irst. There is not a perfect octave however it is always a couple of numbers off the original frequency. log3/log2= continued fraction[1,1,1,2,2,3,1,5,2,23,...], is the best fraction to get closest to the perfect octave. if we take the notes frequencies, and build fifths we get pretty accurate to a perfect octave. Twelve is by far the easiest number to get closest to a perfect octave which is why there are twelve tones in an octave. A whole tone is usually from one whole note to the other or one # note to the other except on tow occasions: b-c and e-f there is no # note in between those notes so from b-c and e-f is a whole tone but anywhere else it is three notes ex. a-a#-b (www.classic-guitar.com)Math is also very important while making a guitar. A normal guitar usually contains 21 frets, the spaces in between the frets is usually found by getting the total length of the neck, and then using the "rule of 18" which is 17.835. You divide the length of the neck by this number and this gives you the length of the first fret. Then you subtract the length of the first fret from the total neck length and then divide the length by 17.835. You do this until you have the full neck fretted ...
