There are other tuning systems, which I intentionally avoided discussing because it starts involving LOTS more music theory very quickly. But to quickly describe it: pleasant sounding combinations of notes generally occur at simple ratios. If you look at a simple major chord, like C-E-G, the E would be at 5/4 the frequency of C, and the G would be at 3/2 the frequency of C. However if you tuned a piano like this, it would be specifically anchored to the root note of C, as that's what we're referencing those ratios from. (This would be "the key of C major.") It just so happens that in 12-TET tuning, we get ratios that are very close to these simple fractions, and since the tuning is "equal", it works for any key/root note.

An octave (for example from a C to the next C) is a doubling in frequency. In the Western diatonic system, there are 12 notes per octave. (C, C#, D, D#, E, F, F#, G, G#, A, A#, B). Notes are "evenly spaced" within the octave - every note has the same ratio between its frequency and the frequency of the next note. Hence, that ratio is ¹²√2

(Both make sense for their respective use cases.)

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