Math is not my thing, I'll admit. The most perplexing job of work I ever did was Algebra II --- I got good grades, but I never "got" what I was going. I did well-enough on the tests, stupidly.
I once had a knock-me-down experience, though, that "revealed" to me that way before Greek or Hebrew, God spoke Trigonometry.
Sang it, probably. HA.
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The math in music theory is not hard at all!
It’s all about the frequencies.
Every time a note rings out, a plethora of other notes ring out alongside it - all the multiples of the note’s frequency.
So if you hear a note with frequency of 400Hz, you will ALSO hear “overtones” at 800Hz (x2), 1200Hz (x3), 1600Hz (x4), 2000Hz (x5), etc.
The first overtone is the octave, which will sound the same as the original note, but higher - as does every doubling of the original note. So octaves for 400Hz are at 800, 1600, 3200, 6400, etc.
This means you can go down an octave as well, by halving the frequency.
So the 2nd overtone of our example note is at 1200Hz. Bringing it down an octave gives us a 600Hz tone, which is the “perfect fifth” in our diatonic scales. Continuing this process with other overtones fills out the rest of our scale... notes more dissonant than major 7ths and minor 2nds are not used because the extra dissonance vs those intervals is not generally musically useful, but theoretically we could add as many notes as we like to our scales using this method.