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I think there is multiple questions here. I can try and explain why we don’t use arbitrary frequencies in music.
Notes can be expressed as fractions of other notes. The key takes the name of the root note of the key and the other notes are fractions of that note. The perfect fifth is exactly 3/2 the frequency of the root note. The perfect fourth is 4/3. The major third is 5/4. The smaller these numbers in the fractions, the more consonant it sounds. The larger the numbers in the fractions, the more dissonant in sounds.
Why do fractions with smaller numbers sound more consonant? I don’t know but I think it might have something to do with the wave pulses lining up and our brains liking that rhythm.
The notes used in a piece cannot be too dissonant otherwise the music sounds like garbage/noise. Too consonant and it can be boring. Typically scales or musical pieces contain the mostly consonant notes (smallest fractions) with some dissonant notes to add flavour.
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