In the last twenty years François Denis’ Traite de Lutherie has revolutionised the way that we understand the geometry of Cremonese violin forms, but there is no criticism to his work in asking questions about how the fundamental shape of the violin was formed long before Andrea Amati perfected. You can see an animation of the process of François’ method in the video right here.
The earliest that we think Andrea Amati was using this kind of geometry must be in the reign of Henry II of France (1536-1559) since there is a fragment of a viola by Andrea Amati that bears his armorial crest. François’ work explains how the instrument is geometrically constructed to make the form that we are familiar with today, but whilst it explains how, there are elements that relate to the question of why that are beyond the scope of the project that he set out to achieve.
My interest for the purpose of this article is far more about how the instrument arrived at its gross proportions of width and length, which appear to have been settled upon several decades before Andrea Amati’s involvement in creating a geometrically ‘perfect’ form. Any ideas are immediately challenged by the harmonic relationship between width and length that François is able to express in the first elements of his geometrical construction, and in some respects I would agree that the length of the violin following François’ schema is a foregone conclusion when constructing the width in the first place. I am grateful to Harry Mairson for sending me this calculation that expresses the numerical consequence of François’ geometrical workings as something to mull over, with the serious and friendly space that every brainwave has to wonder if it is on the wrong track or somehow redundant. At that point in my thought processes, I could have almost happily deleted the draft of this blog and contented myself what has already been discovered. After gratefully sleeping on it, I realised that this didn’t disqualify anything about the origins of the general violin form. It merely made it more interesting.
However, my question is one of genesis from the earliest ideas of the violin, for we see shapes of instruments from places other than Cremona that have an agreeable proportions like a violin.
Proto Violins
Amongst these proto-violins, Benvenuto Tisi da Garafolo’s fresco for the Treasury Room of the Palazzo di Ludovico (Sforza) il Moro in Ferrara, painted in 1503-06, is the earliest instrument with a strong likeness to the violin as we know it. We may be tempting fate too much to recall that Garafolo worked with his uncle, Niccolò Soriano in Cremona and in the same city he was a contemporary of Galeazzo Campi in the studio of Boccaccio Boccaccino around the year 1495 (a trail of happy coincidences may simply demonstrate the tightness of the artistic community of Northern Italy). It shows nothing of the complex geometry demonstrated by François Denis in the Amati system, despite already bearing an overall similarity to the proportions of the violin.
Within a few years of the Ferrarese iconography, Gaudenzo Ferrari’s also includes a number of instruments that qualify as proto-violins similar to the modern-day form. (His name is an inconvenced, because his training was in Milan and his paintings have nothing to do with Ferrara). At the pilgrimage church of the Santuario della Beata Vergine dei Miracoli (on the northern outskirts of Milan) he painted a vast concert of angels in 1532-1535 which shows an array of instruments that stretch the imagination. Here whilst there are instruments that look like they might be violins, but have extravagant forms, there are also those that almost resemble the violin as we know it.
There are good questions as to whether Gaudenzio himself as a musical instrument maker because some of the consistent elements of the construction that are common through all the stringed instruments of different shape, and through those from other paintings that Gaudenzio created including the Madonna of the Orange Trees, an altarpiece in San Cristoforo, Vercelli, painted 1529/30.
Whilst these instruments have have the rough proportions that we are looking for, this is not to say that all instruments depicted around the same time had the same proportions, and it seems that around 1500 the shape of the proto-violin or proto-viol could have gone in any number of directions, indeed the viola da gamba as we know it has a longer body by relation to the width, and the guitar is shorter. Here I have illustrated ideas by Lorenzo Costa, Francesco Francia (with whom he shared a workshop at a time) and Giovanni dai Libri between 1490 and ca.1520, all showing compelling ideas of form that failed to sustain into the later sixteenth century. With these in mind, the question of why the violin settled around the shape we know it by becomes a more interesting question. Any of these could be resolved by its own geometrical schema but lost favour by comparison to the violin shape we know today.
Gaudenzio – Luini – Leonardo
I feel I need to start with a disclaimer about writing anything that moves into the sphere of Leonardo da Vinci, because there is always a certain kind of hype that surrounds his name and he is often invoked in ideas that are discreditable. On the other hand, he was working within the time period in question in Milan, the capital of Lombardy, of which Cremona was an important regional city, so it is not so far fetched to imagine how few the degrees of separation could have been between Leonardo and the creation of the first violins. No! I am not making any claim of Leonardo as the inventor of the violin, but I am conscious of the relatively small world of artist and artisans out of which the violin emerged, and the transmission of musical, intellectual and architectural imperatives that helped to shape the instrument.
However, there is a very direct link to the cupola of the Santuario della Beata Vergine dei Miracoli, for it was Bernardino Luini, both an assistant to Leonardo and a significant promoter of his legacy in Milan after Leonardo’s departure to France in 1515, who was first commissioned to paint the chapel. He died in 1532 having completed frescos on many of the lower surfaces of the church, leaving the cupola to Gaudenzio Ferrari. Very recently in conversation with my colleague Alessandra Barabaschi, we became aware of some fragments of Leonardesque fresco by Luini that form the prototype for the choirs of angels (although we do not know where they came from), and they result in putting some of the ideas expressed in Gaudenzio’s paintings back by a generation, and more directly into the ideas that revolved around Leonardo’s own studio in the court of Milan. One of the instruments depicted in both the cupola and the newly discovered frescos has long been considered an impossibility, but in fact it is anything but. It is an evolution of the three-holed tabor-pipe and Tamborin de Bearne a kind of psaltery that is struck with a stick rather than bowed. Whilst the two instruments were normally played simultaneously by a single musician, the two have been formed into a single instrument. It is frankly impractical, and less acoustically satisfying than the large tambourin instrument that it offered an alternative to, but it has the same spirit of logical and functional impracticality that one gets used to when leafing through Leonardo’s notebooks.
Bernardino Luini came to Milan in 1500 where Leonardo had been since 1483, taking a deep influence from him. Many of his paintings are workings of compositions by Leonardo, and he adopted his chiaroscurro technique. There is much work to be done on understanding the collaboration between the different painters in the orbit of the Sforza court of Milan, and their cooperation with Leonardo because of the obsession of seeing him – like Stradivari – as a singular genius. It seems to me that Luini, Giovanni Antonio Boltraffo and Antonio Solario in particular may have actively completed the ideas and concepts that Leonardo had no time to complete himself, and to maintain his reputation in Lombard art after his departure to France in 1515. A visit to the Pinacoteca di Brera in Milan where many of these painting are kept truly fills the mind with Leonardo’s vision through the eyes of the Leonardesque. In London the National Gallery became home to one of Leonardo’s greatest compositions (it still is) Christ amongst the Doctors – Isabella d’Este commissioned such a work from Leonardo and he never completed it, but the prime version based on Leonardo’s designs was long accepted as an undisputed Leonardo until it became the work of Luini. It is certainly one of the most beautiful paintings of that Lombard school, and one that provokes profound questions about collaboration and studio assistants. Little surprise (although I don’t agree) some suggest that less than 20% of the (in)famous Salvator Mundi is Leonardo, the majority by Luini.
As we come to Leonardo himself, it is the flanking panels painted by his assistants Giovanni Ambrogio de Predis of a red angel with a lute (not illustrated) and Francesco Neapolitano’s green angel with a form of bowed stringy-thing painted to surround the Madonna of the Rocks (1490/91) that are of interest. Specifically the stringy-thing which may be too early to be a proto-violin (the gallery calls it a vielle… it’s complicated). To the eye there are obvious differences separating this from Benvenuto Tisi di Garofolo’s fresco for the Palazzo di Ludovico il Moro, but with a luthier’s eye there is more to the construction that places these in a fundamentally similar class on object: The apparent proportion, the flat overhanging plates, the relationship of the neck and the fingerboard to the body, the flat bridge and similar tailpiece. When contrasted to the huge diversity of design features displayed in paintings of this time and locale these are astonishingly for their similarity including – roughly – the proportions.
Braccios and Gambas… problems of the names of things.
One of the questions that has been nagging me is about the names of things – viola or lira da braccio, viola da braccio and viola da gamba. I’m sorry to say that almost anything you care to google about the viola da gamba parrots the idea that it is so-called because it is played on the leg and not the arm and vice versa, for although this is generally true (try telling a cellist that), I am sceptical that such a simple answer makes any sense in the sophisticated world of the high renaissance. Another confusion that I think exists is the idea that the viola da gamba and the violin appeared simultaneously. I th;ink this is true in terms of the kind of instrument (the idea that the viol is a precursor to the violin is not true), but surprisingly we see the term ‘viola da gamba’ very rarely in the early sixteenth century – six Viole da gamba in a inventory from the Ferrara court of Ippolito, a brother of Isabella d’Este in 1511 seem to be the first known use of the term, but it is possibly not until Jambe de Fer writes in Epitome Musical (1556) ‘The Italians call these instruments viole de gamba’, it is in terms of the Italian nomenclature being out of the ordinary for instruments that are generally known in France as violes. We don’t see the term being used consistently until the second part of the sixteenth century. For the most part, they are simply viols, or even violini. In Brescia, the publication of Giovanni Maria Lanfranco’s Scintille de Musica in 1533 gives us the following descriptions:
Lyra has seven strings, the upper four are tuned in fifths, and the others are drone strings. It is what we call the lira da braccio.
Violette d’arco senza tasti has three strings and is without frets (senza tasti) tuned in fifths and describes what we know as a violin. It is simultaneously called the violetta da braccio & da arco.
Violini da tasti: ad Arco has six strings with frets (da tasti) whose tuning in fourths with a third between is what we know for the viola da gamba.
In England we don’t see the use of viola da gamba or it’s anglicised corruptions until John Dowland in 1597, or voyal de gamboys in Shakespeare’s Twelfth Night in 1601.
So, for some reason, in the absence of the notion of the ‘leg-viola’, the violin and lira both became known as da braccio – of the arm. What could it mean?
Anthropomorphisms
Another of the questions that come together here is about the anthropomorphic nature of the shape of the violin and its predecessors. We are left in absolutely no doubt of this as an intention when we examine an incredible survivor from 1511 of a Lira da braccio made by Giovanni d’Andrea in Verona. As we approach the modern violin family there is the constant ideal that we see in Man Ray’s Violon d’Ingres. It’s worth putting it out here because it best reflects a timeless anthropomorphism that we seem to associate with this shape. I think that between these two extremes, there is something to be said.
Although Giovanni d’Andrea clearly envisaged his idea of the lira da braccio as an instrument with a clear upward and downward end, I have my reasons for believing that this is an outlier and that the design of the violin evolved to be upside down from what we see today. Francesco Neapolitano’s green angel (above) being a typical example from the decades around 1500. In conversation with another colleague, Peter Sheppard Skaerved comes the further observation that when the f-holes are percieved on a violin this way, the shape compliments the ancient Greek lyre, and so perhaps we should call them lyre-holes instead.
When we look at the violin this way, it becomes more interesting for an anthropomorphic idea, because the relationship of the widths of the instrument come closer to the human form. The average female form – the hour-glass figure is one in which there is almost no difference between the width over the shoulders and the width across the waist (1:1.03) – Man Ray’s Violin d’Ingres distorts this because the subject is sitting down. The Male form with a narrower pelvis is anatomically closer to 1:1.18 is a ratio of 5:6. As we shall see, things are not that simple with the addition of muscle and body fat, the dimensions of an Andrea Amati (Ex.Kurtz) of 16.3cm and 20.2cm is more agreeable with a 4:5 ratio roughly how we see the human body with all the muscle and fat attached… let us explore this further.
Proportions
All of my ramblings so far are to lay the groundwork for a theory – perhaps da braccio is a reference to a unit of proportional measurement rather than an instruction of how an instrument is played. This would certainly be more coherent a reasoning within a Renaissance mindset. Bringing these threads together, in another blog I have already pointed to some of the ways in which the ancient Greek Kanon of Polykleitos influenced Renaissance thought through the lens of the revival of Vitruvius’s (Roman) de Architectura in 1486. It would not by until the vulgate edition in 1516 that a printed woodblock image would be published, much less sophisticated than Leonardo’s drawing. I am drawn to the idea that the relatively new ideas emerging from Vitruvius would be an obvious starting place for creating an architecturally idealised shape for the early violin. The (in)famous drawing by Leonardo da Vinci of the Vitruvian man is thought to have been drawn around 1490/91, but like the later woodblock it turns out that the Kanon of Polykleitos eluded – continues to elude – complete interrogation. Some commentators make a fuss that Leonardo’s drawing is inaccurate, but I want to offer a different nuance that it is a comparison between what he understood of anatomy on one hand, and the rules of Polykleitos on the other in order to show the dissonance between the two. In Leonardo’s own words:
Vitruvius, the architect, says in his architectural work that the measurements of man are in nature distributed in this manner, that is 4 fingers make a palm, 4 palms make a foot, 6 palms make a cubit, 4 cubits make a man, 4 cubits make a footstep, 24 palms make a man and these measures are in his buildings. If you open your legs enough that your head is lowered by 1/14 of your height and raise your arms enough that your extended fingers touch the line of the top of your head, let you know that the center of the ends of the open limbs will be the navel, and the space between the legs will be an equilateral triangle.
Leonardo da Vinci describing the Vitruvian Man.
One of several problems that Leonardo encountered was the difference between skeletal and corporal proportions, and indeed how much muscle and fat is required to form the idealised human form. If we look closely at the left and right side of the torso they are notably asymmetrical as if each side is an experiment with another body form, perhaps an indication of the unresolved nature of this particular drawing (the positioning of the feet are a more obvious indication of asymmetry, since they twist the musculature of the legs leading into the torso, though this does not explain all of his artistic choices up towards the chest area), but it does provide a reasoning for why we can be a little loose with our ideas of the anthropomorphic proportions of the violin. Leonardo knew from Vitruvius that the height of a man was four cubits, and so we see the square divided so, with the perineum (crotch) at the centre – the other cubit divisions are below the knees and between the nipples. The other interesting element of the crotch… (umm… Ben don’t go there…) has more to do with the width of the hips where the they join the pelvis. In Leonardo’s drawing he defines the hips as being one foot (four palms) wide. When I fettled an Andrea Amati outline onto the torso I found that when I scaled the width of the upper bouts to this waist measurement, the length and full breadth of the violin was very appealing in respect of the proportions of the torso, especially if we assume to think anatomically that the torso extends to the top of the cervical vertebrae. (There is logic since the spine from the pelvis to the base of the spine is a coherent element of anatomy, it would be strange to think of it otherwise). This is what I found:
I am curious that Leonardo measured a distance at the nipple height that extends for five palms, because this does make sense to the 4:5 ratio of the violin outline. We see however, at the shoulders that the distance between the arms is larger, at a full cubit (6 palms). In fact, the canon of proportions of Polykleitos/Vitruvius begins with measuring the outermost extremity of the human body and working inwards. This being the distal phalange of the middle finger. Four of these digiti makes a palmi, four palmi make a pedi, six a cubit. We can see the scale beginning with the digiti of the distal phalange shown below Leonardo’s Vitruvian Man:
Did I mention? ten palmi makes a braccio!
What I did at this point was incredibly simple – having scaled my outline to the pelvic width, I rotated it over the arm, finding that it corresponds perfectly to a braccio. As I have already written, viola da gamba does not seem to have entered into the Italian language until at least the middle of the sixteenth century. English viols tend to be longer in the body relatively speaking, than the violin, and the consistency of Italian viols from the middle of the sixteenth century gives me pause to for thought before suggesting that it derives its name out of the proportion of the leg – essentially 12 cubits by four instead of ten by four. That is something for discussion.
Viola da Gamba
As far as I am able to discover, there is a single hitherto known reference to the viola da gamba before 1550, in the 1511 inventory of Ippolito d’Este, whilst there are many references to an instrument that we now know to be this. The Violino ad tasti & ad Arco of Lanfranco’s 1533 treatise is significant because of it’s publication in Brescia and his advocacy and apparent friendship with the instrument makers of the city. As we have seen the number of strings, tuning and frets all concord with what we think of as the viola da gamba.
Remarkably, there are infact a handful of viols made by Zanetto de’ Micheli da Montichiaro that survive, a violone in the Musée de la Musique (Inv. No. E.408) and a bass viol in the National Music Museum (Inv. No. 3376), but with the wide variety of viol designs that exist from the middle of the sixteenth century, I am not sure whether even these necessarily fit my thesis.
Hence, my first idea was to wonder if the slightly narrower form that we find in some viols related to a similar braccio / waist proposition, in which the length of the leg rather than the arm explained the size of the instrument. I’m ashamed to show my workings on this, because it became pretty obvious pretty quickly that any instrument reflecting what would become a mainstream concept of the viola da gamba made no sense at all…
Thanks to an inspiring discussion with my friend Joëlle Morton, it dawned on me that one of the big differences between the viol and violin is the proportion of the neck. On a violin if you divide the string-length by five, the neck is two and the distance from the edge of the belly to the bridge is three. However, back in the 1980s my long-ago mentor Michael Heale who had sparked and encouraged my fascination for viol geometry had published the following simple observations:
Amongst these, the most helpful to him as a restorer was the confidence on many English viols that the width of the bottom bout was equal to half the string length. Therefore from the joint between the body and the neck, one could predict the bridge position and the length of the neck with a ratio of 1:1, rather than the 2:3 of the violin family. This means that to help with tuning, you can place an octave fret up against the overstand of the neck, which is particularly helpful for trying to calculate the positions of other fret positions according to mathematical, harmonical (or cosmic) principles.
Having expressed the lira/violino da braccio as essentially representative of the proportionality of the torso in terms of width for purely aesthetic architectural reasons, with fretted instruments the priority is the mathematical relationship between notes. As we see from Lanfranco’s 1533 explanation of the notes of the musical scale, they are laid out on a monochord thus representing the notes of the lower octave of the string (you have to extrapolate a little, trust me).
When we return to Vitruvius we potentially see something harmonic in the height of man, which is four cubits, with the groin being the half way point. There is some faint likeness to the human body if we consider the sound producing torso of the instrument like the body, and the legs, or ‘neck’ of the instrument as the extremity. Hence, from top to toe, if we think about string length, it is 2 cubits to the transition with the body, and two cubits of the body, and everything orbits around that centrality – the groin of the Vitruvian man is the same as the position of the proportio dupla of the Universal Monochord.
This provides a rather simple and unexciting theory which observes that the leg to height ratio provides the position of the octave along the vibrating string, but this seems to be the idea that holds true for the majority of surviving instruments well into the eighteenth century. That this explains the string rather than the architecture of the body does not bother me, because the string is the sacred element of this conception of the instrument, and because to paraphrase Vitruvius, the rest of the instrument follows on from these rules.
At length I would like to write more about how I think that the viol evolves from a consort instrument for the playing of madrigals supplanting the recorder into it’s own paradigm as the bowed instrument most capable of reflecting the mathematical cosmos and expressing human emotions through it’s sound. It seems to me that the starting point of this cosmic viol resides in it’s ability to replicate harmonia, and so in England as the playing the viola da gamba lyra-way evolves as it’s own art form, the celestial representation harmonia exists not in having seven strings for seven planets, but seven frets to mark their relationship to the geocentric cosmos in which the octave fret represents the Earth. In other of my writing I have expressed the further idea that the variation in sizes of English viols is related to the philosophical awareness that music itself is of divine proportion, as is the human form. Hence, to play on an instrument that is of an arbitrary size would be less desirable than to play one in which the musician, the instrument and the music itself are in concordance with one and other, which is why I think that there was a priority that could encourage viols to be tailored to their owner.
Conclusion
I think there are mathematical limitations to this idea, which represents an idealised philosophical representation, and I think that any attempts to express it in a more precise manner than I have outlined may come to grief. But it is worth understanding that to this day the canon of proportions of Polykleitos – Vitruvius – Leonardo are not fully understood, and err towards a conscious metaphor and idealisation of the human form. Moreover there is a period of seventy years that divides Leonardo’s drawing and the violins of Andrea Amati. There is every expectation that he would have idealised the instrument in his own way, according to whatever evolving ideas were emerging from readings of Vitruvius. If my ideas are true, then they certainly provide a compelling conceptualisation of the anthropomorphic violin which fits well within the architectural, artistic and philosophical ideals of the high Renaissance. It certainly gives a far more meaningful solution to why the words da gamba and da braccio were employed to describe these instruments than the assumptions that you can google at your leisure.
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