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A Better Approximation to the Rule of 18

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.

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Beyond the Rule of 18: Intonation For the 21st Century

Beyond the Rule of 18: Intonation For the 21st Century

by Gary Magliari and Don MacRostie

from their 2011 GAL Convention lecture

Originally published in American Lutherie #116, 2013



Don MacRostie: I wear a couple of hats. I do product development with Stewart-MacDonald and build Red Diamond mandolins. This is Gary Magliari, the creator of the intonation system we are going to discuss today. We started working on this about five years ago after Gary showed it to me at the Newport Guitar Festival. His method really seems like a benefit to me, and I think it’s time to make everybody aware of what he’s done.

I believe there are a lot of little things I can do as a builder to make a good or great, or whatever you want to call it, instrument. Things like using glues and woods that have better acoustic properties, tuning those woods, and applying finishes that improve the output create a better instrument. These are little things and if you leave one out, it can still be a good instrument.

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Make a Dished Workboard, Freehand

Make a Dished Workboard, Freehand

by Ryan Schultz

Originally published in American Lutherie #99, 2009



As a first-time guitar builder, I bought a kit from LMI and eagerly began to build my guitar. Very early in the process, I realized that I needed to obtain two radiused sanding dishes (30´ for the top and 15´ for the back) for various tasks as the Robert O’Brien DVD suggests. These sanding dishes are not cheap. They generally cost $60 to $80 each plus shipping. So I was determined to make the sanding dishes on my own if I could.

My research showed that most people make a router jig with the appropriate profile (see AL#74). But I thought I could make a dish quicker and easier, with no jigs, basically routing it free hand.

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Guitar Making as a Teaching Tool

Guitar Making as a Teaching Tool

by Debbie French and Mark French

Originally published in American Lutherie #144, 2021



Guitar making can be many things. To some it is a craft; to some it is a livelihood. And it’s also being used as a compelling teaching tool around the country. We are part of a project called STEM Guitar that is funded by the National Science Foundation, which provides faculty professional development to high-school and community-college faculty and students around the country, so they can, in turn, use guitar making to teach technical subjects. In educational lingo, these are STEM subjects — Science, Technology, Engineering, and Math.

We all know how important it is for students to learn at least the basics of STEM subjects. As luthiers, many of us routinely work with structural dynamics, acoustics, material properties, geometry, and computer-controlled machines. Modern guitar factories wouldn’t work without heavy investments of technology or without trained people. In 2009, industrial arts courses represented just 0.02% of credits taken nationally by high school students (U.S. Department of Education, 2009). However, when an updated report was released in 2013, industrial arts courses were not even included in the NCES reporting; such courses were replaced by engineering and design and manufacturing and technology courses were listed, which represent 0.7% and 0.6% of credits earned by high school students, respectively (U.S. Department of Education, 2013). The guitar program offers an engaging way of exposing students to industrial arts skills through STEM curriculum.

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Calculating Guitar Side Height

Calculating Guitar Side Height

by Mike Doolin

Originally published in American Lutherie #75, 2003 and Big Red Book of American Lutherie Volume Seven, 2015



Back in American Lutherie #58 (Big Red Book of American Lutherie Volume Five), Jon Sevy published the article “Calculating Arc Parameters” which described how to calculate the radius, length, or depth of a curve. I’ve used these formulae extensively ever since for radiusing fretboards, making dished workboards, calculating neck angles, and even nonlutherie shop tasks. Recently it occurred to me that one could use them to calculate the height of a guitar’s side at any point. If the guitar has a spherically domed back, the back falls off from its highest point in an arc in every direction, as in the photo.

This “high point” is effectively the North Pole of the sphere from which the back arch is taken. If we assume a top whose perimeter is all in the same plane, as in Fig. 1, that plane intersects a line of latitude on that sphere. The high point is therefore the point on the back which is farthest from the plane of the top perimeter. All measurements of side height are then distances between that plane and the surface of the sphere of the back arch. I adapted Jon’s formula to calculate the falloff from the high point on the back to any point on the side:

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