shutter speed - Is there a sane reason why ¹⁄₁₂₅ is not, instead, exactly half of ¹⁄₆₀?

Here are some common shutter speeds you will find on most DSLR cameras:

• 1/15, 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000, 1/2000, 1/4000

As you move from left to right, or as you increase the shutter speed, you are halving the amount of light that hits the sensor. In other words, you are decreasing the amount of light by one stop for each step. So 1/30 is half of 1/15, and 1/60 is half of 1/30. But then you come to 1/125, which is not half of 1/60. Half of 1/60 is 1/120. This is basic math.

So you break the sequence or pattern. But as you continue, it starts to make sense again. So 1/250 is in fact half of 1/125, and 1/500 is in fact half of 1/250, and 1/1000 is in fact half of 1/500, so on and so forth.

So there appear to be two distinct sequences here.

• 
  

  1/15, 1/30, 1/60

  
  



• 
  

  1/125, 1/250, 1/500, 1/1000, 1/2000, 1/4000

  
  

Is there a sane reason for this?

I know that people sometimes talk about half stops or even thirds of a full stop. But then what is 1/125 the half stop, or third stop of? If you increase 1/60 by a third you get 1/180. This setting does not exist in the standard sequence. The closest you will get is 1/160. If you increase 1/60 by a half, you get 1/120 and it doesn't exist either.

Is this all arbitrarily set by the camera manufacturers, or is there perhaps some reason and history behind this?