The science behind musical pitch is actually super interesting! So you’re right that in western music notation we have 7 different letters, but if you include sharps and flats, there are actually 12 different notes in an octave.
What we hear as the pitch of a sound is really the frequency of the sound wave, or how fast it repeats. An octave is a special interval because it represents multiplying the frequency of the sound by exactly 2. In other words, C at the top of a scale is exactly twice the frequency of C at the bottom of that scale.
A perfect fifth, or the distance from C to G, represents multiplying the frequency of the sound by 3/2, and a perfect fourth is 4/3. Notes whose frequencies are in simple ratios like these are said to be in resonance, and our ears like resonant sounds, which is why we’re drawn to these specific intervals.
As for why we have exactly 12 notes in a scale though, that is an arbitrary choice that was made centuries ago by early musicians. There are plenty of other musical systems with more or fewer notes; the only difference is how they chose to split up the octave.
There is a good reason why having 12 notes is objectively better than, say 11, or 13. It has to do with those resonant intervals, and the fact that every interval in our western music scale is the same size (this is known as an equal temperament scale). It turns out that there is no way mathematically to create and equal temperament scale which exactly hits all those nice resonant frequencies we talked about earlier. If you’re playing an equal tempered piano, your perfect 5ths will always be a tiny bit flat and your perfect 4ths will always be a tiny bit sharp. However, depending on how many equal intervals you choose to split your octave into, you can end up with better or worse approximations of those nice intervals, and it just so turns out that 12 notes is the smallest number of notes that gets us a relatively good approximation of all the intervals we want.
You can also get relatively nice sounding intervals with 17 equally spaced notes, so some lo-fi musicians have adopted 17 note scales as well which sounds really cool and kind of disorienting to listen to.
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