Although it is possible to build world class stringed musical instruments without the direct application of math, science, or technology, it is difficult to design instruments without some engineering basics. It is not impossible, mind you – trial and error is a perfectly sound approach to a design effort, but it can be costly both in time and effort. This page contains technical resources for those who want to design instruments. Included are some useful tools, formulae, data tables, technical discussions, research and links to other technical resources for stringed instrument designers.
Last updated: July 17, 2014
A downloadable tool for Windows PCs that can make the job of designing guitar body outlines and fingerboards fast and easy.
A ten octave table of musical notes and their frequencies, to three decimal places.
How to measure the scale length of an instrument. It is not necessarily as simple as measuring the vibrating length of the open strings.
The tension of the strings exerts a down force on the bridge and top of an archtop instrument. The force is a function of the string tension and the angle at which the strings bend over the bridge. The formula for calculating down force is included here.
The lengths of the parts of bass strings are important to bass builders, especially those that build archtop bass guitars and electric upright basses. Tables of length data are provided for both bass guitar and double bass strings.
The construction of so-called flattop guitars and similar instruments involves the use of various fixtures that feature long radius arcs. It is simple to approximate these arcs using bent splines but to do so one needs to know how far to bend the spline for a given radius arc. The key to this is calculating the deflection or displacement of the highest point of the arc from the midpoint of the chord that connects its end points. This quantity is called the sagitta or sag.
The description of the surface of the top or back of an archtop instrument (archtop guitar, violin, etc.) is quite complex, but experienced builders generally just wing it when carving these, maybe checking progress with some simple gages. But first time builders and designers typically have a difficult time visualizing the transition from a rectangular blank to a fully carved plate. This article, originally published in American Lutherie #69 has step-by-step instructions for deriving the contours of a plate from the outline and a few parameters.
A simple paper and pencil method for calculating the area of an arbitrary plate (stringed musical instrument top or bottom) is presented.
Guitarmakers and violin makers often use spreadsheets or other math software to generate 2D curves for body outlines and arching profiles. The resulting arrays of coordinates can be converted directly into an open polyline in a DXF or SVG file using this tool, then the curve can be imported into CAD or other drawing software.
Documentation for the units conversion tool that appears in the right column of each page on this site.
American Lutherie #111 featured a comprehensive article on calculating the geometric relationship between a guitar's fretboard and its top, for all kinds of guitars. There was a lot of math. Here is a calculator that will do all that math for you.
Here are tables that contain typical string action values for guitars and bass guitars, for use in setting up your instruments.
An online calculator that will estimate bridge saddle compensation for fretted instruments.
Also see the Lutherie Myth/Science section, which contains many other general technical articles on lutherie topics.
Spectrographic analysis in lutherie is described. If you understand the harmonic nature of musical sound then you have everything you need to begin using audio spectroscopy in your lutherie investigations. A list of readily and inexpensively available components is provided, and three examples of the use of spectroscopy are presented.
Bass guru Ed Friedland wrote a great article on tendinitis in the January 2003 issue of Bass Player magazine. I started to write a letter to the editor with some more info on the subject, but the letter got out of hand and turned into this article. There is some info here for anyone suffering from tendinitis of the fretting hand, and for those who would build instruments for those with short arms, small hands, and thin wrists.
A positive review of an introductory text on psychoacoustics, a subject which should be of interest to anyone seeking answers to why instruments sound the way they do. This article originally appeared in American Lutherie.