Demystifying Harmonics of Stringed Instruments

Instruments like violins and cellos produce harmonic tone vibrations, involuntarily or by intent, from strings other than the string being played.

Students of stringed instruments who also have an affinity for physics are likely delighted with the subject of harmonics. They not only understand how vibrations are at the core of producing sounds, but that all things are related – including the strings of a violin, cello, bass, harp or guitar that are not directly involved in the principle note being played in any particular instance.

Indeed, when the E-string is being played, the G-, D- and A- strings vibrate as well, producing what are known as overtones. The effect on human ears is that a warmer, well-rounded sound is perceived. An overtone is a full octave higher than the played note. Interestingly, the listener doesn’t explicitly perceive the overtones.

There two types of harmonics, with decidedly different effects and requirements of the player:

1. Naturally-produced (“open string”) harmonics. This is the harmonic that just happens, due to the physics of vibrations of the played (“fundamental”) string, causing a sympathetic vibration among the other strings. One need not be a physics major nor even a music theoretician to create or understand it. Natural harmonics happen…naturally.

2. Artificial (intentional or “string”) harmonics. This requires training, practice and skill on the part of the musician – all useful, as some musical scores specifically have harmonics written in. It involves the soft placement of a second finger on a second string as the violin bow plays the primary string.

The harmonic created by the artificial method is done so by (lightly placing the third or fourth finger on the string where the harmonic node would be found (nodes are the ½, ¼, or 1/8th place on the string, where the natural overtone is otherwise produced). By placing the finger at these points, the violinist interrupts all the other overtones except this one.

This is science and math applied to music. But there remains a fine art and human physicality in producing an artificial harmonic as well: just the right amount of pressure – not too little and not too much – has to be applied.

The sheet music calling for string harmonics is identifiable by tiny diamonds shapes over a note or notes (in some cases a circle above the note, along with the finger number, is the notation). In most cases, the composer is driving for a bell-like quality to the tone, which can create a better blend of tonality with flutes and piccolos (instruments that also have a bell-like sound). Because violins and violas have a shorter neck, the players of these instruments have to think with a bit more mathematical precision to produce the harmonic. Cellists and bassists have a bit more freedom because of the longer necks of those instruments.

What is the most likely instance of a stringed instrument harmonic? A sound that is two octaves and a major third above the fundamental tone – tones that are otherwise inaccessible on the instrument. Harmonics are more easily achieved on fine stringed instruments, which are generally easier to play than poorly crafted ones.

It involves a stretch of the effects of vibrational frequencies that any physics student could love.

The Violinmaking School of Venice

Venice stood apart from the other Italian city-states, a blend of culture and art from a bigger world beyond southern Europe. Violins from there reflect this.

When music lovers describe the violinmaking school of Venice, they’re not referring to an educational system per sé, with buildings and faculty and matriculated students and an alumni association. Unlike in Cremona, there is no official institution that carries on the traditions of local luthiers, despite the fact it is historically a very musical city.

Instead, the Venice “school” is an approach to making fine stringed instruments – violins, cellos, violas and the like – that harkens back to the 16th century. Violinmaking all largely began in Italy, although historians like to point out that so much of what is “Italy” today were city-states at the time. The cultures, economies, and governance varied from Milan to Cremona, Brescia, Padua, Pisa, Rome and Naples, among many others. Dialects varied from one city to the next and were sometimes hard to decipher between them.

But Venice itself stood apart. The city was never a part of the Holy Roman Empire: In fact, Pope Julius II excommunicated the entire city in 1606-1607, part of a larger political conflict, but also consistent with the cosmopolitan nature of Venice, the city and its ports being a crossroads of commerce with the (non-Christian) Near and Far East. Today, it is possible to find multiple examples of how this very Italian city with plenty of Catholic churches and religious art – which should make any pope happy – nonetheless exhibit Islamic influence, remnants of the close and friendly mixing of Venetians, Ottomans, Persians, Arabs, Jews and Mamelukes in the lagoon city.

The polyglot nature of Venice, and its political independence from the Church of Rome, very clearly had an effect on music and violinmaking there. During the Baroque period, it birthed composers Girolamo Dalla Casa, Ippolito Ciera, Giovanni Picchi, and the very popular Antonio Vivaldi. The style of music was expansive, splendorous, sometimes described as “colossal,” with compositions using multiple choruses and instrumental groups.

Violins crafted by a Venice violin maker were not for the courts of royalty, as was the case with those from Cremona. This mercantile city, where one writer once remarked that an instrument or voice was making music at all times in every home, was less concerned with the aristocracy despite its legendary wealth. The first great Venetian luthiers, Martinus Kaiser and his son-in-law Matteo Goffriller, made violins to order and according to price. Rich clients received instruments of the highest quality made of expensive woods and varnish. For instrumentalists with fewer funds, lower quality materials were used.

Later Venice school violin makers, Domenico Montagnana and Francesco Gobetti, were originally shoe makers, a trade that translated well to musical instrument craftmanship. Venetian violins from them and others were known for superbly rich bass tones and a full, projecting sound. These are concert hall stringed instruments, capable of being heard in row 50 – not just the small rows of chairs set up in a baron’s palace.

How have these instruments, and the nature of Venice violin making, stood the test of time? Internationally acclaimed cellist Yo Yo Ma considers his Montagnana cello his primary instrument (appraised value is $2.5 million). That rich Venetian violin or cello sound continues to play well in the gilded, rococo style La Fenice opera house, rebuilt in 2004 after a 1996 fire. This city, and its musical instruments, is the collective result of people who always loved music that was unrestricted by papal decrees, social class and cultural homogeneity.

The Violins of Yehudi Menuhin

The prodigy Menuhin had a taste for the best violins in the world, and his virtuosity made him deserving thereof. For all he was given he also gave in kind.

What is the connection between virtuoso violinist Yehudi Menuhin (1916-1999) and Fallout video games, devised in the early 2000s? The former is among the foremost violinists of the 20th century, and the latter provides virtual roleplaying in a fictional post-apocalyptic universe set in the 22nd and 23rd centuries.

What they share in common is the Soil Stradivarius, built in 1714 by the legendary Cremonese luthier and one of seven famous violins owned and played by Menuhin during his illustrious career. In the fictional Fallout story, the Soil Stradivarius is thought to be the only Strad that survived a nuclear war, and it is therefore hidden in a vault to preserve it.

Back to real life, Menuhin played the Soil Stradivarius (so named for an 18th century Belgian industrialist) from when he purchased it in 1950 until some time before he sold to its current owner, violinist Itzhak Perlman. French luthier Jean-Baptiste Vuillaume once owned the instrument, distinguished by its red varnish and two-piece maple back. Like Stradivari, Vuillaume provided musicians at the time with fine stringed instruments for sale, crafted in his fine violin shop and by his gifted hands.

It was not Menuhin’s only Stradivarius-crafted instrument. He used the Prince Khevenhüller 1733 Stradivari, in addition to three by the house of Guarneri (Lord Wilton Guarnerius 1742, Guarneri filius Andrea 1703, and Guarneri del Gesu 1739). Menuhin also played a Milanese violin from Giovanni Grancino (1695), and another from Giovanni Bussetto (1680), a luthier in Cremona, whose violins are very rare because he was active for only ten years (1670-1680).

Recognized at a young age for his talent, Menuhin’s first public appearance was at the age of seven as a solo violinist with the San Francisco Symphony Orchestra. His career trajectory set, he was soon in demand around the world. Born in New York City, his parents moved with him to Paris where he studied under George Enescu and Adolf Busch in Basel.

But Menuhin and his violins were not confined to the great concert halls filled with the European aristocracy. He played for Allied soldiers during World War II and for liberated survivors of concentration camps in Germany in 1945. Himself born to a family of religious Jewish immigrants from Lithuania, he nonetheless played with the Berlin Philharmonic in 1947 as a gesture toward reconciliation, a mere two years after liberation and the close of the Holocaust.

Itzhak Perlman remains forever grateful for having received the Soil Stradivarius. He told Strings Magazine in 2015, “When Menuhin agreed to let me try it, I felt it was the greatest sound that I had ever experienced. It was my dream to own it, and one day that dream came true.”

Which suggests the developers of the Fallout video games understand well what should be preserved, come what may in a nuclear future.

The Violinmaking School of Brescia

Political of the Renaissance ordered northern Italian cities in violinmaking. But bubonic plague hit Brescia a little harder as most of its luthiers perished.

The distance between Brescia and Cremona, Italy, two bastions of fine stringed instrument making in the 16th century forward, is only 29 miles (46 kilometers). But relative to the world of violins, violas, and cellos from that period, they are considered by some to be at the opposite ends of the earth – back then and even today.

The violin making school of Brescia, which traces its roots to the crafting of liras, violettas and violas as early as the late 14th century, is known for distinct aesthetics and methods of construction. And due to the geopolitics of the time, Brescia was actually best known for its violas, cellos and double basses/violones, while Cremonese luthiers (Stradivarius, Guaneri, et al.) get more credit for their violins.

Why is that? It’s because Brescia was under Venetian rule, and in Venice the music was largely written for groups and ensembles. Therefore, in demand was the full complement of instruments, in particular violas, cellos and double basses. In contrast, Cremona oriented to Spain, under which it was ruled (1535-1707). There, the soloists who performed for Spanish royalty and the aristocracy favored the upper-register instruments, violins in particular. Consider the work of composers Grandos, De Falla, Sarasate and Rodrigos, as well as the showy “Spanish Rhapsody” composed by the Hungarian Jaroslav Vanecek in memory of Sarasate.

The Venetian demand for instruments from the Brescia school included a taste for secular music, involving commentary and satire on events of the time. But sacred music was very much a part of the city-state as well, largely based out of the Basillica of Saint Mark, with motets defining the Venetian polychoral style (e.g., Giovanni Gabrieli).

A sad factor of the earliest Brescian instruments is that few instruments exist today from the first luthiers: Jacobo Dalla Corna and Micheli Zanetto and his son, Peregrino Zanetto. Following them were Battista Doneda, Francesco Inverardi, Palanzino Palancini, Guglimo Frigiadi and Giovita Rodiani. Evidence of what they did is found in such places as tax records, where one’s occupation would be included. Related tax records include where components were purchased and instruments were sold – Gaspar ‘da Salo, a famous violin maker from 16th century Brescia, sold many of his instruments to musicians in France, and those records also indicate his wood was acquired in Venice and strings were from Rome. From 1568 to 1581 his fortunes increased, indicating his success as a sought-after luthier.

Characteristics of fine violins, violas, cellos, citterns (popular in the day), double basses and viola da braccia (also popular) from Brescia include rich ornamentation on pegheads, pegboxes, on the back, and sometimes f-holes with large eyes and pointed wings. In Gaspar’s case, it’s unclear if he himself was the woodcarver or if that was outsourced, perhaps to a contemporary known as Girolamo Virchi, who with family members was known for carvings found in organ lofts of Brescian churches.

Despite the geopolitical distinctions of Brescia and Cremona, both cities lost most of their violinmakers in the 1629-1631 Italian Plague, which eliminated about 25 percent of the population of northern and central Italy (about half of Milan’s population died). A handful of luthiers in Cremona survived (including Nicolo Amati), allowing that city to take a definitive lead in violin making.

But high-end violins and other fine stringed instruments are made in both cities today. One contemporary luthier who illustrates how lines are more easily crossed is Ioannis Apostolou, born in Greece, educated in Cremona, and moved in 2010 to Brescia where he today has his own violinmaking workshop in the center of the city.

The Lowdown on Fine Instrument Investing

Rare musical instruments as investments are attractive because a growing wealth market appreciates the finite supply of fine violins and other instruments.

Whether in a strong economy where market-traded securities are performing well, or in economic downturns when such securities aren’t, a perennial topic among the investor class is the wisdom of owning fine, scarce objects.

Those objects range from fine art to rare coins to antique cars to other collectibles such as stamps, first-edition antique books and precious jewelry, gems, silver and gold. But unique among these items are fine musical instruments – in particular the most storied and rare violins, cellos, violas, stringed bass and harps. Pianos are also in this category, albeit with huge costs relating to moving them from one owner to the next.

The most valuable violins are those crafted by the Italian master luthiers, Stradivari and Guarneri. As of mid-2019, the most expensive violin on earth is the Messiah Stradivarius (1716), valued at $20 million (US). The Vieuxtemps Guarneri, at $16 million, is the second-most valuable, followed by the Lady Blunt Strad ($15.9 million), the Carrodus Guarneri ($10 million), and the Ex-Kochanski Guarneri ($10 million). These prices are round numbers because most are held by museums or anonymous owners and not recently sold.

Interestingly, those instruments held by unnamed owners are often on loan to exceptionally talented players who themselves cannot afford to purchase the instruments, despite soaring career accomplishments.

For would-be investors, there are several critical questions to ask before bidding to buy one of the few thousand or so rare, fine stringed instruments made by a notable violin maker.

Is it a smart investment?

No reputable investment or auction house can legally predict the future value of a stock, a fund, an antique car, or a fine violin. An investor in fine objects very often looks beyond its monetary value to appreciate something more transcendent.

A Toronto based dealer, Ric Heinl, says a $10,000 instrument today could double in about 20 years, essentially a 3.6% rate of increase, which would be considered a laggard. But that doesn’t hold for all instruments. A 2013 study by economists at Brandeis University looked at rare violins as compared to the S&P 500 Index in the years 2007-2012 and found the musical instruments outperformed market securities; note this period bridged the global financial crisis that began in 2008, perhaps indicating these are counter-cyclical investments (i.e., they outperform the market in recessions).

Can it be bought in shares?

It is entirely possible for a collection of individuals to pool their funds to buy an instrument, although the legal arrangement for that would be on them, not the seller.

Another option is for the investor to purchase a portion of an instrument from a middle-aged player who intends to continue playing it for some time into the future. The agreement would be to purchase the remainder upon their retirement or death. What this does is provide liquidity to a player while allowing him or her to continue playing it.

Speaking of liquidity, it should be clear that the sale of these investments do not happen quickly. The global market – with an expanded base of wealthy collectors, particularly in Asia – means dealers sometimes must travel extensively with the instrument to show it to prospective buyers. Even a domestic sale takes months if not years to execute.

What is the size of the inventory?

About 650 Stradivari instruments – violins, cellos, violas, harps, guitars) – survive, and catalogs list at least 148 Guarneris that are extant. But instruments made by Maggini, Amati, da Salo, Stainer and others remain highly valued. And that is just the stringed instruments, not counting the Steinways and other remarkable instruments around the world.

The point is that value for all instruments is driven by scarcity. There will be no more Stradivariuses. Further, demand increases with increasing wealth in parts of the world that previously were not involved in such investments.

What are the transactional costs?

Reputable dealer and auction house commissions range from 5 to 20 percent of the sales price. Unless the investor is also very schooled in the instrument under consideration, it makes most sense to purchase through a dealer or auction house that can attest to the instrument’s authenticity (maker, provenance, condition, etc.).

What do you do with a fine instrument once you own it?

Better-preserved instruments should be played – because the world needs beautiful music, and the condition of the violin fares better with careful use and appropriate maintenance. This is why investors who are not players should and do loan their instruments to virtuosos.

Demystifying the Violin Bridge

The bridge in all stringed instruments is a simple, unheralded part that transfers vibrations from the strings to the instrument body. It’s all physics!

There’s an argument in education theory circles that the 21st century emphasis on STEM – preparing students for careers in science, technology, engineering, and math – leaves out something important: the arts. This is why more progressive school systems are now calling it STEAM, with the A representing the visual and performing arts.

That more progressive stance isn’t just about tacking on music or painting classes to coursework in physics, calculus and coding. It’s about integrating all of the above into a relationship, where understanding one might help with understanding another. Better yet, something like studying the violin might help a student gain a better understanding of such things as the Doppler effect, bridge cables, and friction.

Take for examples the violin, viola, cello or stringed bass. All include a small but vital part called the bridge. It’s a simple piece of maple wood, cut in fanciful ways, serving as a lift on the strings to provide their tension. The bridge also raises the strings on a slope that makes the instrument more playable. When the instrument is played, the bridge transmits vibrations of the strings to the body of the instrument, where the sound is then amplified.

Fine stringed instruments require customized bridges that cannot be purchased stock. A violin shop with a reputable in-house luthier who makes or repairs fine cellos, violins and violas, will usually handcraft a fine bridge for a high-end instrument. Though an experienced player can learn to properly place their bridge, placement of the bridge on an instrument is typically best left to professionals.

The engineering of cable-tension bridges – of the type that span rivers and carry vehicular traffic over them – is similar in that the tension has to be very closely engineered for it to work. What’s different with the violin bridge is that, as the supporting structure over which the strings are laid, it is not firmly anchored deep into the “ground” (instrument). The violin bridge is completely and easily removable.

This movability in the violin bridge is an essential characteristic. It would fail to provide that vibration transfer to the body of the instrument if it were glued or otherwise permanently affixed to the instrument.

But as any bridge engineer could explain, the supporting structure like the violin bridge needs to be perfectly (or as close as possible to perfect) perpendicular to the instrument body surface. Any kind of lean, any deviation from a 90-degree angle perspective, would likely be unsustainable.
Importantly, when tuning any stringed instrument the shifting of the strings can affect this bridge angle; the violinist should therefore make manual adjustments to the bridge when tuning.

A collapsed highway bridge is a disaster, and particularly with early 20th century designs several did. A collapsed violin bridge may not involve the loss of life, but to a violinist it could lead to a disastrous situation nonetheless. Not only is the instrument at least temporarily unplayable (the strings would go limp), but could happen with such force as to damage the body and displace the soundpost in the interior of the violin body.

One mystery of music physics that remains to be solved – listen up, STEAM students – is whether there is value in drilling holes into a bridge. Discussion boards on various violin-interest sites offer a mixed review: some say it adds to the vibration transfer, others say it ruins a perfectly built violin bridge. One commenter even went so far as to say that drilling holes, then filling them with lead shot sealed inside, can produce “some really interesting buzzes and rattles.” Which isn’t called for in any of the compositions of Tchaikovsky, albeit one can always devise their own interpretations of the music.

The same poster warns “there’s a lot of rubbish out there on the Internet.” Better to figure this out in a physics and music class.

The Violinmaking School of Cremona

The traditions that gave us the best violins ever made continue in this northern Italian city. This heritage is even recognized by UNESCO.

It might be hard to understand the shared characteristic between traditional violin craftsmanship in Cremona, Italy and the following: polyphonic singing (Georgia), yoga (India), the hopping procession of Echternach (Luxembourg), the Charreria equestrian tradition (Mexico), wedding costume traditions of Tlemcen (Algeria), tango dancing (Argentina and Uruguay), lavash bread making (Armenia) and avalanche risk management (Switzerland and Austria).

All are on the UNESCO Lists of Intangible Cultural Heritage, which seeks to protect “important intangible cultural heritages worldwide and the awareness of their significance.”

For the Cremonese, the pride they hold in their fine stringed instruments – violins, violas, cellos and bows – is both historical and contemporary. Beginning with the luthiers (violinmakers) of the 16th century, family names on instruments that survive today are revered by musicians, audiences and auction houses alike: Stradivari (yes, makers of the Stradivariuses), Amati, Guarneri, Rugeri and Bergonzi.

Some argue that the fine Italian violins, violas and cellos crafted in each violin shop of the early violin makers are due to the specific growing conditions for the maple and spruce woods at the time. A “mini Ice Age” occurred from the 15th to 17th centuries in Europe, where low summer temperatures led to slower growth of the trees and thus a more dense wood (tree rings were more closely spaced). This finding isn’t universally accepted, but what most people in the world of stringed instruments agree on – seconded by UNESCO – is that the methods of skilled craftsman are the reason violins made in this region have exceptional tonality and overall quality.

The Cremona International Violin Making School (Scuola Internazionale di Liuteria di Cremona), founded in 1938, is a key bulwark in keeping this tradition alive. Students study sound and technique, develop the craft, and learn the cultural background of the Cremona violinmaking heritage. Over 80 years of operations, the school has produced almost 1,000 graduates, a little more than a third of whom are Italians, another third non-Italian Europeans, and the remainder non-Europeans. In a recent year there were 176 enrolled students.

The Cremona technique is considered unique to all other violin making around the globe. As the 70 different molded pieces of wood of each instrument are made and applied, they are adapted to the other parts of the violin. Given the vagaries of wood, a natural product of trees, this means that every instrument varies from one to the next.

Two official bodies supervise the creation of violins in Cremona: the Stradiari Violin Makers Consortium, and the Violin Making Italian Association. Since 2013, the Violin Museum of Cremona, in the Palazzo dell’Arte, has a display of new and old instruments, in addition to an auditorium where performances by masters are held.

So let the Swiss save people from avalanches, the Armenians keep their bread traditions alive, and the people of Buenos Aires tango the night away. In Cremona, the working luthiers, faculty and students all ensure that new violins live up to the legacy of the city’s famed masters.