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Parametric Models of Guitar Cutaways

Parametric Models of Guitar Cutaways

by R.M. Mottola

Originally published in American Lutherie #99, 2009

See also,
A Method for the Design of the Guitar Body Outline by R.M. Mottola
A Method For the Design Of the Guitar Body Outline Part 3: Compound Radius Curves by R.M. Mottola



In the article entitled “A Method for the Design of the Guitar Body Outline” in AL#97, I introduced the concept of parametric models for the design of the guitar body outline. That article addressed symmetrical body outlines only. In this article I want to consider parametric models for the body cutaway. Taken together the two articles demonstrate a complete method for the design of typical guitar body outlines.

Although it was possible to devise a simple parametric model for the design of the symmetrical guitar body outline that was adequate for most of the “standard” guitar body outline types, things are a bit more complicated where the cutaway is concerned. The basic problem is that, except in the most basic designations, cutaway styles have not yet settled out into a small number of distinct types. Rather than pursue a model that would accommodate all existing cutaway designs, I chose instead to derive basic models for the two primary cutaway types, leaving enough configurability to insure that most existing cutaway outlines could at least be approximated.

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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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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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Geometric Design of the Stradivari Model G Violin, Part One: Mold and Template

Geometric Design of the Stradivari Model G Violin, Part One: Mold and Template

by Robert J. Spear

Originally published in American Lutherie #93, 2008

see also,
Geometric Design of the Stradivari Model G Violin, Part Two: f-holes by Robert J. Spear
Geometric Design of the Stradivari Model G Violin, Part Three: The Scroll by Robert J. Spear



I have little doubt that artists, artisans, and architects of the Renaissance and Baroque used some system of guidance for their drawings that was based on the knowledge of geometry and the use of straightedge and divider. I began my drawing adventure almost five years ago by following the guidelines for the geometric design of the Model G in Sacconi’s book and soon discovered errors. Even so, I was convinced that it would be worthwhile to use a classical Cremonese approach based on geometry because I wanted to see if I could integrate it with Hutchins and Schelleng’s scaling theories used for the New Violin Family. While the acoustical aspects of the exercise are not germane here, I worked to realize a design system that would essentially produce a second generation of octet instruments close to a classical Cremonese violin in the style of the Model G Stradivari. My goal was to impart a greater uniformity to the octet family’s models, but to keep this article within bounds I have confined my remarks to the violin.

There are those who question whether geometric design really played an important role in violin design and suggest that the model outline could be designed freehand. Others allow that some sort of geometrical or proportion scheme was used, but that it was not based on the golden section. A few ask why one can’t just get a good photo of a good model and enlarge or reduce it at the local copy center. You can (and I did at first), but because strange things start to happen in the larger and smaller instruments during the scaling process, straight scaling does not hold up. Still others, including Sacconi, stress that the eye was the final arbiter of any design, no matter how it was derived. I will attempt to address all of these points in this series of articles.

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Geometric Design of the Stradivari Model G Violin, Part Two: f-Holes

Geometric Design of the Stradivari Model G Violin, Part Two: f-Holes

with Robert J. Spear

Originally published in American Lutherie #94, 2008

see also,
Geometric Design of the Stradivari Model G Violin, Part One: Mold and Template by Robert J. Spear
Geometric Design of the Stradivari Model G Violin, Part Three: The Scroll by Robert J. Spear



The Cremonese design for the f-holes of a violin, at first glance, would appear to be based on the same design philosophy as the body and to make extensive use of the golden section. A. Thomas King, in his article “The Cremonese System for Positioning the f-Holes” in The Strad, shows rather convincingly that golden-section divisions based on the distance between the pins on the body was employed to fix the location of the f-hole eyes, which further reinforces this idea. However, when it comes to f-holes, I would like to suggest that there are a couple of additional jokers in the deck. First, the late Cremonese f-hole is derived from an earlier system of design, and some of the important parts of the predecessor system remain in use; second, an entirely different modulus is used for the f-holes than for the body; and, third, little is based on the golden section.

The Forma G violin, upon which my model is based, is not quite the longest violin Stradivari ever made, but it is the widest. The most notable increase in width is in the center bout, which has another direct impact on the design of the f-hole and its placement. King notes that there is a general method for most Cremonese violins and a specialized adaptation for Stradivari violins. King explained the rather unintuitive step of taking the golden section of the distance between the locating pins in the top as the modulus for positioning the f-holes. I have used his approach here because it has many good points of correlation, and because I found an additional correlation that has convinced me even further that his hypothesis is correct.

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This article is part of our premium web content offered to Guild members. To view this and other web articles, join the Guild of American Luthiers. Members also receive 4 annual issues of American Lutherie and get discounts on products. For details, visit the membership page.

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