A STUDY IN SCARLET

Jesús Alejandro Torres reports on a study by the Violin Making School of Mexico, in which three copies of Stradivari’s ‘Titian’ violin were made using wood of varying densities, to examine their signature modes and player preferences

FIGURE 1 Fusion of a real copy of the ‘Titian’ Stradivari with its digital version

FIGURE 1 JESÚS ALEJANDRO TORRES

How not to mention their exorbitant prices – but every day we develop more scientific tools that can help us construct new violins with similar performance attributes. As luthiers, we know there is no such thing as ‘the perfect violin’, but when a musician tells us, ‘I want a violin that sounds like this particular instrument,’ of course we can aspire to fulfil that kind of request. This article looks at three violins that have been crafted with this in mind.

For the past few years, the team at the Violin Making School of Mexico’s acoustics laboratory have been performing in-depth studies on how the violin works, focusing especially on the development of scientific tools for luthiers. We capture the violin measurements, process them and make visualisations using our own software, which we have made available for anyone to download for free. We also research the wood’s material properties, and are publishing new experimental techniques for exploring the violin’s behaviour. We hope this will all serve as an aid to luthiers in the violin making process; in any instrument there are countless factors to consider, so any help should be very welcome. Think how difficult it would be to claim: ‘If I do this to the wooden blank, then the finished violin will sound more like this than like that.’ It would be a bit like seeing a cluster of grapes and predicting the exact taste that a wine made using them will have.

But then, how can you reproduce the vibrations of an Old Italian violin on a new instrument? Before answering this question, let us remember it is the vibrations of the wood on the whole soundbox that are the main source of a violin’s sound; and since every piece of wood is unique, so is the sound of each violin. As a consequence, if you are trying to replicate the sound of a violin, there is little point in, for example, trying to copy the exact thickness (unless you have wood samples cloned from the original instrument, which is impossible – at least for now). Each new highquality instrument must be carefully designed on an individual basis, and hence, much of our attention is focused on the vibrational behaviour of the soundbox. This is worth mentioning because, although this knowledge is widely disseminated among acousticians, we have found that without background on the physics of the violin, one tends to overestimate the contribution of the f-holes to the total sound radiated – or even assume it is the only source of the sound in a violin! The sound radiation from the f-holes is mainly relevant at very low frequencies of the violin response, while the vibrations of the wood are responsible for almost all the quality of the violin’s tone.

The three ‘Titian’ copies, made with plates of (left–right) low, medium and high-density wood

ALL PHOTOS JESÚS ALEJANDRO TORRES

Like most acoustic researchers, we use modal analysis to examine the vibrations of a violin soundbox. To summarise the principle in brief: think of a printer with three cartridges, each containing a primary colour. It can generate a wide range of colours by mixing the pigments in the right proportions. If you want to obtain the same range of colours using another printer, you need to employ exactly the same primary colours. Translating this example to vibrating systems, modal analysis delivers mode shapes that are analogous to primary colours. Once the mode shapes of a system are known, you can express the vibrations of the structure as a mixture of them. Accordingly, trying to replicate the mode shapes of an Old Italian violin in a new one seems to be a good strategy to reproduce its sound.

THE VIBRATIONS OF THE WOOD ARE RESPONSIBLE FOR ALMOST ALL THE QUALITY OF THE VIOLIN’S TONE

Nowadays we know much about the mode shapes of Old Italian violins, none more so than the 1715 ‘Titian’. This violin has been scientifically analysed more than any other by far (one can find reports on it since at least 1946), and yielded the most vibratory data of the three instruments used in the 2009 Strad3D project (see The Strad, February 2009, for an account of this research). The ‘Titian’ was therefore selected as the reference for three violins made for the current project. For this, we established a multidisciplinary working group comprising makers, musicians and scientists. It was financed by two Mexican non-profit organisations, the Music, Art and Culture association, and the Art, Science and Technologies programme of the National Foundation for Culture and the Arts. Our main aim was to assess whether the vibrational behaviour of the copies would be similar to that of the original instrument, while also paying attention to their final visual appearance.

FIGURE 2A Signature modes of the original ‘Titian’, experimentally measured for the Strad3D project. Laser sensors scanned the vibrations over a mesh on the whole soundbox. For clarity, the deflections obtained are overscaled.

FIGURE 2A AND 2C IMAGES JESÚS ALEJANDRO TO RRES.

FIGURE 2B Computer simulation showing the signature modes of a virtual version of the ‘Titian’, calculated using the geometry of the original instrument and data regarding its material properties. Deflections are overscaled while the maximum displacements are indicated in red.

FIGURE 2B IMAGES USED COURTESY OF ANSYS, IN C.”

FIGURE 2C Signature modes experimentally measured from one of the copies made for the current project. This data was patiently scanned by moving a small accelerometer, shown in the left image, over the whole soundbox. The mesh obtained by following each measured point was over-deflected to exhibit the deflections for each mode shape.

Computer-aided design (CAD) can be particularly useful in the development of a new violin because the decision making process in this initial stage is crucial in defining the tonal quality of the finished instrument. Essentially, this software allows us to draw the proposed violin geometry in the computer, indicating the material properties of the specific wood to be employed, and choosing the type of analysis to calculate. In 2020 we published a computational algorithm (see bit.ly/31M4Tq7) allowing us to analyse the changes in vibration that are produced by a violin soundbox – based on the ‘Titian’ – as a consequence of variations in the materials, geometry, soundpost location and so on. Then we employed it during the development of the three instruments.

Given the huge capacity for calculation by modern computers, one may assume that every unknown issue about violin design will soon be solved, but this is not the case. Despite all the cutting-edge technology available, machines are incapable of doing anything by themselves. Users will always need a clear view of what must be executed in the computer, and mostly, for what purpose. Achieving this clarity when the violin is analysed is much more difficult than it may appear.

We limited the tuning of each copy to some of their low-frequency mode shapes according to those of the ‘Titian’. More specifically, the modes to be copied were the so-called signature modes: CBR, B1- and B1+ (see figure 2), which have been a source of great concern for acousticians. The CAD software was an invaluable help in the task of tuning the new violins’ signature modes.

In this project, we worked using the traditional woods employed for violin making, but each sample was markedly different from one another. One violin was made using high-density spruce and maple, the second of medium density, and the third of low density.After we had recorded the elastic properties in each of the wooden blanks, we used those values to overwrite the original values of the ‘Titian’ in the computational model to calculate the modal analysis. For this we used Ansys Mechanical APDL 2021 R2 software (downloadable at bit.ly/3kl8mm1). We could then evaluate how close our numerical estimations were to the expected values from the corresponding modal frequencies of the ‘Titian’. Next, we adjusted the thickness of the top and back plates in the simulations to improve the performance. Surprisingly – at least for us – the results suggested that to reach the relatively high frequencies of the ‘Titian’ signature modes, it was the denser wood that required the thicker plates.

However, the holistic conception of these violins implied much more than performing calculations and measurements. We paid attention to the aesthetics and playability of each violin while crafting each one, which resulted in several constructive discussions between scientists and makers. For example, CT scans have revealed that the ‘Titian’ is a markedly asymmetric instrument, but new instruments are usually made symmetrically. Symmetry is even one of the criteria for evaluating instruments in violin making competitions! So this aspect of design presented us with a dilemma.

TO REACH THE RELATIVELY HIGH FREQUENCIES OF THE ‘TITIAN’ SIGNATURE MODES, IT WAS THE DENSER WOOD THAT REQUIRED THE THICKER PLATES

For this and all other disputes, we held to the same principle: musicians must have the last word. In this case, the musicians in our team preferred the asymmetrical design, to obtain an instrument visually closer to the ‘Titian’ in its present form. However, in cases relating to the comfort of the instrument – such as the height of the fingerboard or the thickness of the neck – musicians advised us to modify the specifications measured from the ‘Titian’. To approximate the violin’s iconic orange colour, we performed several tests on small wood samples before applying it to the new instruments.

When the instruments were finished, we tested the vibrations on the soundbox to mimic those performed on the ‘Titian’ for the Strad3D project. Measuring our violins in this manner was quite challenging because we needed to average more than a thousand single tests per violin, each one carefully and patiently done. It meant, though, that the vibratory similarities of the copies could be objectively evaluated by direct comparison with the original instrument data. Figure 2c shows one of the copies being measured with an ultra-miniature vibration sensor – an accelerometer – that is glued below the f-hole on the treble side, while the locations to be scanned were illuminated using a projector with the pattern to be followed. The experimental set-up to measure the ‘Titian’ is also shown in the first row (taken from Polytec Scan Viewer 2.6 software displaying data from Strad3D).

Figure 3 shows the vibratory response of the new violins and ‘Titian’. Generally speaking, the frequency of the peaks corresponding to the signature modes of the copies are in agreement to those of the ‘Titian’. To illustrate this, the response of the ‘Plowden’ violin made by Guarneri ‘del Gesù’ has also been included, to show another Old Italian instrument that shows behaviour closer to the ‘Titian’ than to the copies. (see, for example, the B1+ peak for the five instruments).

On the other hand, do any of our copies sound similar to the ‘Titian’ in practice? It is possible, but we do not know for certain because we do not have the ‘Titian’ violin available for a live comparison. You can hear the Bruch excerpt recorded in the same session with the three violins at bit.ly/3oTLJ9u. Since the ‘Titian’ has very low wood densities, which is very common in Old Italian instruments, we had high expectations for our low-density violin. Our first impression was that this was the best of the three, but obviously we cannot be the most impartial judges of our own work. The Music, Art and Culture Association contacted a number of solo violinists with prominent careers, allowed them to play all three violins for a few days and deliver their opinions. All of them quickly selected the lowest-density violin as the best by far. In addition, one of the soloists played the lowest-density violin in front of an orchestra, followed by his own. He told us: ‘The new violin was unanimously judged better than mine, which is good news for you but not so much for me!’ Another soloist reported that these were ‘three beautifully constructed instruments with outstanding potential. Each one has its own distinct personality, timbre and voice. I am very happy to see that the Violin Making School of Mexico is producing such first-class instruments.’

FIGURE 3 JESÚS ALEJANDRO TORRES

We also noted how interested the musicians were in the instruments’ visual resemblance to the ‘Titian’. Aesthetic details are often ignored by scientists (or at least by the present author before undertaking this project). In this respect, we strongly suggest that anyone trying to copy the sound of an Old Italian violin will also need to put considerable effort into copying its visual appearance.

Of course, many questions continue to emerge about the performance of the three copies. The first issue to be highlighted is that the sound of each one was clearly different from the others. This is not necessarily a surprise because we have three violins of intentionally different woods, forced to have similar mode shapes for low frequencies. While we obtained similar signature modes on all the copies, the consequences of this on middle and high frequencies are still uncertain. The behaviour of the violins in these higher frequencies is being studied in our laboratory through new characteristics in the computational model, as part of an improvement that allows us to generate sound. For the next generations of CAD violins, we are planning to make new instruments based on the ‘Plowden’ violin, also using data from the Strad3D project. ●