A Better Approximation to the Rule of 18

by Mark French

Originally published in American Lutherie #132, 2017



Historically, luthiers often used the Rule of 18 to lay out fretboards for guitars and other fretted instruments. (See “Classic Guitar Intonation” by Greg Byers, AL#47; Big Red Book of American Lutherie Volume Four.) While builders seldom now use the number 18 as the coefficient for calculating fret positions, the name is still used as a shorthand way of identifying the method.

While 18 is a very convenient whole number, it is far enough from the exact value of 17.81715 that noticeable errors can accumulate. Still, it is often convenient to use a simple approximation for a long decimal number — many of us have used ²²/₇ as an approximation to π and ³⁵⁵/₁₁₃ is even better. With this in mind, you can replace the number 18 with ²⁸⁵/₁₆ and lay out frets very accurately. Let’s see where these numbers come from and why the approximation works.