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Inharmonicity of Guitar Strings

Inharmonicity of Guitar Strings

by Mark French

Originally published in American Lutherie #100, 2009



Strings are uniquely well suited to make music because all their resonant frequencies are very close to being integer multiples of the fundamental frequency.1 The octave is the most consonant interval and the resonant frequencies of a vibrating string are separated from one another by octaves. The expression for the resonant frequencies of an ideal string is familiar to many luthiers.

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The Right CAD Curve

The Right CAD Curve

Bezier Curves, Not Splines, Are Truly Smooth Curves

by David Golber

Originally published in American Lutherie #72, 2002 and Big Red Book of American Lutherie Volume Six, 2013



Bezier curves, as opposed to splines, have been known since the 1970s. They are supported by AutoCAD and AutoCAD LT, but not by many other popular CAD packages. What are they, and why do we care?

It’s easiest to start with an example. Fig. 1 shows the outline of a harpsichord. Look at the curved side. The coordinates of the points are from Kielklaviere,1 which describes the curved side of the instrument by listing the coordinates of points along the side. The curve in Fig. 1 is the ordinary spline through those points. Fig. 2 shows that one of the points is erroneous enough that it clearly makes the curve bumpy.

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A Different Way of Defining Body Shapes

A Different Way of Defining Body Shapes

by Mark French

Originally published in American Lutherie #88, 2006



As I look through American Lutherie, I am struck by the advances in the tools some of us use to make our instruments. While there will always be the traditionalists who do most of their work by hand, more of us are using computer-controlled machines to make jigs or parts. Even the musical instrument lab here at Purdue (www.metalsound.org) has its own CNC router. Large manufacturers like Taylor Guitars use CNC equipment for the majority of their building operations.

An obvious advantage of all this cool stuff is that parts can be made much more precisely. However, the parts can only be as precise as the instructions that are driving the machines. Look through your favorite book on guitar making and find the section on laying out the body shape. Even the best books, like Making an Archtop Guitar by Benedetto and Guitarmaking: Tradition and Technology by Cumpiano and Natelson, offer only the most basic description of the shape. It’s pretty common for the instructions to start with something like “draw a straight line on a sheet of brown wrapping paper to use as a centerline.”

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Thoughts on Soundboard Vibration

Thoughts on Soundboard Vibration

by Paul Wyszkowski

Originally published as Guild of American Luthiers Data Sheet #200, 1981



The classic guitar, like the harp but unlike the violin, the mandolin or the zither, has its strings attached directly to the soundboard. In the case of a violin, it is pretty clear that the bridge communicates primarily vibrations which are perpendicular to the surface of the soundboard. But it is not so obvious how the strings of a guitar transmit their vibration to the soundboard. However, a few minutes’ thought and a simple experiment can settle that question.

Back in 1954, J.K. Sutcliffe stated in an article in Guitar News that the fundamental action linking the string to the soundboard is the rocking of the bridge in response to the longitudinal (along the length) vibrations of the string. That is, the front and back edges of the bridge rise and fall as the string becomes tighter and looser (see Fig. 1). Later, Michael Kasha used this idea in his theory of guitar design. As a consequence, this view was accepted by many luthiers as correct.

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The Power of Circles

The Power of Circles

by Michael Darnton

from his 2004 GAL Convention lecture

Originally published in American Lutherie #87, 2006



Violins and guitars that are strong visually have a solid underlying structure that you might not see if you’re just casually looking. But it’s there. Designers of the past constructed a shape with straightedge and compass on concrete geometric forms.

There are many equally valid ways to look at designs, but I hope everyone will at least consider the concept that I’m going to talk about today: that strong instrument design comes most easily from the consistent use of very simple geometric shapes. This doesn’t eliminate creativity and new forms. Rather, it can strengthen the impact of any design, traditional or modern, by drawing on a common language to promote immediate visual understanding, usually on a subconscious, but effective, level.

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