The compound interest formula for six percent found a new
 application when it came up as the equal temperment design.
Applied to string length you add .06 until the octave tone 
is reached. It is also applied to fixed length guitar strings.
Fret Division(from fret to fret+1)= String Length X [
                   { 12th root of 2 }to power -(fret positon n)    
                -  { 12th root of 2 }to power -(fret position n+1) ]
So n=0 to 1  gives L x (0.056) or 1 & 1/3 inch for a 2 foot string.
Or in 16ths, 2' = 384 16ths, 21 16ths and I measured 23 on my 
 guitar. 
For each following division, multiply by (0.94) although I used
more places for calculations. The n is good till 12, then start
over again using L/2 so the 13th fret is 10.5 16ths.
If you go to fret 25, its L/4 or 5.25 16ths; for a 2 foot string,
you won't go there except for a longer string. 

  Fret     FD       Fret    FD
   1       21        13     10.5
   2       20        14     10.0
   3       19        15     9.5 
   4       18        16     9.0
   5       17        17     8.5
   6       16        18     8.0
   7       15        19     7.5
   8       14        20     7.0
   9       13        21     6.5
  10       12.8      22     6.4
  11       12        23     6.0
  12       11.4      24     5.7