Why 12 notes in Western music?
Another possible explanation, which I'm surprised the author didn't go through is the "Circle of Fifths" which basically says:<p>Since Fifths sound so great, why not just keep doing that?  When we get to the next octave, then come back down.  If we get to a place that's "pretty darn close" to another note, then stop.  The Python explanation looks like:<p><pre><code>  f = 440
  for i in range(13):
      print(i,f)
      f = f * 3/2
      if f > 880: f=f/2.0

  0 440
  1 660.0
  2 495.0
  3 742.5
  4 556.875
  5 835.3125
  6 626.484375
  7 469.86328125
  8 704.794921875
  9 528.59619140625
  10 792.894287109375
  11 594.6707153320312
  12 446.00303649902344
</code></pre>
Note that after exactly 12 steps, we're back at 446 which is "pretty close" to 440.  So, we take this set of notes, sort them, and just jigger it a little bit to get the 12 notes we know today.