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: March 06, 2024

## Tools, Formulae and Data

Acoustic Guitar Design Tool

"G" Thang is a web application that can make the job of designing guitars and similar instruments fast and easy.

Calculating Fret Positions

How to figure out the distance from the nut to each fret, given the scale length of the instrument. There is also a Javascript calculator here for those that don't want to do the math.

Table of Pitch Frequencies of Musical Notes

A ten octave table of musical notes and their frequencies, to three decimal places.

Measuring the Scale Length of a Stringed Instrument

How to measure the scale length of an instrument. It is not necessarily as simple as measuring the vibrating length of the open strings.

Pitch, String Tension, String Length, and String Weight

The tension of a string is a function of its mass (or weight) per unit of length, the vibrating length of the string, and the pitch of the note produced when the string vibrates. The formula for determining string tension and other string tension related information and tools (including Javascript calculators) are included here.

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.

Calculating Heel Displacement for a Neck Reset

Resetting the neck of a guitar requires removing some material from the heel to effect a new neck angle, thus lowering the action. The amount of material removed is always small, even for big changes to the action. The formula for determining how much material to remove from the heel for the desired action is presented here. There is also a Javascript calculator for those that don't want to do the math.

Bass String Length Data

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.

Calculating the Sagitta of an Arc

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.

Deriving Archtop Plate Contours (.pdf)

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 Method for Calculating the Area of a Plate

A simple paper and pencil method for calculating the area of an arbitrary plate (stringed musical instrument top or bottom) is presented.

Golden Age Cremonese Mean (GACM) Arching Profiles

GACM arching profiles are curves that are generated by averaging arching profiles from classic golden age instruments. As such they come as close as is possible to capturing the essence of these classic curves, and in a manner that can be expressed in a relatively simple formula. This page contains a Javascript calculator which generates these curves as a series of points with regular x or y intervals.

Calculating Curtate Cycloid Points

Curtate cycloid curves are used by some violin makers and guitarmakers for the arching profiles of carved plates. This page contains a Javascript calculator which generates these curves as a series of points with regular x or y intervals.

Converting Spreadsheet Data to DXF or SVG Polylines

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.

Woodworkers' Popup Units Conversion Tool

Documentation for the units conversion tool that appears in the right column of each page on this site.

Geometric Relationship Between Guitar Fretboard and Top

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.

Tables of Typical Guitar Action Values

Here are tables that contain typical string action values for guitars and bass guitars, for use in setting up your instruments.

Fretted Instrument Bridge Saddle Compensation Calculator

An online calculator that will estimate bridge saddle compensation for fretted instruments.

An online calculator that will calculate how much the saddle string contact point will have to be moved to compensate for an intonation error at the 12th fret.

Rosette Circle Calculator

An online calculator that will calculate which pivot pin hole to use when cutting rosette channels using a Jasper circle guide router baseplate.

Download-able gauges that can be used to measure the radius of cuvature of the fingerboard playing surface.

## General Articles on Technical Topics

Also see the Lutherie Myth/Science section, which contains many other general technical articles on lutherie topics.

Audio Spectroscopy in the Analysis of Stringed Instruments and Their Components

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.

Tendinitis Among Bass Guitar Players: An Instrument Builder's View

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.

Was the Rile of 18 Good Enough?

An analysis of the old-fashioned way frets were located on the fretboard, compared to the way they are located now. Turns out the old way was not so bad.

## Book Reviews

Book Review: Music, Cognition, and Computerized Sound - An Introduction to Psychoacoustics

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.

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