Posted on October 9, 2025October 9, 2025 by Dale Phillips 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: Become A Member to Continue Reading This Article This article is part of the Articles Online featured on our website for Guild members. To view this and other web articles, join the Guild of American Luthiers. For details, visit the membership page. MEMBERS: login for access or contact us to setup your account.
Posted on June 21, 2025September 15, 2025 by Dale Phillips The Helmholtz Resonance The Helmholtz Resonance A Brief and Not-Too-Technical Introduction to the History and Theory of the Lowest Sound-Producing Mode, and Some Practical Considerations for Instrument Designers by R.M. Mottola Originally published in American Lutherie #82, 2005 and Big Red Book of American Lutherie Volume Seven, 2015 Research in physics and acoustics of stringed instruments shows us the mechanism by which sound is produced by those instruments. The plates of the instruments and the air inside vibrate in various patterns, each pattern producing sound in a range around a certain frequency. Each of these patterns can be considered to be a resonator, each with its own characteristics. Some of these resonators exist as modes of vibration of different areas of the plates of an instrument, and some are modes of vibration of the air inside the instrument. One of the air resonators is composed of the mass of air inside the instrument and the mass of air within and around the soundhole. The natural frequency of this resonator is near the lowest note that an instrument can make. It is generally labeled the A0 resonance, the letter A standing for the word “air” and the numeral 0 indicating that this is the first in a series of air resonances. This resonance is also referred to as the so-called Helmholtz resonance. Understanding how this resonance works in stringed instruments is not difficult, particularly given a historical perspective. Complete understanding involves some math, but a practical understanding can be had without it. Therefore, I am putting off presenting the formulae in the main article and have included them in a sidebar. Become A Member to Continue Reading This Article This article is part of the Articles Online featured on our website for Guild members. To view this and other web articles, join the Guild of American Luthiers. For details, visit the membership page. MEMBERS: login for access or contact us to setup your account.
Posted on June 21, 2025September 15, 2025 by Dale Phillips The Helmholtz Formula The Helmholtz Formula by R.M. Mottola Originally published in American Lutherie #82, 2005 and Big Red Book of American Lutherie Volume Seven, 2015 The resonant frequency of a mass spring resonator can be determined by the following formula: Become A Member to Continue Reading This Article This article is part of the Articles Online featured on our website for Guild members. To view this and other web articles, join the Guild of American Luthiers. For details, visit the membership page. MEMBERS: login for access or contact us to setup your account.
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.
