same key as each other because it works well.
You can pick the starting note of your key to be anywhere, but the principles of those fractional wavelength relationships will stay the same as you move up the scale.
Music is generally about finding a balance between tension (imperfect relationships) and satisfaction. Songs all in the same note provide no tension. Songs all in haphazard and random wavelengths create no satisfaction. Songs in a single “key” provide a balance of both for composers to work within.
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