The Pythagorean scale is made by stacking of fifth.
It was used throughout the middle ages.
The scale comes by multiplying the frequency with 3/2, and dividing with an extra 2 every time you come over an octave.
It can be proven that it is impossible to get a multiplier of a prime number to be equal to the multiplication of another prime number. (The two numbers are furthermore even and uneven)
The difference on B# and C is 531441/524288 or 1,013643265. This is called the the comma of Pythagoras.