🚀 go-pugleaf

Thanks for helping out.  If you could reformulate the calculation once
again to double check the number I would feel more comfortable with the
number you generated.  The correct formula given in math books for
obtaining roots is: 

(key) 2, (key) INV, (key) Yx, (key) 12, (key) =.

I just can't do it.  I'm using a friend's computer, he doesn't have a
mathematical software program, and his calculator only goes out as far as
the number I've given which is correct up to that figure.  

The reason I must have the complete number is because the way all
guitarmakers determine fret spacing based on Pythagorian constants is as
follows:

12th root of 2/12th root of 2 -1 = (?) x Scale length!
          
or 

1.059.....\.059..... = ? x say 25.5 or whatever scale length is desired!

So as you can see if the first number is incomplete it will only compound
the inaccuracy of the last number.  Which has been the case industrywide
up till now which has resulted in an increasingly flatting intonation the
higher you move up the fretboard!

The way you calculated the figure put an automatic stop of the calculation
after 1000 digits.  If you could please try using the formula I've given
then saving the number to memory and then multiplying the figure by itself
12x you will know how close to 2 you are.  

In other words:
axa=a2xa=a3xa=a4xa=a5xa=a6xa=a7xa=a8xa=a9xa=a10xa=a11xa=a12 which should
be 2.0 on the nose!

If you are successful in obtaining that number if you would be so kind as
to subtract the 12th root of two figure you have by 1.0 to obtain .059...
and dividing the 12th root of 2 by that number I would then have the
correct number to calculate fret spacing with.  

Thank you

Charles S. Thomas
Luthier