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Some Historical Background

The earliest known bowed instrument is the Ravanastron of India. It is very similar to the Erhu of China, or the Haegeum of Korea. It has two strings with tuning pegs, and a small round sound body with a membrane as its upper surface. The strings are made of silk.

Other old bowed string instruments are the Rebec, and the Viol, which was the immediate predecessor of the violin.

The violin, viola, cello, and double bass took the place of the instruments of the viol family. At one time, it was believed that they were also directly developed from the viol; except for the double bass, it is now thought that this is not the case.

Instead, it is believed that the mediaeval fiddle, generally referred to its French name, the vielle, was the direct ancestor of the violin family, and that the line of progress passed through the lira da braccio. Unlike the vielle, the lira da braccio often had a strong resemblance to the modern violin, although there were still some differences during most of the lifetime of that instrument; a later specimen, made by Andrea Amati after the violin was already in existence looked almost like a modern violin.

The lira da braccio, pictured at right, was a somewhat specialized instrument.

Its strings were (in one common tuning) tuned an octave below those of the violin, so, like the violin, and unlike the viol, it was tuned in fifths, rather than fourths. That statement, however, is something of an oversimplification, since a violin has four strings, and, most commonly, a lira da braccio has seven. However, those seven strings were in five courses.

A twelve-string guitar is played much the same way as a six-string guitar, as if it only had six strings. That is because it only has six courses; its strings are in six pairs, with the two strings in each pair spaced closely together, so that they would normally, and almost inevitably, be struck and fretted together.

Thus, from the viewpoint of the player, it is really the courses, rather than the strings, that are the basic unit of the instrument.

In the case of the lira da braccio, the five courses are nominally tuned in D, G, d, a, e', with the course tuned in D starting from a point off to the side of the pegboard for the other courses so that its strings do not pass over the fingerboard; it is used as a drone.

The seven strings are tuned to (D, d), (G, g), d, a, e'; thus, both the drone and the course corresponding to the lowest string on a tenor violin are augmented by including both one string at the nominal pitch of the course, and another string an octave higher.

The lira da braccio had an even more specialized relative, the lira da gamba. This instrument was sufficiently obscure that it was only recently rediscovered. A lira da gamba might have twelve or more strings. The bridge was curved, but in a shallow curve, so that when the instrument was played, three or more adjacent strings would usually be bowed at one time.

So that adjacent strings would form chords, this instrument was tuned in a zig-zag fashion; the lowest string would be followed by a string tuned a fifth higher, and then that string would be followed by a string tuned a fourth lower. Then the next string would be a fifth higher than that one, and the pattern would continue.

This arrangement does not quite lead to adjacent strings forming either major chords or minor chords, but the notes they produced were still harmonious, and the instrument was used for playing continuo.

The oldest surviving violins are those made by Andrea Amati of Cremona; at one time, violins made by Gasparo Bertolotti, usually known as Gasparo da Salo, in Brescia were thought to have been older, but recent historical research has overturned this belief.

Another person once mistakenly believed to be the earliest known violin maker was Gasparo Duiffoprugcar; it is now believed that while he made the bowed instruments which preceded the violin, he did not make any actual violins. His last name is a variant spelling of Tiefenbrucker; a different German surname, Tiefenbacher, found its way to Canada in a different variant spelling: Diefenbaker; so he does not belong to the same house as a former Canadian Prime Minister.

In Cremona, Andrea Amati was succeded by his son Gerolamo Amati, and then he in turn was succeded by his son Nicolò Amati. Each of them produced violins that were considered to be even better than the violins of their fathers.

It has been generally accepted that Antonio Stradivari was one of the apprentices of Nicolò Amati. However, I am inclined to accept the conjecture offered in the book Stradivari's Genius: Five Violins, One Cello and Three Centuries of Enduring Perfection by Tony Faber, and also echoed by the book Cremona Violins: A Physicist's Quest for the Secrets of Stradivari, by Kameshmar C. Wali, which is about the researches of William F. "Jack" Fry, that Stradivari only worked for Nicolò Amati in the capacity of a woodworker, formerly apprenticed to the woodworker Francesco Pescaroli, to produce decorated violins, and then he later became an apprentice of another violin maker, likely Francesco Ruggeri, based on similarities in their technique of carving the back and belly plates of the violin in order to tune them properly.

Francesco Ruggeri and Andrea Guarneri were undoubted apprentices of Nicolò Amati. Andrea Guarneri was succeeded by his sons Pietro Guarneri and Giussepe Guarneri; the latter had a son also named Giuseppe, famed as Guarnerius del Gesu. Although today a Guarnerius is recognized as a reasonable alternative to a Stradivarius, while Stradivari was successful and wealthy, Giuseppe Guarneri the younger struggled to make a success of his business.

Antonio Stradivari was succeeded by his sons Francesco Stradivari and Omobono Stradivari, who hired Carlo Bergonzi, already an established violin maker, to assist them.

Also, Lorenzo Guadagnini made violins in Stradivarius' workshop, and his son Giovanni Battista Guadagnini is often considered to be the third greatest maker of violins after Stradivarius and Guarnerius.

The old violins of Cremona are held in very high repute, particularly those of Antonio Stradivari; as they were considered the finest violins available at the time they were made as well, about a thousand were made, and a commonly quoted figure is that about 650 of them survive. Those of Guarnerius del Gesu, of Giovanni Guadagnini, and some of those by Carlo Bergonzi, and a select few other early luthiers, are also considered to be nearly as good, but there are far fewer of those instruments extant, so these violins, and other fine violins from this era of violin making, do not greatly reduce the scarcity of violins of the first rank from what it would be if no other violins had even approached the excellence of a Stradivarius - although the scarcity is such that we must be thankful for each fine violin that exists.

Fritz Kreisler is associated with a Bergonzi, and Vanessa-Mae with a Guadagnini.

One name that comes up is that of Domenico Montagnana; he was a luthier in Venice, rather than Cremona or Brescia; while the violins of Stradivarius are praised, among other things, for making it easier for a performer to obtain the best tone from them, those of Montagnana are notoriously difficult to play; yet, they are still highly valued because of the beauty of the tone that can be obtained from them by a sufficiently able performer. Yo-Yo Ma is a performer associated with one.

The earliest surviving Stradivarius was made in 1666, and already bears the stamp of his genius, but his earliest violins were not necessarily superior to those of Nicolò Amati. By 1683, this had changed, and his violins were already superior to any others, but they had not yet reached the peak of their quality, as displayed by the violins of his "golden period" from 1700 to about 1725.

While the violins of Stradivarius were recognized as the best violins available during his lifetime, as the years passed after his death, his reputation passed into obscurity. It was revived by the efforts of Luigi Tarisio in rescuing forgotten Stradivarius violins, and incidentally making a fortune through buying them cheap and selling them dear, and by a concert by Giovanni Battista Viotti in 1782 where he played a Stradivarius violin made in 1709.

Before 1782, it was widely considered that violins such as those made by Jacob Stainer represented the summit of the art of violin making; as Stainer died in 1683, he was a contemporary of the Cremonese violin makers, but he worked in the Tyrol, part of Germany.

At the time Stradivarius made violins, there were some differences in the basic design of a violin compared to the way that violins are made today.

The diagram above shows a Baroque violin on the left, and a modern one on the right. The differences between them are that the neck on a Baroque violin is not tilted back going up; instead, the fingerboard itself is shaped so as to be angled forwards going down at the front, rather than being almost flat and deriving its slope from the neck. As well, the modern neck is somewhat longer, and the modern fingerboard significantly longer.

While a few Stainer violins have not been converted to the modern form, all surviving Stradivarius violins have been so converted.

Internally, the Baroque violin is different as well; the bass bar is shorter, and the sound post is thinner.

They Don't Make Them Like They Used To

It is generally believed today that not only are the violins of Stradivarius and the other great Cremonese masters are the best ever made, but that the violins of today, even those made by the best luthiers of today, do not even come close.

There is clearly only one possible explanation for this: space aliens!

In fact, many explanations have been offered. One of the earliest is that Stradivari used a special secret varnish; there is even a legend that his rival Guarneri once arranged a break-in at the Stradivari shop to steal its formula. Another old theory is that violin production led to the extinction of a tree known as the Balsam Fir; but, apparently, this had never actually happened.

Three recent theories that attempt to account for the superior sound of the old Cremonese violins are based on observations that the variation in the density of the wood associated with its grain is less pronounced than in modern wood.

This is variously attributed to the trees growing during a period of low solar activity, resulting in cooler weather, to a bacterial infection that the trees suffered (with a proposal that a particular fungus can be used to more safely produce a similar effect), and, by Dr. Joseph Nagyvary, to a preservative bath given to the wood.

In the case of Dr. Nagyvary, he found that the techniques he tried of applying a preservative bath to wood did not result in the level of mineral content he found in old violins, so instead he uses wood salvaged from the waters of Lake Superior which does have the desired characteristics.

Looking at information about wood preservatives considered safe to use today, most of them were chemicals with long names that doubtless were not available in the time of Antonio Stradivari. The only exception to that I noticed was boric acid, a substance also used in dilute solution as an antiseptic eyewash. It is suitable for use for items that will be used indoors, but water can remove it from wood - so it shouldn't be added prior to "stewing", to be explained below.

In 1938, the physicist Frederick A. Saunders reported that a violin by Franz Josef Koch had a sound confirmed by measurement as closely resembling that of the fine old violins. Franz Josef Koch made violins in Dresden during the 1920s, and had designed them based on his own scientific studies. In particular, he used "a resin that imparted uniform qualities to the wood"; thus, reducing the effect of wood grain has a long history as being considered as an important step in attempting to attain the heights reached by the Cremonese masters.

Another old technique to modify the wood used in a violin was called "stewing": the wood was gently heated in a salt solution. The purpose of this was to accelerate the degradation of hemicellulose in the wood that would take place as the wood ages normally. Hemicellulose absorbs moisture to a greater extent than other parts of wood, so reducing the amount of hemicellulose in wood helps to prevent changes in sound quality, or even cracking of the wood, resulting from changes in humidity. This technique was known and used in old Cremona; there is reason to believe that it was used by Guarneri del Jesu, but there is also reason to believe that it was not used by Antonio Stradivari.

A brochure from Yamaha notes that a technique called A. R. E. (Acoustic Resonance Enhancement), used with their premium Artida series YVN500G and YVN500S violins, accelerates the natural maturing process of the wood, and so other approaches have been attempted to obtain the improvement that time brings to a violin's sound.

A paper on a project in Sweden to replicate old violins using computerized tomography to find their shape, and Computer Numerical Control (CNC) milling to reproduce it, noted that one obstacle which might prevent success is that the wood of the old Cremonese violins had unique properties; not only hemicellulose, but also resins and other items were thoroughly removed from that wood, giving it an excellent strength to weight ratio.

A comparison of new and old violins in another paper found that the average of along-grain and cross-grain strength was the same for ordinary wood and that found in those violins, but the ratio was less unequal. However, one new violin, with a belly made from conventionally treated spruce which had not even been marked as treated in the lumber yard, had characteristics in the old Cremonese region of the graph.

It has been established that Stradivari varnished his violins in three coats:

That is, three coats of varnish. One thing that is often ignored is that before applying the first coat of varnish, a ground coat can be, and is likely to be, applied for the purpose of preventing any of the varnish from soaking into the wood, thus significantly mitigating any harmful effects of varnish - even that bugbear, spirit varnish - on the tone of a violin.

Dr. William Fry had to dilute casein wood glue by 50% to make it soak into the wood and work as a stiffening agent: if not diluted, casein glue is one possible ground coat. The commercial product of today, Polyfilla, is shown in one paper as penetrating no further than the first layer of cells in wood, in an electron microscope photograph.

A discussion group on violins gave a formula for a ground coat that would have involved ingredients available to Stradivari:

Make hide glue, such as is used in violin-making. Dilute it with one part of glue to 25 parts of water.

Make a saturated solution of alum.

Add the alum solution to the hide glue carefully, drop by drop, stirring constantly. Stop when the consistency of the mixture changes to that of phlegm.

The final step, making the formula complete, was presented by one Jose Catoira, who credited it to a teacher of lutherie in Newark, New Jersey.

The book by Simone F. Sacconi, I "segreti" di Stradivari (The "Secrets" of Stradivari; the English translation has the same title, but without the quotation marks) denies that Stradivarius himself had any such secret; his superiority to other Cremonese makers of his day was solely due to his own superior craftsmanship.

Since there is a narrow gap between Stradivarius and Guarnerius violins, but a wide gulf between them and other fine early ones (Bergonzi, Guadagnini, and numerous others) and later ones, that could well be entirely true, while yet leaving a lost Cremonese secret that needs to be discovered.

While no "gimmick" would enable an indifferent luthier to make violins the equal of a Stradivarius, if the most experienced and accomplished luthiers of today are unable to approach the excellence of the violins of the Cremonese masters, it is not at all unreasonable to consider the possibility that some unknown factor, such as the lack of the right wood or the right varnish, is standing in their way.

But there is also the null hypothesis: perhaps all the fuss about Stradivarius is just due to hype, and we've all been fooled by Luigi Tarisio and his successors, who have been laughing all the way to the bank.

While some blind listening tests of recent date have lent some support to this notion, I am inclined to reject out of hand an idea that basically requires that every single one of the world's greatest violinists is either a liar or a fool.

Given that the excellence of a Stradivarius lies more in its playing qualities than its sound, and that to get the best out of even a Stradivarius requires time to become fully familiar with its individual qualities, blind testing under controlled conditions could easily be missing what is important.

But, in any case, objective scientific measurements carried out by Heinrich Dünnwald show that there are very real differences between the classic Cremonese violins and the violins made by the master luthiers of the present time.

A famous graph, reproduced in a number of books and papers, showing the responses of a large number of different violins divided into three groups shows the following:

The frequency response of the old Cremonese violins does not look, from a casual visual inspection, to be too much different from that of inexpensive modern factory-made violins. But there are definite differences.

From about 900 to 1800 Hz, the response of the old Cremonese violins is significantly lower. Excessively prominent resonances in this region tend to make a violin sound "shrill", and so reducing them is an improvement.

Since I wrote this, I found from a paper which cited Dünnwald's measurements of one Stradivarius violin that the first peak on the graph was the A0 fundamental resonance of the air inside the violin, and that the graphs were normalized so that the highest peak in a particular frequency region had the value of 25 dB.

Thus, it had been a mistake on my part to compare the graphs for the three categories of violins solely on the basis of their general visual appearance. Instead, I needed to shift them so that the height of the peak for A0 was the same for each graph.

Once this is done, it becomes apparent that the way to make a violin sound like one by Stradivarius or his most esteemed contemporaries is not, somehow, to implement in wood a filter that reduces response by about 8 dB from 900 to 1800 Hz while having little or no effect outside that range, something difficult enough to achieve with analog electronics, never mind in the design of an acoustic instrument.

Instead, what old Cremonese violins have that others don't turns out to be a series of stronger resonances in the range of 1700 to 2500 Hz, and possibly also a couple of stronger ones at around 3000 Hz and 3500 Hz.

From about 2000 Hz upwards, all the way to 7000 Hz, as far as the measurements were taken, the response of the old Cremonese violins is significantly higher. Stronger response in this area is associated with a "silky" tone, hence a better sound, and with a violin that is able to project its sound better in a concert hall.

The frequency response of the violins by modern luthiers, on the other hand, looks strikingly different from that of cheap factory-made violins.

After about 2500 Hz, the frequency response of a cheap factory-made violin goes downhill, and so does that of an old Cremonese violin, but more slowly. In the case of the ones by fine modern luthiers, though, the frequency response hardly declines at all from 2500 Hz up to at least 6500 Hz.

So the violins by modern luthiers seem to, at least in this respect, have an even better sound, and definitely their sound should project better.

But in the area from 900 Hz to 1800 Hz, where the frequency response of the old Cremonese violins is reduced, that of the violins from fine modern luthiers is not, but is instead even higher than that of cheap factory-made violins.

Incidentally, at least one paper has been published criticizing Dünnwald's method on the basis that it obscures many real differences between violins that can be made evident by bowing their strings rather than hammering their bridges. This, however, does not reduce what I find significant about his findings; it would make questionable any conclusion based on his measurements that some distinction does not exist, but it doesn't diminish the validity of a conclusion that a difference does exist, if the test that found it is limited in its sensitivity.

Here are the conclusions I draw from this:

The differences between the old Cremonese violins and those made today are real, and not due to a placebo effect.

However, since the fine luthiers of today are able to make the sound characteristics of their violins differ from those of cheap ones to an even greater extent than the old Cremonese masters did, the suspicion naturally arises that it is not that they aren't making violins that sound like those of Stradivarius because they are unable to, but because they aren't trying to.

Given the high prices that a Stradivarius violin can fetch, that is something that requires an explanation. And the most obvious possible explanation would lead to the conclusion that there is a grain of truth to the very hypothesis that these graphs have disproven - that the Stradivarius phenomenon is due to hype generating a false mystique.

If they aren't trying to make violins as good as those of the Cremonese masters, it could be that they feel that were they to do so, the virtues of their violins would not be recognized, and so they're better off concentrating on improving sonic aspects of their violins that are more obvious during a short demonstration in a violin showroom.

That may not be the only explanation, though; reducing the response in the 900 Hz to 1800 Hz area may be a particularly difficult task, or, at least, it may be particularly difficult to do so without affecting the sound of the violin at other frequencies in such a way as to make it sound "dead". So there could still be a lost secret, even if the secret is not a simple one, but which instead relates to how a violin is tuned by carefully shaving away wood from its top and bottom plates.

Two researchers, who have both been praised by their supporters and advocates as having approached the classic Stradivarius sound, stand out above the rest.

The luthier Carleen Mayley Hutchins, who worked with the physicist Dr. Frederick A. Saunders until his passing in 1963, although she is most famous for proposing a set of eight proportionally-sized instruments to replace the four instruments of the present-day violin family, made an extensive study of plate tuning, showing how and where the thickness of violin plates should be varied to cause their modes of vibration to resemble those of the fine old violins.

The physicist Dr. William F. "Jack" Fry also studied the tuning of violin plates, paying particular attention to how the fibers in the wood affected the behavior of the plates. One of his early basic findings was that the back of the violin should be made thinner on the side opposite the sound post, so that the part of the back around the sound post could move as a unit. In dealing with the portion of the front of the violins between the f-holes, which he found to be relevant to the violin's high-frequency response, he did find it useful to increase the stiffness of the wood across the grain. However, he achieved this without using exotic ingredients; he used normal casein-based wood glue, diluted half-and-half with water to improve penetration.

(This is not necessarily an ideal solution; it works by adding stiffness across the grain, whereas wood preservatives and the other items suggested tend to reduce stiffness with the grain. Since varnishing a violin adds stiffness, and is detrimental to its tone, a question is raised. However, if stiffness were all bad, we would be making the fronts of violins out of rubber, or at least balsa wood; if the wood has more stiffness, then reducing the thickness of the wood will balance that. Since Franz Joseph Koch used a resin to equalize the wood, it is likely that his method also added stiffness rather than reducing it.)

The frequency range that leads to shrillness in a violin, was, according to him, associated with modes in which the bass bar tilts in response to impulses from the bridge. One way to reduce this would be to make the bass bar effectively symmetrical around the foot of the bridge (that is, since it extends further above that point than below it, make it thinner above the bridge so that the product of the amount of wood and its distance from the foot of the bridge, considered as a fulcrum, is balanced), but instead of doing that, he thinned the wood in selected regions of the front of the violin which he referred to as "Stradivari holes", as they were areas which were observed to be thinner on some Stradivarius violins.

In addition, he devised tools which allowed him to continue removing wood from the inside of the top and bottom plates of a violin after it was assembled, by reaching with the tools through the f-holes.

Subsequently, on a visit to the Stradivari Museum in Italy, he saw tools used by Stradivari which he believed were intended to perform a similar function.

I am particularly impressed by that particular finding, as it is indeed obvious that assembling a violin will allow its actual sound qualities to be heard. Of course an experienced luthier can anticipate what a violin will sound like from the sound of the plates, but there might be gaps in that knowledge, while having the actual sound available to hear obviously diminishes the room for uncertainty and error.

If contemporary luthiers have, essentially, all been making violins with one hand tied behind their backs, it's hardly surprising that they have been unable to match the achievements of Stradivarius!

The Violin's Second Bridge

When the strings of a violin, resting in grooves on the top of the bridge, move the bridge from side to side, they don't stop moving after they pass the bridge. Not only do they vibrate from the top nut to the bridge, they're also vibrating from the bridge down to the tailpiece. This is why, occasionally on the violin, and more commonly on larger instruments in the violin family, weights are placed on the strings between the bridge and the tailpiece to shift the frequencies of wolf tones away from where they cause trouble.

And both the bridge and the tailpiece transmit vibrations from one string to all the other strings.

The tailpiece isn't attached to the belly of the violin; the tension of the strings holds it up above the belly. Instead, the tailgut, hooked on the tail button, is what holds the tailpiece against the tension of the strings.

And the tail button is round. So it changes a side-to-side force on the tailpiece from the strings into a motion of the tailpiece around the center of the tail button.

Thus, the saddle - the small piece of wood protecting the belly of the violin from the pressure of the tailgut, not the base of the neck of the violin - will also recieve vibrational forces normal (perpendicular) to its surface.

Unlike the belly under the bridge, though, there is no bass bar and sound post combination to prevent the opposed forces from cancelling, and the saddle is above the lower end block of the violin, a solid piece of wood.

While this second bridge, therefore, doesn't have the opportunity to make much sound, possibly if one puts a piece of suitable wood on the violin as the saddle, it might selectively absorb certain frequencies of sound, adjusting the timbre of the violin. Absorb the frequencies from 700 Hz to 1900 Hz well enough, and you just may have found the old Cremonese secret, if Dünnwald's graph is to be believed!

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