It's harmony produced the root (any frequency), the major third (5/4 ratio), the 5th (3/2 ratio). They're approximated in the 12TET scale so that they harmoniz

It's harmony produced the root (any frequency), the major third (5/4 ratio), the 5th (3/2 ratio). They're approximated in the 12TET scale so that they harmonize across keys and octaves. I always say I hate musical notation (letters and classical notation) being it so horrifically obscures the mathematical relationships of the 12TET scale. It's literally just approximations of: Major Scale Root frequency (C 262hz, whatever) 2: 9/8 root (D) 3: 5/4 root (E) 4: 4/3 root (F) 5: 3/2 root (G) 6: 5/3 root (A) 7: 15/8 root (B) 2x root (C, 524 hz) 2: 9/8 2x root and so on. Minor scale is simply the starting the whole thing at the Major 6th instead of at the root. 12TET in comparison to just temperament is slightly harder to explain because of the way it allows harmonies to scale without distorting when changing keys, but there really isn't much more to western music than that.