Posted on October 10, 2025October 10, 2025 by Dale Phillips Derivation of Formula for High Point of Back Derivation of Formula for High Point of Back by Jon Sevy Originally published in American Lutherie #75, 2003 and Big Red Book of American Lutherie Volume Seven, 2015 Quantities: S = height of guitar sides at neck block B = height of guitar sides at end block E = B - S (difference in height at shoulders and butt) L = length of guitar body A = length of body measured at angle (see diagram) D = deflection in arched back (see diagram) R = radius of back arch 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 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 February 28, 2025April 24, 2025 by Dale Phillips Fall Collection 2024 Articles Online Fall Collection 2024 GAL Members – Login first before clicking on article titles to read the full articles. Not a member? You can join or renew here. Radiation from Lower Guitar Modes by Graham Caldersmith (1985) Caldersmith discusses the efficiency and pattern of sound radiation in the classic guitar produced by the four lower resonance modes, which he calls monopole, cross dipole, long dipole, and tripole. Inside Pacific Rim Tonewoods by Steve McMinn (1993) McMinn’s lutherie wood business has turned out to be a pretty big deal. Here we gain perspective by seeing it at the very beginning. The Great White Sitka by Jeffrey R. Elliott (1993) Holy Moby Spruce! How does one hack a log that’s eleven feet wide into 4000 guitar tops? Very carefully! By the way, this is a log that Steve McMinn rescued from the pulp mill. Meet the Maker: Bernard Millant by Jonathon Peterson (2006) Millant is a violin maker, a bow maker, an appraiser, an author, and a man of high repute within the violin world. The depth of training behind many old-school fiddle people will astonish most guitar makers, and it makes for entrancing reading. Meet the Maker: Dmitry Zhevlakov by Federico Sheppard (2007) This is not only the story of a Russian luthier who also makes beautiful rosettes for other builders, but is another example of how the Internet has changed the world — in this case for better. Aluminum Sonatas: A Brief History of Aluminum Stringed Instruments in the Last 120 Years by James Condino (2007) Every luthier knows how fickle and finicky the market is, so it’s no wonder that musical instruments made of aluminum didn’t catch on. Examined here are a violin, a mandolin, and a pair of bass viols. Fun stuff! Mechanical Compliance for Soundboard Optimization by David Hurd (2007) Hurd believes that the fastest way to great instruments is science, and it’s hard to argue with such a rational man. His jigs measure the deflection of top plates while under tension, and once he carves the top and braces to the numbers he wants, he’s done. This could be math heavy, but he offers an Internet spread sheet to ease the pain. Construction of the Colombian Tiple by Anamaria Paredes Garcia and R.M. Mottola (2007) Cross a 12-string flattop with a classical guitar and you get the Colombian tiple. The tiple has four courses of three steel strings, but on the inside, it’s a classical. Follow Alberto Paredes as he builds the instrument in this photo tour. See GAL Plan #51. Meet the Maker: Mervyn Davis by Rodney Stedall (2007) Davis’ South African upbringing inspires a wonderful decorative sense in his instruments. He’s built a ton of different stuff but may end up best known for his wildly unique modular guitars called Smooth Talkers. Cricket: A Reclaimed Salvage Recovery by James Condino (2007) Condino’s mandolin is made from recycled materials, mostly Douglas fir and katalox. It is unique and beautiful, and the story behind it is pretty cool, too. Grading on the Curves: Fitting Bars and Bridges on Archtop Guitars by Steve Andersen (2007) This is a very detailed look at how a notable builder of archtop guitars fits tone bars and bridges to his instruments. The Venezuelan Cuatro by Aquiles Torres (2008) Traditionally, this instrument is a small 4-string guitar with 14 frets clear, no frets over the body, a flush fretboard, and a large veneer tap plate. Note that the cuatro built for the article has 17 frets clear of the body. See GAL Plan #58. The MacRostie Mandolin Deflection Jig by Don MacRostie (2008) MacRostie’s clever jig measures the top deflection of a carved mandolin under string load at any stage of its construction. It is a valuable tool within the reach of any luthier. The “Corker” Guitar: A Sideport Experiment by Alan Carruth (2008) Carruth built a classical guitar with many small ports drilled in the side. By plugging the ports in various combinations he investigated the usefulness and physics behind them. Though this guitar did not make a believer out of him, he admits that his results are somewhat inconclusive. Electric Guitar Setup by Erick Coleman and Elliot John-Conry (2009) Two disciples of Dan Erlewine explain the latest techniques of setting up the electric guitar. All the details and specs are there, as well as a bit of philosophy. Dulcimer 101 by John Calkin (2009) Dulcimers are needlessly maligned and in need of advocates, and the author is a strong one. Tools and jiggery are kept to a minimum to make construction of this entry level instrument as accessible as possible. The Guitar as a Structure and Some Practical Information on Bracing by James Blilie (2009) A structural engineer and guitar builder sees the guitar as a thing buffeted by forces and stresses. Total Flame Out: Retopping a Harp Guitar by Harry Fleishman (2009) Harry replaces the failed soundboard on a complicated instrument with as little refinishing and other stress as possible. Strings: The (Often) Forgotten Accessory by Fan Tao (2010) D’Addario's resident scientist Fan Tao helps us understand string issues in relation to custom instruments and customized tuning. Practical Acoustics by Michael Cone (2010) Cone describes his advanced apparatus and method for acoustically testing classical guitars. Meet the Maker: James Ham by Roger Alan Skipper (2010) Ham operates from a shop in Victoria, B.C. where he repairs and restores violin family instruments and constructs world class double basses. It’s All About the Core or How to Estimate Compensation by Sjaak Elmendorp (2010) Mathematics and parameters used to address the problem of string compensation estimation. Articles Online Fall Collection 2024 Radiation from Lower Guitar Modes by Graham Caldersmith (1985) Caldersmith discusses the efficiency and pattern of sound radiation in the classic guitar produced by the four lower resonance modes, which he calls monopole, cross dipole, long dipole, and tripole. Inside Pacific Rim Tonewoods by Steve McMinn (1993) McMinn's lutherie wood business has turned out to be a pretty big deal. Here we gain perspective by seeing it at the very beginning. The Great White Sitka by Jeffrey R. Elliott (1993) Holy Moby Spruce! How does one hack a log that’s eleven feet wide into 4000 guitar tops? Very carefully! By the way, this is a log that Steve McMinn rescued from the pulp mill. Meet the Maker: Bernard Millant by Jonathon Peterson (2006) Millant is a violin maker, a bow maker, an appraiser, an author, and a man of high repute within the violin world. The depth of training behind many old-school fiddle people will astonish most guitar makers, and it makes for entrancing reading. Meet the Maker: Dmitry Zhevlakov by Federico Sheppard (2007) This is not only the story of a Russian luthier who also makes beautiful rosettes for other builders, but is another example of how the Internet has changed the world — in this case for better. Aluminum Sonatas: A Brief History of Aluminum Stringed Instruments in the Last 120 Years by James Condino (2007) Every luthier knows how fickle and finicky the market is, so it’s no wonder that musical instruments made of aluminum didn’t catch on. Examined here are a violin, a mandolin, and a pair of bass viols. Fun stuff! Mechanical Compliance for Soundboard Optimization by David Hurd (2007) Hurd believes that the fastest way to great instruments is science, and it’s hard to argue with such a rational man. His jigs measure the deflection of top plates while under tension, and once he carves the top and braces to the numbers he wants, he’s done. This could be math heavy, but he offers an Internet spread sheet to ease the pain. Construction of the Colombian Tiple by Anamaria Paredes Garcia and R.M. Mottola (2007) Cross a 12-string flattop with a classical guitar and you get the Colombian tiple. The tiple has four courses of three steel strings, but on the inside, it’s a classical. Follow Alberto Paredes as he builds the instrument in this photo tour. See GAL Plan #51. Meet the Maker: Mervyn Davis by Rodney Stedall (2007) Davis’ South African upbringing inspires a wonderful decorative sense in his instruments. He’s built a ton of different stuff but may end up best known for his wildly unique modular guitars called Smooth Talkers. Cricket: A Reclaimed Salvage Recovery by James Condino (2007) Condino’s mandolin is made from recycled materials, mostly Douglas fir and katalox. It is unique and beautiful, and the story behind it is pretty cool, too. Grading on the Curves: Fitting Bars and Bridges on Archtop Guitars by Steve Andersen (2007) This is a very detailed look at how a notable builder of archtop guitars fits tone bars and bridges to his instruments. The Venezuelan Cuatro by Aquiles Torres (2008) Traditionally, this instrument is a small 4-string guitar with 14 frets clear, no frets over the body, a flush fretboard, and a large veneer tap plate. Note that the cuatro built for the article has 17 frets clear of the body. See GAL Plan #58. The MacRostie Mandolin Deflection Jig by Don MacRostie (2008) MacRostie’s clever jig measures the top deflection of a carved mandolin under string load at any stage of its construction. It is a valuable tool within the reach of any luthier. The “Corker” Guitar: A Sideport Experiment by Alan Carruth (2008) Carruth built a classical guitar with many small ports drilled in the side. By plugging the ports in various combinations he investigated the usefulness and physics behind them. Though this guitar did not make a believer out of him, he admits that his results are somewhat inconclusive. Electric Guitar Setup by Erick Coleman and Elliot John-Conry (2009) Two disciples of Dan Erlewine explain the latest techniques of setting up the electric guitar. All the details and specs are there, as well as a bit of philosophy. Dulcimer 101 by John Calkin (2009) Dulcimers are needlessly maligned and in need of advocates, and the author is a strong one. Tools and jiggery are kept to a minimum to make construction of this entry level instrument as accessible as possible. The Guitar as a Structure and Some Practical Information on Bracing by James Blilie (2009) A structural engineer and guitar builder sees the guitar as a thing buffeted by forces and stresses. Total Flame Out: Retopping a Harp Guitar by Harry Fleishman (2009) Harry replaces the failed soundboard on a complicated instrument with as little refinishing and other stress as possible. Strings: The (Often) Forgotten Accessory by Fan Tao (2010) D'Addario's resident scientist Fan Tao helps us understand string issues in relation to custom instruments and customized tuning. Practical Acoustics by Michael Cone (2010) Cone describes his advanced apparatus and method for acoustically testing classical guitars. Meet the Maker: James Ham by Roger Alan Skipper (2010) Ham operates from a shop in Victoria, B.C. where he repairs and restores violin family instruments and constructs world class double basses. It’s All About the Core or How to Estimate Compensation by Sjaak Elmendorp (2010) Mathematics and parameters used to address the problem of string compensation estimation.
