guitarmaking: frets & calculators.
I'll post some photos of my fretcutting jig soon (basically a modified miter saw box with a depth-of-cut adjustment) but in the meantime I was reminded of a question somebody asked me recently: "how do you know where the guitar frets should be located, and how accurate must you be?"
Easy question first -- accuracy within one one-hundredth of an inch (0.01") is the industry standard and about all one can hope for. Consider, too that the fret slots (the grooves the metal fret fits into) are 0.023" wide and most frets are 0.050 - 0.080" wide. And, since it's wood, the dimensions will change a bit as humidity levels change!
My procedure, then, is: mark --> slot --> fret --> pray for the best!
So back to the question of "where?" There are at least 3 techniques:
1) use a "fret rule". Basically an aluminum rule that is already marked with fret locations for common (e.g. Gibson, Martin, Fender) "scale lengths". Just cut a fret slot where you see a line. Easy, but without understanding. And about $30.
2) use an online calculator to do the work for you, such as:http://www.stewmac.com/freeinfo/Fretting/i-fretcalc.html
3) Use the ancient "rule of 18s" technique where one successively subdivides the scale length by the previous fret position. [note, ancient luthiers used "18", we, however, will us 17.817 which puts the 12th (octave) fret at exactly half the scale length. Why? Without getting too technical, discussing compensation, harmonics, etc... because it sounds right.)
Divide the scale length by 17.817 to get the position of the first fret, then divide the remainder again to calculate each successive position.
Example using the Martin 25.34" scale length.
Distance from nut to 1st fret = scalelength / 17.817 = 1.422"
distance from 1st to 2nd fret is then (scalelength - last fret) / 17.817 = 1.342"
Of course, using Excel or a java applet is much more convenient (some online tools even create a full-size PDF which may be taped to the fretboard for marking/cutting which increases the accuracy of marking, cutting... those thousandths of an inch errors can add up quickly! http://www.ekips.org/tools/guitar/fretfind2d/
Using Excel, use a field formula: "=(B$1-B2) / 17.817 + B2"
HOWEVER.... I've saved the best for last.
4) Calculate the first division, draw a line intersecting the scale end, and use a compass to subdivide.
Take the scale length, divide (and subdivide) by 17.817, then use a compass to subdivide. It's remarkably simple and fun. Tip:use a mechanical pencil with fine lead to avoid changes in line length (and thus, accuracy).
Here's a cute set of drawings illustrating the process. http://www.theweebsite.com/renman/frets.html