VIEWS ON THE BRIDGE

BRIDGES

TOP PHOTO PAULINE HARDING. ALL OTHER PHOTOS, GRAPHS AND DIAGRAMS JOSEPH CURTIN

The bridge and soundpost are ground zero for set-up. Where the post is a simple, timeless design – a spruce rod whose important parameters are mainly its length and position, the bridge is a complex structure whose design has changed dramatically over the centuries, and whose important parameters are, after several decades of scientific research, only now becoming clear. This article outlines some of the experiments done at the VSA/Oberlin Acoustics Workshop, and the light they shed on both the evolution of the bridge and the possibilities for optimising violin sound via ‘bridge tuning’.

Because they are so often replaced and then discarded, there is scant evidence charting the bridge’s evolution. That said, the five bridges depicted in Figure 1 suggest a line of development. Comparing the Stradivari bridge (1a) with the Hill bridge (1e), the upside-down heart set beneath the waist of the former has become the upright, blunted heart above the waist of the latter. The Baroque design has, in effect, been inverted – the way the subject of a fugue might be. François Tourte did something similar when he inverted the camber of the Baroque bow and gave us the modern stick. The inversion of the Baroque bridge design allowed the modern bridge to have a relatively narrow waist with a relatively large amount of wood above it. The acoustical implications of this will be a central focus of this article.

Unlike the modern bow, no single maker can be credited with inventing the modern bridge. In the late 1700s, makers in Italy were evidently rethinking the bridge, and came up with so-called ‘transitional’ models (such as 1b and 1c). Although we don’t know the maker of either, the former has an unusually glamorous provenance, having been fitted to Paganini’s ‘Cannone’ Guarneri ‘del Gesù’. According to Alberto Giordano, one of the violin’s caretakers (The Strad, October 2004) Paganini seems to have favoured this bridge, for it remained on the instrument after the neck was reset and the fingerboard replaced. A similar bridge from the museum of the Conservatoire de Paris has a tag that attributes it – albeit unverifiably – to ‘Guarnerius del Gesù’.

PAGANINI’S BRIDGE

This transitional bridge from unknown hands was evidently what Paganini preferred on the ‘Cannone’. It is just 3.6mm thick at the treble foot, 3.2mm at the bass, and weighs 1.8g.

Paganini’s bridge is hardly more than a wooden blank with two slots opening into small, circular kidneys. Gone are the club feet, long ankles and swooping underbellies seen in Baroque designs. We now have two diminutive feet connected by a flat underbelly – and this clears the arching by a scant 2.5mm. What isn’t apparent from Figure 1 (which is not to scale) is how small this bridge is. Its dimensions are given in the box above.

To my eye, transitional bridges have the back-to-the-drawingboard feel of quick sketches, the details to be filled in later. As indeed they were: the 1820 Forster bridge (1d) has a heart in the now-familiar position, and is essentially a modern bridge.

WHY A WAIST?

If one were to ignore tradition and set about designing a violin bridge from scratch, there is no obvious reason to cut a slot in each side of it. The resulting reduction in stiffness makes the bridge more prone to warping, and also allows the treble side to sink over time due to the greater tension on the E-string side. Why, then, are waists universal on bridges from all periods? We did a simple experiment at the 2017 VSA/Oberlin Acoustics

Workshop: a set of bridges were milled from a single block of maple, but with the slot in the waist left uncut. This gave the bridges the approximate lateral stiffness of one with no waist at all. After fitting them to five violins, acoustical measurements were taken. The slots were then cut, and the instruments re-measured. My assumption was that the stiffness of the uncut waist would result in greater treble output. Figure 2 shows how wrong I was. Opening the waist actually increased radiation in the 1–7kHz range. Gains were modest – but if brilliance and power are the goal, a waist seems a step in the right direction.

Alex Currin opening the waist of a bridge

Bridge with uncut slots in waist

FIGURE 2 Averaged sound radiation for six violins fitted with nominally identical bridges, with the slots in the waist uncut (black) and cut (red)

BAROQUE TO MODERN

A second experiment at the 2017 Workshop investigated the tonal differences between Baroque and modern bridges. Two sets of bridges were milled from the same wood – a Baroque model based on Stradivari’s, and a modern design of equal mass. These were fitted to six violins. Figure 3 shows that the modern bridges produced, on average, more sound across the frequency range, particularly above 2kHz. Where the Baroque spectrum has a broad hump centred around 3kHz, the modern has two humps, one centred near 2.2kHz, the other around 4.2kHz. (Note that the ear’s sensitivity peaks at about 3.8kHz.) Not too much should be made of these results, especially since Baroque bridges were intended to go with the shorter bass-bars of the time. Still, this does bolster the commonly held belief that the modern bridge was adopted to increase power and brilliance.

Baroque and modern bridges of equal mass were fitted to each of six violins

FIGURE 3 Averaged sound radiation for six modern violins with Baroque bridge (black) and modern bridge (red)

BRIDGE ACOUSTICS

The bridge is often modelled as a simple resonator: the top portion acts as a mass, and the waist as a spring. The top can vibrate in a number of ways – from side to side (in-plane), towards and away from the fingerboard, and in a variety of twisting motions.

It is in-plane vibration, however, that causes the feet to move up and down, and thus transmits vibration to the top. The lowest in frequency of the in-plane modes involves a side-toside rocking of the top portion about the waist. Its resonance frequency (which will be referred to as ‘f-rock’) is typically in the 2.7–3.4kHz range. The exact value depends mainly on the mass of the top and the stiffness of the waist, which in turn depends mainly on its width. A heavier top and/or a narrower waist will lower the frequency, whereas a lighter top and/or wider waist will raise it. An extreme case is the Baroque bridge. The Stradivari model used in the above experiment had a 20mm waist and relatively little wood above it. F-rock was in the 5.5kHz range.

Well below the resonance frequency, the bridge behaves like a rigid body, allowing the strings to act directly on the top. As resonance frequency is approached, the bridge allows an increasing amount of energy to be drained from the strings, transmitted to the body, and radiated as sound. Above resonance frequency, stringvibration is increasingly reflected back into the strings, effectively decoupling them from the body and reducing sound radiation. All of which suggests that an ability to control f-rock gives the maker a kind of tone-control knob. How much this knob might affect the sound of an instrument was the subject of a landmark experiment.

At the 2003 VSA/Oberlin Acoustics Workshop, a group of makers led by Gregg Alf worked with physicist George Bissinger to investigate the effects of varying both f-rock and overall mass

FIGURE 4A Paris violins with lowest and highest sound radiation

FIGURE 4B Andrea Guarneri average output with four bridges tuned at 2.8kHz (black) and 3.6kHz (red). For clarity, the curves have been smoothed using a semitone window

Violins by Andrea Guarneri (1660) and Gregg Alf (2003) were each fitted with 4 separate bridges, each weighing 2g and tuned to 3.6kHz. By suitable trimming, f-rock was reduced in 200Hz increments from 3.6kHz down to 3.4kHz, 3.2kHz, 3kHz, and 2.8kHz. Mass was also varied from 2g down to 1.88g in increments of 0.04g. Acoustical measurements were made at every step. The results were reported in Bissinger’s paper ‘The Violin Bridge as Filter’ (Journal of the Acoustical Society of America, July 2006).

Reviewing the experimental data a few years ago, I found a problem. The variations in mass were smaller than the margin of experimental error, meaning that mass variations were essentially random. On average, bridge mass remained constant throughout the experiment, +/- 0.1g. This means nothing can be learnt from the study about the effects of varying mass. On the other hand, it does provide a larger-thanplanned data set on the effects of changing f-rock while keeping mass constant. The results are, to my mind, astonishing.

As a reference, Figure 4a compares the sound output levels for two of the twelve violins used in the Paris Experiment (see The Strad, June 2017): the new violin (N5) that had the highest levels of all, and the Stradivari (O3) that had the lowest. The spread between the two curves in Figure 4b is not as wide as for the Paris violins – but this is a single violin (a 1660 Andrea Guarneri) with two different bridge tunings (2.8kHz and 3.6kHz).

Each curve in 4b is the averaged output of the violin with four different bridges, all tuned to the same frequency, and with almost identical masses. Space permitting, much more could be said about this experiment, but these particular results were enough to convince me that bridge tuning is a vastly underused tool.

THE EXPERIMENT’S RESULTS CONVINCED ME THAT BRIDGE TUNING IS A VASTLY UNDERUSED TOOL

MEASURING F-ROCK

A now-standard way to measure f-rock is by clamping the bridge feet into a massive vice and then ‘plucking’ a corner with a fingernail. A smartphone positioned near the opposite corner picks up the sound, and an FFT app (such as FFT by Studio Six Digital) calculates the spectrum. The below photo shows a typical example. F-rock is to the right, at 2.982kHz. The other peaks involve out-of-plane motion, with the bridge bending front to back or twisting about the waist in various ways. To help identify f-rock, pluck in both the in-plane and out-of-plane directions, and see which peaks respond.

Measuring bridges with the ‘FFT’ iPhone app

Because f-rock can be relatively low in amplitude when measured with a microphone, it can get lost in noise or otherwise be difficult to identify. With practice, however, the process becomes almost as straightforward as measuring taptones.

To trust a measurement like this, you need to be able to get the same measurement after removing and remounting the bridge, preferably several times in a row. F-rock is sensitive to how far up the foot the clamp extends, so consistent mounting conditions are essential. To this end, one jaw of the bridgetuning vice (right) has three pins in its face, making it easy to reposition the feet accurately. The other jaw face is angled slightly, complementing the taper of a typical bridge. Because the two bridge feet are not always identical in thickness it helps if the jaw can swivel slightly. The vice should be solid and heavy, otherwise it may have resonances in the frequency range of interest. These can muddle the results beyond recognition.

BRIDGE TUNING

The basic process is to fit a bridge and take it close to its final dimensions, but with the waist left full. F-rock can then be lowered by narrowing the waist. From the Oberlin bridge experiment, reducing the waist by 1mm typically reduced f-rock by about 180Hz. The overall mass barely changed.

To raise f-rock, remove mass from above the waist – by enlarging the heart, for example, or by thinning the top portion of the bridge. F-rock is only slightly sensitive to the thickness of the bridge, front-to-back, so an overall thinning can reduce mass without lowering f-rock. A thin bridge, however, will have a reduced resistance to warping. Note that getting f-rock up to 3.6kHz typically requires an 18mm waist.

WHAT ABOUT MASS?

The average mass of the 800-odd violin bridges listed at the website, www.bridges.uk (an invaluable resource for anyone interested in the subject) is 2g. Individual bridges vary from below 1.5g to 3g – a full doubling of the mass. What difference does this make? Imagine two bridges with identical geometries and resonance frequencies, but one weighing twice as much as the other. The heavier bridge must also be stiffer, or the frequencies wouldn’t match. This heavier, stiffer bridge has a higher impedance – a greater tendency to reflect the vibrational energy from the strings back into them, instead of passing it through to the body, so less sound is radiated. As frequencies rise, vibration involves ever more acceleration, and so mass becomes an ever increasing obstacle. For this reason, changing bridge mass will have the largest effects at high frequencies.

Figure 5 shows sound radiation for a viola with three different bridges, all tuned to the same frequency (2.83kHz), but with masses of 2.7g, 2.4g, and 2g. As mass goes down, sound output increases across the spectrum. As expected, the effect is most pronounced at higher frequencies. This is just a single example, but I believe further research will confirm the trend. The tonal effect of reducing bridge mass might be described as ‘unmuting’ the instrument. Whether this is desirable or not depends very much on the particular instrument and the particular player.

An efficient way to discover the optimal bridge for a particular instrument is to swap out a set of pre-tuned bridges. An ideal reference set would cover the 2.8–3.6kHz frequency range in 100Hz increments, with each frequency represented in a number of different masses. Once the desired mass/frequency combination is found, it’s a matter of making a new bridge to match. In researching this article, we milled three nominally identical copies of Paganini’s bridge, using maple of various densities. They weighed 1.5g, 1.56g, and 1.79g. Their tunings were remarkably close – 2.85kHz, 2.94kHz and 2.83kHz respectively. This suggests f-rock is determined more by bridge geometry than wood properties, and that Paganini’s bridge itself had an f-rock around this frequency.

Did the Old Italians tune their bridges? One can easily imagine them using taptones while graduating tops and backs, though there’s no evidence to suggest they did. Bridge-tuning, however, is virtually impossible without electronic equipment, and it’s a stretch to imagine that early makers somehow intuited the underlying concepts. What they did do was experiment with different bridge designs, and then adopt those that worked best. The very high values for f-rock one tends to get with Baroque bridges helps explain their eventual abandonment. With the modern design, f-rock tends to fall naturally at values that maximize sound output, especially in the range associated with brilliance and projection.

It seems that a small, transitional bridge tuned somewhere near 2.85kHz served Paganini well. On the other hand, a tuning of 3.6kHz got the most sound out of the Andrea Guarneri tested at Oberlin, while a bridge tuned to 3.2kHz did the same for the Gregg Alf violin. All this suggests that a wide variety of bridge tunings – and indeed, bridge designs – are worth considering during the set-up process. Bridge tuning, like plate tuning, is a means to an end and not a quest for some ideal set of values.

Pins in the jaw ensure consistent positioning of the bridge

FIGURE 5 Sound radiation measurements of a 16.25-inch viola with three bridges, all tuned to the same rocking frequency (2.83kHz), but with mass varying from 2.7g (black line), 2.4g (blue), and 2.0g (red). For clarity, lines have been smoothed with a semitone smoothing window