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Technical Information
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 formulae, data tables, technical discussions, research and links to other technical resources for stringed instrument designers.
Last updated: Saturday, November 03, 2007
Formulae and Data
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.
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 a Javascript calculator for string tension) are included here.
Calculating Downforce on the Bridge
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.
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.
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.
Plywood: Some Observations and a Report on the Use of Laminated Wood in Lutherie
Laminated wood is not used in the best of instruments but there may be situations where it is not only acceptable but even superior to solid wood.