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Using the Golden Section to Design a Kamanché

Using the Golden Section to Design a Kamanché

by Ahanali Jahandideh, Mitra Jahandideh, Hadi Abbaszadeh, and Samad Jahandideh

Originally published in American Lutherie #98, 2009



The kamanché is a Persian bowed string instrument related to the violin. (See “Building the Kamanché” by Nasser Shirazi, AL#4, p. 27 and BRBAL1, p. 126, and GAL Instrument Plan #9. The kamanché has a long neck and a spheroid sound chamber made from gourd or wooden staves, which is usually covered on the playing side with skin from a lamb, goat, or fish. It is widely played in classical music of Iran, Azerbaijan, Uzbekistan, and Turkmenistan, with slight variations in structure.

The Golden Section (also known as the Golden Mean, Ratio, or Proportion) is a ratio defined by the number phi (Φ=1.618033988...). It has been used in designing violins and other musical instruments, but for the first time we used it to design an Iranian instrument.

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Calculating Soundbox Volume

Calculating Soundbox Volume

by Dave Raley

Originally published in American Lutherie #70, 2002 and Big Red Book of American Lutherie Volume Six, 2013



Want to design a new guitar shape and maintain an equal volume of enclosed air by adjusting the height of the sides? Here’s how to calculate volumes. Accuracy is a function of how long you want to spend measuring and calculating.

Consider two bodies: Figs. 1a and 2a. The body in Fig. 1 is 18" on the X axis and 4" on the Z axis. Suppose that you wish to make the body in Fig. 2 have the same volume as the body in Fig. 1 while maintaining the same X axis. Fig. 3 defines the axes regardless of the way the figures are turned.

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Questions: Guitar Air Cavity

Questions: Guitar Air Cavity

by Art Davis, Alan Carruth, and Joe D. Franklin

Originally published in American Lutherie #63, 2000 and Big Red Book of American Lutherie Volume Six, 2013



Tom Blackshear of San Antonio, Texas asks:

Is there a formula for measuring the air cavity of a guitar box, then figuring out how to keep the same amount of air with slightly different box dimensions?


Art Davis of San Diego, California responds:

Use bird seed. It’s not totally accurate but it’s easy. Pour it in, pour it out, and measure it. Hold the guitar really well because ten or twenty pounds of bird seed is heavy. Also, as per W.D. Allen’s, “Basics of Air Resonances,” in The Big Red Book of American Lutherie Volume 1, changing the air volume doesn’t always do what you think it’s going to.

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Parametric Models of Guitar Cutaways

Parametric Models of Guitar Cutaways

by R.M. Mottola

Originally published in American Lutherie #99, 2009

See also,
A Method for the Design of the Guitar Body Outline by R.M. Mottola
A Method For the Design Of the Guitar Body Outline Part 3: Compound Radius Curves by R.M. Mottola



In the article entitled “A Method for the Design of the Guitar Body Outline” in AL#97, I introduced the concept of parametric models for the design of the guitar body outline. That article addressed symmetrical body outlines only. In this article I want to consider parametric models for the body cutaway. Taken together the two articles demonstrate a complete method for the design of typical guitar body outlines.

Although it was possible to devise a simple parametric model for the design of the symmetrical guitar body outline that was adequate for most of the “standard” guitar body outline types, things are a bit more complicated where the cutaway is concerned. The basic problem is that, except in the most basic designations, cutaway styles have not yet settled out into a small number of distinct types. Rather than pursue a model that would accommodate all existing cutaway designs, I chose instead to derive basic models for the two primary cutaway types, leaving enough configurability to insure that most existing cutaway outlines could at least be approximated.

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Inharmonicity of Guitar Strings

Inharmonicity of Guitar Strings

by Mark French

Originally published in American Lutherie #100, 2009



Strings are uniquely well suited to make music because all their resonant frequencies are very close to being integer multiples of the fundamental frequency.1 The octave is the most consonant interval and the resonant frequencies of a vibrating string are separated from one another by octaves. The expression for the resonant frequencies of an ideal string is familiar to many luthiers.

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