Scale Western

Trying to understand western music?
Almost all western music has a 12 or 24-tone system. Is there some logic behind this, or is it just the arbitrary way it came to be? Why not 16 notes? What is the advantage of 12?
Also, what is the reasoning behind the diatonic scale? Is it simply tradition, or is there some kind of mathematical significance?
Our system seems to be instinctive.
All over the world, people both isolated and Westernized divide the octave much the same as we do.
The only significant exception is the Javanese people, who divide the octave into 5 roughly equal units.
The culprit seems to be the overtone series.
http://en.wikipedia.org/wiki/Harmonic_series_(music)
The first five overtones give us a major chord, which is where we get our system of harmony.
In his book The Craft of Music Composition, Hindemith rejected newfangled methods such as atonality, polytonality, and microtonality on the grounds that conventional tonality was accepted by people all over the world, and therefore proved to be the system in alignment with out instincts.
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