Instrumentation and the art of violin making

A Brief History of the Violin

The roots of the violin go back to eighth- or ninth-century single-stringed Asian instruments that were played using a bow. This prototype spread into Europe, where the forerunner of the violin was made in the 13th century. This instrument, a vielle, was shaped like a flattened pear and played in the same manner as its modern counterpart. The 16th century brought the German klein geigen, or little fiddle. The three strings of this instrument were tuned a fifth apart, like those on today's violin.

The first true violin makers came from the towns of Brescia and Cremona in northern Italy. By the 17th century, Cremona had become the leading violin-making city in the world. The instruments of this period, unsurpassed in beauty, tone, and craftsmanship, were essentially the work of three families. The Cremona school was founded by Andrea Amati in about 1560; his grandson Nicolo became the family's most eminent craftsman. Nicolo, in turn, trained the famous Antonio Stradivari and Andrea Guarnieri, who designed the particular styles that bear their names.

The secret of Stradivari's best violins, made between 1700 and 1725, remains a matter of opinion; some believe it lies in the varnish he used for the finish, others credit the age of the wood. Ray Doerr and other violin makers have always contented that no two pieces of wood are exactly alike. Each has its own character, which a good craftsman will identify in order to get the most out of it. Most violin makers agree that the wood must be air-dried for at least 10--and preferably 50--years before construction begins.

How the Violin Works

The modern violin consists of about 70 parts fitted together so perfectly that the entire assembly vibrates as a unit. The basic parts are the upper face, called the soundboard; the side walls, or ribs; and the back. A narrow fingerboard, extending from the top of the soundboard, ends in a peg box and scroll. Four strings of cat gut are tied into the holes of the tail piece and stretched over the bridge, terminating at the pegs below the scroll. The soundboard and back are joined by a small dowel called the sound post. The only function of the sound post is to transmit vibrations from the soundboard to the back. The vibrations are generated by a resin-treated horsehair bow pulled by the player over the strings.

From the standpoint of sound production, the most sensitive parts of the violin are the back and the belly. Because of the sound post, the back receives vibrations directly from the section of the belly activated by the first and second strings. The belly, on the other hand, is more responsive to low tones because of the bass bar mounted beneath the third and fourth strings. The back is constructed of dense maple wood; spruce, which is less dense, is used for the belly. The fingerboard and scroll are made from the same piece of wood as the back.

The sound post consists of a spruce dowel whose grain runs perpendicular to the soundboard and back. It is situated such that vibrations travel from the soundboard to the back, and then return to the soundboard sufficiently out of phase to complement the sound without causing "gravel" (reverberations) or "wolf sounds" (wavering sounds occurring at certain frequencies). If the sound post is missing or out of place, the violin will play like a guitar, or at best produce wavering sounds.

When the bow is drawn over the strings, they vibrate in elliptical patterns. These vibrations cause the bridge to rock from side to side, which, in turn, causes two small pieces of wood on the bridge--called feet--to rock up and down. The foot next to the sound post transmits the high range of sounds; the other foot, located over the bass bar, transmits the low notes.

At the turn of the 19th century, the German physicist Ernst Chladni discovered that when a piece of wood shaped to the general form of a violin's soundboard or back is excited with a sharp tap, a definite series of nodes is formed. This can be demonstrated with iron filings or Christmas glitter. When the wood is tapped, the filings collect in the regions where there is no motion. Chladni classified these regions of deadness, or nodal curves, according to geometrical shape, noting for each the corresponding pitch.

Of particular interest is the fifth eigenfrequency. If the soundboard or back is held at this frequency and tapped, the soundboard will ring at a particular tone determined by the properties of the wood. Moreover, it was discovered early on that if the soundboard and back are tuned so that they vibrate between one and two semitones apart, the finished violin is likely to have a beautiful tone. If the tones are less than one or more than two semitones apart, the violin is likely to be "dead" or to ring with harmonics. Violin makers have also long been aware that the location of the fifth eigenmode and the tone of the violin can be altered by removing wood from certain areas of the board.

In her exhaustive analysis of the instruments of the violin family, Carleen Hutchins was able to quantify some of the characteristics of a good violin (see Scientific American, Oct. 1981, pp. 170-186). For instance, mode 5 must have a relatively large amplitude and its frequency must be within one tone of the back plate. If the top plate has the higher frequency, the overall tone of the violin will be brighter. She also found that smooth playing results when the frequency of the top plate is within 5 Hz of mode 2 of the back plate. Moreover, if the frequencies of mode 5 are the same for the top and back plates, they must be within 5 Hz of each other. It also appears that violins of exceptional quality result when mode 2 and mode 5 are an octave apart in each plate and at corresponding frequencies with high amplitudes in both plates. Finally, the frequency of mode 1 in the top plate should be placed an octave below that of mode 2, so that modes 1, 2, and 5 are in a harmonic series.

Old Tests

Five physical properties of wood are important to a violin's sound: elasticity along and across the grain; shear modulus; internal friction (the damping characteristics of the wood); density; and velocity of sound through the wood. Each of these tends to affect the way a violin reacts to the various frequencies of vibration imparted by the strings.

When one tests the top and back plates of a violin, the most important factor is the patterns taken by the various resonant modes. For tuning the back and belly, modes 1, 2, and 5 are the most important. The traditional method of checking these modes is to bend the plates in various directions and test their resistance with the fingertips. To assess the characteristics of mode 1, the violin maker holds the plates at each end and makes a twisting movement. The resistance of the plates indicates the characteristic pattern of the mode. The second mode is tested by holding the plates at one end with both hands, thumbs on top and fingers spread out over the bottom, and twisting the hands towards each other. To test the stiffness characteristics of mode 5, the violin maker holds the plates with one hand at each end and presses down at the center with the thumbs.

These are tried-and-true methods, but they are very subjective. It takes many years of experience to determine the stiffness necessary for a good-sounding violin with any degree of certainty. Moreover, using such traditional methods and hand tools, the violin maker requires between 500 and 600 hours to construct an instrument. Ray and Keith Doerr, by means of modern technology and engineering skills, claim they can transform a block of raw wood into a concert violin in just under 180 hours.

New Tests

The Doerr brothers have identified five tests that are crucial in tuning violin plates for vibrational compatibility. These combine physical tests of such factors as weight and thickness with tests of the modal characteristics. The first test is to weigh the plates at particular points in the wood-removal process. The second is to measure the specific thickness of a plate. These values indicate how far plate development has progressed. Careful attention to the relative weight and thickness patterns gives the violin maker an idea of the density of the wood and hence of the velocity of sound passing through it.

The third test is used to determine the actual modal patterns at various points in the wood-removal process. Using a method developed by Hutchins in her work with Harvard physicist Frederick Saunders, Keith Doerr mounts the plate on soft rubber above a speaker driven by a frequency oscillator. He then views the Chladni patterns at various frequencies. Next, deflections at various checkpoints are measured using a meter that Ray Doerr devised about 30 years ago. The deflections are created by a two-pound weight resting on a quill, which deflects the plate at particular locations. By manipulating the plate and the quill, modes 2 and 5 can be checked.

Finally, tests of the shear modulus are made using Keith Doerr's most recent device, the Torque-O-Meter. This instrument was designed to determine the resistance of the plates to twisting. Essentially, it applies a calibrated torque to the plates, thus duplicating the traditional practice of hand twisting.

To match the plates, Ray Doerr uses a calibrated cello string. Experience has shown that for best results the belly should be tuned so that its tone is between C#3 and D3, and the back should be between D3 and D#3. In a finished violin, the difference between the back and belly is between one and two semitones. In most cases, a good-sounding violin can be obtained if the belly is two semitones below the back before varnishing. The allowance is needed because varnishing causes the pitch of the belly to increase more than that of the back. It has also been determined that the effect of cutting the F holes into the top plate is just offset by the mounting of the bass bar.