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Taking the Guitar Beyond Equal Temperament

Taking the Guitar Beyond Equal Temperament

by Don Musser

Originally published in American Lutherie #30, 1991 and Big Red Book of American Lutherie Volume Three, 2004



If someone were to tell you that the simple C chord you just played on your perfectly intonated, handmade guitar was in fact significantly out of tune with itself, you might have a few doubts and perhaps some curiosity about just what he was talking about. If that person were Mark Rankin and he happened to have his little Martin set up with the just intonation, key-of-C fretboard, and you compared a C chord on that guitar to the C chord on your guitar, instead of doubts and curiosity you would have something else: the beginning of a revelation, a revelation not only about the guitar itself, but about the foundation of the music we play on it.

Back in 1987, David Ouellette, a Eugene, Oregon musician for whom I had built several guitars in the early 1980s called and wanted a new, unconventional instrument built. It was to be a special guitar with magnetic interchangeable fretboards having staggered frets set up for alternative tunings of the scale steps within the octave. The standard guitar fretboard we all play on is based on the equal-tempered scale where the octave is divided into twelve equal half-step intervals. This equal division of the octave is good in that it allows modulation from key to key without intolerable dissonance. Its drawback, though, is that the scale intervals are tempered, i.e., harmonically inaccurate and slightly out of tune with one another.

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The Anti-Murphy Concert

The Anti-Murphy Concert

by Alan Carruth

Originally published in American Lutherie #39, 1994



I recently had the privilege of attending a somewhat unusual concert by the Tokyo String Quartet, with some acoustics experiments thrown in. Or maybe it was a physics lecture with live accompaniment? And then there was the quiz show part... I guess I’d better explain.

The whole thing seems to have started with the coming together of a number of good ideas. One of the first was a plan by the Acoustical Society of America to produce an educational video on acoustics for grades K–12. This, of course, would require money to do, and the suggestion was made that a benefit concert be held. The members of the Tokyo String Quartet were contacted, and graciously consented. So far, so simple.

But remember, we’re dealing with acousticians here. Why not use the opportunity to do a little research? For one thing, while the acoustics of empty halls are reasonably well understood, nobody is really sure what happens when you put in the audience. Since the object of most concert promoters is to have as large an audience as possible, and nobody likes to listen to music in an acoustically lousy hall, it seemed like a good subject for an experiment. And how about that violin thing; you know old vs. new and all? And while we’re at it...

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The Acoustical Characteristics of the Concert Cimbalom

The Acoustical Characteristics of the Concert Cimbalom

by Janos Pap

Originally published in American Lutherie #61, 2000



We may be surprised that the sound of the concert cimbalom, or Hungarian hammered dulcimer, is occasionally similar to that of the piano. But we can be sure that it is not a piano, only related to it. The cimbalom produces a little more nasal sound, with a rougher timbre. The acoustical differences derive from the construction of the instrument and the manner of playing. I have devoted much time to making acoustical measurements on concert cimbaloms at the Acoustic Research Laboratory of the Hungarian Academy of Sciences in an anechoic chamber, and on a cimbalom model at the Institute of Musicology at Cologne University, hoping to satisfy my curiosity about the causes and effects of the cimbalom’s sound.

In instruments of the hammered dulcimer family, the form is determined by the mode of playing. The player strikes the strings with two hammers. The strings must be divided to give a large range of notes, and the struck parts of the strings must be raised for playability. The string-dividing determines the damping features, and thus the timbre and the decay. The raising of the strings results in high downward force on the bridge, which determines the sound indirectly, by the mode of energy transport and radiation.

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Conical Fretboard Radiusing Jig

Conical Fretboard Radiusing Jig

by Mike Nealon

Originally published in American Lutherie #66, 2001



How flat does the top surface of a fretboard need to be? A good working estimate would be to equate the tolerance to the gap between the top of the 2nd fret and the bottom of a string fretted at the 1st fret. The tolerance must be less than this gap or the 2nd fret will come into contact with the string. With the bottom of the open string about .01" above the top of the 1st fret and about 1/16" from the top of the 20th fret, the gap between the fretted string and the top of the second fret is about .005".

Making a hardwood board flat to within .005" is not too difficult using ordinary woodworking tools. The router table and movable plate described here will produce a machine-carved surface smooth enough to require only a minimal amount of sanding or leveling.

Photo 1 shows the jig fully assembled, with the router. Photo 2 shows the jig partially disasembled to show the function of the parts. The conical fretboard made with this jig has a 10" radius at the nut, flattening to a radius of 16" at the last fret. The fretboard blank is 3/8" × 2 1/2" × 21", and is flat on one side. The finished fretboards are 7/32" thick at the crown, and taper from 1 11/16" at the nut to 2 3/16" at the 12th fret (12.670" from the nut).

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Violin Free Plate Mode Tuning Reprised

Violin Free Plate Mode Tuning Reprised

by Edgar B. Singleton

Originally published in American Lutherie #103, 2010



In the early stages of violin building, the outline of the top and back plates are established, as is the contour of the outside surfaces. Wood is removed from the underside of each plate until the thickness of the plate is a millimeter or so thicker than expected to be in the final form. The f-holes are cut; the bass bar and purfling are installed. The time has then come to graduate the plates, i.e., regulate the thickness of the plates in an attempt to assure that the finished violin will have all of the desired characteristics. Some builders “graduate to thickness” by carefully copying thickness measurements from important old violins. They listen to the pitches of tap tones and have learned ways to adjust these pitches. They have also learned to bend and twist the plates in their hands with the goal of assessing elastic properties, using experience to relate these “felt” properties to the finished violin.1 These processes involve as much art as science and require many years of carefully evaluated experience. This experience is very difficult to articulate to the novice builder.

One process associated with graduating the plates that is related to tap tones is referred to as “free plate mode tuning.”2 3 4 5 The following exposition is intended to help instrument builders, familiar with the material contained in the above references, understand the basis of free plate mode tuning as it is based on some simple physics and to provide a technique to fine tune each mode (tap tone) individually. The purpose of this paper is to give the builder a new basis on which to visualize where, and to understand why, to remove wood if one wishes to tune the free plates of a violin.

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