2024
AL#151 p.58
Mark French
▪ Its amazing what you can do with a smart phone these days. Think you would need an anvil, a block-and-tackle, and a bathrom scale to measure the breaking strength of a guitar string? Nope. Theres an app for that. Mentions Fine Chromatic Tuner.
2023
AL#150 p.14
Sjaak Elmendorp
▪ When you tighten the strings on an archtop guitar, the neck lifts forward and the action height increases. At the same time, the bridge pushes the top down and the action height decreases. Its a win-win! So you can just feel lucky about it and proceed naively along your life path, or you can do what Elmendorp did: get a bucket of water, a piece of wire, and a dial indicator; collect some data; then crunch the numbers.
2023
AL#149 p.50
Mark French Eddy Efendy
▪ Putting a tube in the port of a loudspeaker box changes the lower resonances. Makers of classical guitars have known about that for a century and a half. They call that tube a tornavoz. French and Efendy give us the math on how it works.
2022
AL#146 p.44
Mark French Alyssa Fernandez
▪ How stiff is that neck blank? You could cut all your blanks to the same dimensions and then set up a rig with a hanging weight to measure deflection and such. But hey, got a smart phone? It can listen while you tap on a bunch of neck blanks, and then tell you how stiff each one is.
2021
AL#144 p.56
Debbie French Mark French
▪ There is a national movement to teach teachers how to teach STEM subjects (science, technology, engineering, and math) to high-school students; you have them make guitars. Turns out people think it’s fun to make guitars. Who knew?
2019
AL#136 p.69
James Blilie
▪ How much clamping force do different types of clamps exert? Blilie shows us how to calculate the force for some kinds of clamps, and comments about how much force is enough.
2019
AL#137 p.58
R.M. Mottola
▪ Mottola gives short, not-too-technical summaries of two articles recently published on-line by Savart Journal. The first is an update of frequent author Mark French’s efforts to define stringed instrument body outlines by use of math equations. The second looks at what can be learned about lutherie wood by reading ancient Chinese texts.
2018
AL#135 p.67
R.M. Mottola
▪ Info on slotting a fretboard to have 24 frets to the octave.
2019
AL#136 p.42
Massimo Maddaloni Lizabeth-Jane Hella Giacomo Parimbelli
▪ From the time that the violin was invented, Cremona was the world center for the highest quality string instrument making, until it gradually became known for lower-quality mass production of fiddles. After its dark age, Cremona has more recently seen a renaissance of its lutherie heritage. This article looks at an unusual guitar made by a Cremonese luthier in the 1930s and sees echoes of the old masters in its design. Mentions Stradivari, Panormo, Fibonacci spiral, Archimedean spiral, golden ratio.
2019
AL#136 p.48
R.M. Mottola
▪ What’s the scale length? Isn’t it just twice the distance from the nut to the 12th fret? Yeah, kinda, but there can be a lot of complicating factors when working on old instruments. Like maybe the nut position was compensated, or just cut wrong. Or maybe the 12th fret was a little off. The fret positions might have been calculated using the old rule of 18. Here’s how to find out what’s really going on.
2018
AL#134 p.69
Fan Tao
▪ How do I adjust string gauge to keep playing feel constant when changing scale length?
2018
AL#135 p.45
Juan-Oscar Azaret
▪ Tap on a guitar. Or listen to just the first fraction of a second as you pluck a note. Those tiny samples contain a wealth of information. Our brains already form an impression of the guitar’s sound, long before the first second has elapsed. Computers can reveal the math behind the music and help us understand and visualize what is happening. Good basic info about the FFT, that is, the Fast Fourier Transform, and how the information in a guitar tap can be viewed in the time domain or the frequency domain.
2018
AL#133 p.70
Andy Powers
▪ Thoughts about short-scale guitars.
2018
AL#134 p.52
Chris Herrod
▪ You’ll often read article in American Lutherie where scientists explain the sound of guitars in terms of resonant frequencies and onset transients. On the other hand, longtime wood merchant Chris Herrod is here to give the metaphoric pendulum a big old shove back to the right-brain tradition of using evocative adjectives like “dry,” “creamy,” and “poignant.” He also discusses psychoacoustics research and how confident we should be about our “ears.”
2018
AL#134 p.60
Mark French David Zachman
▪ There are times when a luthier may want to draw a good long-radius arch. If jury-rigging a 25-foot compass seems like a hassle, you may have been tempted to just bend a straight stick a little and call it good. Turns out that’s a better solution than you may have thought. This article evaluates several techniques and gives the math that undergirds them.
2018
AL#133 p.48
James Blilie
▪ We all have ideas about the stiffness of brace wood, probably based on a combination of intuition, hearsay, and informal flexing. Blilie aims to accumulate more quantitave data. Here he reports on his latest tests. He also describes his methodology and the reasoning behind it. This is Blilie’s third article on this topic.
2018
AL#133 p.54
Edmond Rampen
▪ OK, we are probably some distance yet from pushing a button and 3D-printing a functioning guitar. And if you think that something about that sounds kinda crepy and disappointing, you just might be a luthier. But what we are talking about in this article is entirely different: Using surprisingly inexpensive printers to make templates, tools, and parts for guitars. The future is here, people. Get into this while you wait for your hover car.
2017
AL#131 p.53
James Blilie
▪ Unless you are really messing it up, the glue line is stronger than the wood. And here’s more numbers to prove it. Blilie uses real lab gear and standard statistical analysis to drive the lesson home.
2017
AL#132 p.62
Mark French
▪ We think the old boys found the 1st fret position by dividing the string length by 18. Then they divided that by 18 to get the 2nd fret. Sounds like a job for that nerdy apprentice kid. But 18 is just an approximation of the “right” number; that is, the 12th fret won’t be right in the middle of the string. If you want to do it by hand, here’s some thoughts and numbers about what would be a better approximation, and how much better it would be.
2017
AL#130 p.52
R.M. Mottola
▪ Did ancient folk know what they were doing? Or did they just have the bad luck to be born too soon? This article can’t settle that question definitively, but it does give some new and helpful information for luthiers. Graphs compare the pitch accuracy of fret scales calculated by the 12th-root-of-2 method vs the Rule-of-18 method. Appropriate string length compensation is considered.
2009
AL#100 p.48 read this article
Mark French
▪ Guitar strings need to be the “wrong” length in order to sound “right.” The gloriously simple math of Pythagoras doesn’t accomplish this. French uses lasers and spreadsheets, more numbers, and Greek letters to attempt to get closer.
2009
AL#99 p.52
Ryan Schultz
▪ There’s just enough math here to make our brains cloud over, so most folks should get along fine. It’s still not as easy to build as a spoke-built dish, but if you’re cheap and must have a one-piece dish it should work just fine. With 4 photos, a depth chart, and one drawing.
2009
AL#99 p.60 read this article
R.M. Mottola
▪ Do you know why certain parts of our lives can’t be altered? Because smarter people than us are in control. If you are artistic enough, you can lay out a nice guitar shape with just a pencil and paper. If you are smart enough (not that being smart negates the possibility of artistic talent) you can use geometric forms and even a computer to shape a graceful guitar. If you are neither artistic nor smart you’ll have to copy something that’s already been done. This story is for smart people. With 12 drawings.
2009
AL#99 p.66 read this article
Bill Greenwood
▪ This book is aimed at “a niche audience of mathematically literate students who are relatively new to the details of guitar structure. . . .” The reviewer decides it is a successful effort.
2009
AL#98 p.57 read this article
Ahanali Jahandideh Mitra Jahandideh Hadi Abbaszadeh Samad Jahandideh
▪ The Kamanche is a Persian bowed instrument with a skin head. The authors use a ratio of the value of phi to define its size, a trick violin makers have used for a long time. With one photo and 4 drawings.
2008
AL#96 p.26
David Cohen
▪ There are reasons why you might wish to describe the arch of an instrument mathematically. You might also wish to create an arch template by using math. Here’s a way to go about it. This is not for the math challenged among us. With 4 photos and 9 charts/diagrams.
2008
AL#96 p.62
William Leirer
▪ Did you know that the Google search engine has a calculator? This piece is a math lover’s dream. There’s lot of formulae. The goal is to lay out a fret pattern for any scale length, then find the perfect intonation point for it. You’ll need a pretty good guitar tuner to take advantage of the process. All you math challenged luthiers out there, just say “Duh. . . .”
2008
AL#95 p.44 read this article
Robert-J. Spear
▪ Did the Cremonese fiddle makers use geometry to plot the design of their violins? Can geometry explain the size relationships of violin parts and details? Spear thinks so. This is the third and final installment printed in sequential issues of AL. With 3 photos and 9 diagrams/charts.
This article has been nominated as one of the Guild’s best articles published before 2010.
2008
AL#94 p.30 read this article
Robert-J. Spear
▪ The second installment of how geometry might have been used to design the Cremonese violin. Part One was in AL#93. With 10 graphs and a photo.
This article has been nominated as one of the Guild’s best articles published before 2010.
2008
AL#93 p.46 read this article
Robert-J. Spear
▪ The author’s goal is to demonstrate that the Cremonese fiddle makers used geometry based on the Golden Mean to design their instruments. This installment concerns the body outline. With 2 photos and 9 graphs/drawings.
This article has been nominated as one of the Guild’s best articles published before 2010.
2006
AL#88 p.52 read this article
Mark French
▪ The author discusses the curve fit, a mathematical method of describing a shape that a computer, and thus a CNC machine, can understand. Curve fits have other benefits, too, but computer illiteracy prevents them from being described here. Includes a plethora of charts and graphs.
2005
AL#82 p.38 BRB7 p.344
R.M. Mottola
▪ It’s not necessary to understand the physics of sound to be a great instrument maker, but it can’t hurt. Many of us would like to believe that we succeed using experience and strong intuition and don’t need science. Maybe an analytical mind just gets in the way, no? Or maybe the science guys are just smarter than the rest of us and we need an excuse not to stand in the same light that they do. Who knows? Anyhow, the Helmholtz resonance is the lowest vibratory mode of an instrument, though not necessarily the lowest note that instrument is capable of. All the rest of sound physics is built on top of the Helmholtz resonance, and Mottola devolves the science enough for the rest of us to understand. It’s fun but in the end it’s not clear that it really matters. For the few among us with operational math brains all the formulas are presented in a sidebar.
This article has been nominated as one of the Guild’s best articles published before 2010.
2005
AL#82 p.41 BRB7 p.348
R.M. Mottola
▪ Here’s the numbers and how to use them.
2005
AL#81 p.36 BRB7 p.296
Jon Sevy
▪ All those cool pre-war Martins not withstanding, many luthiers believe that domed guitar tops are the way to go. But they can complicate construction in unforeseen ways. Sevy offers a mathematical cure, a set of formulas for predicting neck pitch and saddle height. Probably not for the math challenged, but give it a look before you abandon this path. With 4 charts and 5 diagrams.
2005
AL#81 p.59 BRB7 p.528 read this article
R.M. Mottola
▪ The right side of the brain is creative and the left side is analytical. It’s nice when they can work together, but for most of us one side or the other is dominant. The reviewer (who is admittedly left-brained) would like even right-brained luthiers to read this book, though he admits that they may struggle. Intelligent people shouldn’t ignore any source of information that may improve their work. Those who become luthiers to escape from real work may not grasp this concept.
2003
AL#76p.65 BRB7 p.491
Alain Bieber
▪ A method for matching the curl when making 4-piece curly maple backs.
2003
AL#75 p.39 BRB7 p.96
Mike Doolin
▪ Doolin enlists the aid of Jon Sevy to work out the math used in determining the side height of an instrument with a spherically-domed back. Knowing the side height will allow you to profile the sides to fit the guitar design before they are bent. With a photograph and three drawings.
2003
AL#75 p.40 BRB7 p.98
Jon Sevy
▪
2003
AL#76 p.6
David Quinn
▪ Quinn offers a math correction to Mike Nealon’s compound radius jig found in AL#66.
2003
AL#76 p.6
William Nesse
▪ Nesse offers a math correction to Rodney Stedall’s dished workboard article in AL#74.
2002
AL#70 p.52 BRB6 p.347 read this article
Dave Raley
▪ There are a number of reasons you might wish to know the volume of an instrument. Raley uses a spreadsheet program and some careful measuring to determine this figure.
2002
AL#70 p.53 BRB6 p.349
R.M. Mottola
▪ The author has simplified a computer technique for use with graph paper and pencil, and maintains that the system is accurate to about .5%. If you know the area of a plate you can figure out the volume of the soundbox, as in Raley’s article on p.52.
2000
AL#63 p.63 BRB6 p.65 read this article
Alan Carruth Joe-D. Franklin
▪ Changing guitar dimensions while maintaining the same size air cavity.
1999
AL#58 p.42 BRB5 p.355
Jon Sevy
▪ If first-year college math pushed your left-brain functions to the limit (been there, done that) you may cringe at the sight of the simplest equation. If so, check out this article. Modern luthiers build arcs into many of their instruments, and if you don’t know how to create them to lay out your own jigs you’ll be forever at the mercy of tool suppliers. Worse yet, when someone asks what the radius of your back plate is you can shrug your shoulders and look like an idiot. Let Sevy solve your problem. You can do it!
1996
AL#47 p.34 BRB4 p.368
Greg Byers
▪ Finding perfect intonation through deep math and jiggling the string length at both ends. For some luthiers the quest for perfection knows no bounds. The rest of us are just jealous.
This article has been nominated as one of the Guild’s best articles published before 2010.