I guess Sun Tzu didn't realize there are 12 (actually infinite if you include out of tune notes as notes)

No, it's much more complex than that. :)

12 tones per octave is just a Western standard that we have merely culturally and habitually gotten used to.

And even if we accept those 12 tones as a given, the mysterious thing about music is that it that the harmonics of frequencies never add up, you cannot build a perfect musical system, you always have to compromise, with the Equal Temperament mainly used today (not in Bach's time) being the dullest of them all really.