Posted on June 6, 2024May 14, 2025 by Dale Phillips Another Method for Calculating the Area of a Plate Another Method for Calculating the Area of a Plate by R.M. Mottola Originally published in American Lutherie #70, 2002 and Big Red Book of American Lutherie Volume Six, 2013 There are a number of reasons to calculate the area of the plate of a stringed instrument. The area of a flat plate can be used to determine the volume of the instrument by simply multiplying the area by the depth. This value is useful in the design of electric guitars and basses to determine the weight of the body of the instrument before it is built. This info can aid in the design of an instrument that balances well when hanging from a strap or sitting on the leg. In the design of acoustic instruments, the volume can be used to calculate the nominal Helmholtz resonance of the soundbox, which may be useful in the tuning of the resonance characteristics of the instrument. The technique specified here will work for any arbitrary shape and is both simple and relatively quick. It is the essential algorithm of a CAD script I use, and is based on a computer graphics rasterization technique. Modified and simplified for use with pencil and paper, it yields a good enough approximation of the area of a plate for the purposes outlined above. Become A Member to Continue Reading This Article 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. If you are already a member, login for access or contact us to setup your account.
Posted on June 6, 2024May 14, 2025 by Dale Phillips Google Calculator and the Guitar’s Magic Number Google Calculator and the Guitar’s Magic Number by William Leirer Originally published in American Lutherie #96, 2008 Since the frequency of the octave note at fret 12 is two times the frequency of the open string, the fret positions can be determined by finding a number that can be multiplied by itself 12 times to get 2. That’s the guitar’s magic number: the 12th root of 2. In one form or another, it is a part of every calculation related to scales, fret placement, intonation, compensation, and much more. When Google perceives an entry in its search field to be math, it switches from search mode to calculator mode and displays the answer. Any calculator can solve a math problem, and there are plenty of online fret calculators. But with Google Calculator we can view the entire equation at once and see the effect of substituting one part at a time, helping us to understand the “why” behind the numbers. Become A Member to Continue Reading This Article 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. If you are already a member, login for access or contact us to setup your account.
Posted on March 6, 2024May 14, 2025 by Dale Phillips Using the Golden Section to Design a Kamanché Using the Golden Section to Design a Kamanché by Ahanali Jahandideh, Mitra Jahandideh, Hadi Abbaszadeh, and Samad Jahandideh Originally published in American Lutherie #98, 2009 The kamanché is a Persian bowed string instrument related to the violin. (See “Building the Kamanché” by Nasser Shirazi, AL#4, p. 27 and BRBAL1, p. 126, and GAL Instrument Plan #9. The kamanché has a long neck and a spheroid sound chamber made from gourd or wooden staves, which is usually covered on the playing side with skin from a lamb, goat, or fish. It is widely played in classical music of Iran, Azerbaijan, Uzbekistan, and Turkmenistan, with slight variations in structure. The Golden Section (also known as the Golden Mean, Ratio, or Proportion) is a ratio defined by the number phi (Φ=1.618033988...). It has been used in designing violins and other musical instruments, but for the first time we used it to design an Iranian instrument. Become A Member to Continue Reading This Article 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. If you are already a member, login for access or contact us to setup your account.
Posted on October 25, 2021May 14, 2025 by Dale Phillips 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. Become A Member to Continue Reading This Article 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. If you are already a member, login for access or contact us to setup your account.
Posted on October 25, 2021May 14, 2025 by Dale Phillips 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. Become A Member to Continue Reading This Article 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. If you are already a member, login for access or contact us to setup your account.
