ALL SET UP AND READY TO GO

COURTESY JOSEPH CURTIN

The evolution of the violin is often told in heroic terms: a sudden emergence in the early 1500s, an ascent to perfection at the hands of Stradivari and Guarneri ‘del Gesu’, then a rapid decline followed by centuries spent trying to recapture what was lost. A more reasoned view is that the structural and acoustical development of the violin continued and even accelerated throughout the 19th century, with radical changes to the neck, fingerboard, tailpiece, bass-bar and bridge. Granted, these were changes to the set-up rather than the violin proper, but it was just these changes (along with equally radical ones to the bow) that enabled the spectacular flowering of violin music that now forms the bulk of the standard repertoire. This article focuses on the tailpiece and fingerboard. While these are arguably of secondary importance to the sound of the violin, such is the nature of the instrument that studying even its most straightforward components can feel like taking the back off a watch to ponder the jewelled complexities within.

FIGURE 1 Sound radiation measurements for a violin with a lOg lump of modelling clay atop its bridge (blue line), then moved back 2.5mm (red), 5mm (green), and 10mm (purple). Subsequent positions of 20, 30, 40, 50mm, and atop the tailpiece saddle itself, are all in black. Measurements were taken by tapping the bass corner of the bridge horizontally with an impulse hammer, and recording the response from seven different microphone positions. Each curve represents the real average of all seven positions. For clarity, the curves have been smoothed with a quartertone running average. The horizontal lines represent averages over four frequency bands.

TAILPIECES

In that spirit, let’s start with a basic question. Why does a violin have a tailpiece? The strings could, after all, be attached to the lower saddle somehow. One possible reason is a reduction in the overall length of the strings, and so their overall cost. A tailpiece designed with this in mind might extend right up to the bridge, but this would immediately create a new problem: for the bridge to vibrate, it would have to drag the tailpiece back and forth, and the tailpiece would act as a giant mute. The muting could be offset by leaving some space between bridge and tailpiece. The question becomes, how much?

This is best answered experimentally. Figure 1 shows how a violin’s sound output changes when a 10g lump of modelling clay is placed on the bridge and then moved back incrementally along the afterlengths. With the mass on top of the bridge, there are devastating losses across the spectrum – as one might expect from a practice mute. Moving it back just 2.5mm restores much of the instrument’s treble output, but leaves the bass attenuated. At 5mm the treble has fully recovered (and is even slightly enhanced), and the bass is partway there. At 20mm the entire spectrum is back, with only slight changes at 30, 40, and 50mm, and directly on top of the tailpiece saddle. It seems that the standard afterlength of 54.5mm is quite sufficient to prevent muting by the tailpiece.

If the best that can be said of the tailpiece is that it doesn’t mute the violin, why not get rid of it altogether? It is sometimes said that the length of string behind the bridge affects the overall string tension. In fact the strings could extend several miles behind the bridge with no effect on tension. Bringing the strings up to pitch, however, would then mean winding in hundreds of yards of slack. This means that the longer the afterlength, the smaller the change in pitch for a given amount of peg rotation.

So, attaching the strings to the lower saddle might make tuning a little easier, especially for the E string. But there would be side effects.

The afterlengths can be thought of as sympathetic strings set into motion by bridge vibration. The distance between the bridge and lower saddle is typically almost half the overall string length. One can therefore imagine a saddle design that places the afterlengths an octave and a major 2nd above the open strings – i.e. at A, E, B, and F sharp above the first harmonics. Their combined resonance might be a welcome addition to the overall mix – if only it were possible to keep them in tune.

Unfortunately, friction prevents the strings from sliding freely over the bridge, so there is no guarantee that tuning the open strings would also tune the afterlengths. Any rocking forward of the bridge would only make things worse. Given that players use the ringing of the open strings as a reference for intonation, a set of mistuned sympathetic strings in the middle of the playing range would do no one any favours.

A tailpiece sidesteps the issue by keeping the afterlengths short. The current standard represents one sixth of the string length, which tunes the afterlengths to the notes at the very end of the fingerboard, two octaves and a 5th above the open strings. This high up, the ring time is short, and it is further shortened by damping from the string wrappings. If you flick the bass corner of the bridge with your fingernail, you will hear a resonant thud (the response of the violin body) along with the ringing of the open strings. If you damp the open strings with one hand and flick the bridge again, you will hear the same thud, but with no appreciable ringing of the afterlengths.

Lest anyone become preoccupied with getting the afterlengths precisely in tune, any attempt to do so is foredoomed. Apart from the problem of friction at the bridge, the fact that the G, D, A, and E strings are of differing tensions means that the tailpiece gets pulled off-centre, leaving the afterlengths shorter on the treble side. Without some kind of adjustable saddle, only one afterlength can be perfectly in tune. And to what end? Even an expert player would be hard pressed to tell the difference. A primary function of the tailpiece is, I believe, to make the afterlengths musically irrelevant.

FIGURE 2 An afterlength one sixth of the string length allows the space between the tailpiece saddle and the bridge to match the space between the bridge and fingerboard (+/-2mm). The resulting tailpiece length of 108-110mm matches the distance between tailpiece and fingerboard, and the width of the C-bouts (+/-~2mm).

ALEX SOBOLEV

Still, it is worth asking why makers have settled on one sixth of the string length, rather than a fifth or seventh, or somewhere in between. The reasons are surely aesthetic. As shown in Figure 2 this length allows the space between the tailpiece saddle and the bridge to match the space between the bridge and the fingerboard (give or take a millimetre or two). Moreover, the resulting tailpiece length of 108–110mm matches the distance between tailpiece and fingerboard, the width of the C-bouts, and the length of the scroll (again, give or take a millimetre or two). The violin body is built on these kinds of visual rhythms, and the modern set-up does it full justice.

A PRIMARY FUNCTION OF THE TAILPIECE IS TO MAKE THE AFTERLENGTHS MUSICALLY IRRELEVANT

None of the above implies that length is the only important thing about a tailpiece. Anything that touches a violin – the chin rest, the shoulder rest, the player’s neck, the air in the room – becomes part of its acoustical system. If the room were suddenly filled with helium, there would be measurable changes to the instrument’s acoustical behaviour. When a chin rest is clamped on to a violin, its resonances – or ‘modes of vibration’ – couple with those of the instrument to create a new acoustical system. Whether the change is important or not must be considered on a case-by-case basis.

The tailpiece differs from the rest of the set-up in that it is not glued, clamped, or otherwise held rigidly in place. Rather, it is suspended between the afterlengths and the tail-gut. This allows a series of modes in which the tailpiece behaves like a rigid mass bouncing around on a set of springs. Resonance frequencies are determined by factors such as tailpiece mass, the length of the tail-gut and afterlengths, and string tension. These modes have been described by Bruce Stough (CAS Journal, May 1996) and Ted White (see The Strad Accessories 2012, pages 8–16). The lowest are below 200Hz, and therefore outside a violin’s playing range. The next typically falls between 180Hz to 230Hz, though with a lightweight tailpiece it can approach the frequency of A0. (A0 is a much-studied mode in which the air in and around the f-holes bounces up and down on the enclosed air, typically around 275Hz. A0 is the only mode radiating significant amounts of sound in the instrument’s lowest octave.) When the tailpiece resonance approaches A0 frequency, it splits the A0 radiation peak into two smaller peaks, one higher in frequency than the original, the other lower. Because the tailpiece is far too small to radiate sound at these frequencies, the effect of the coupling might be called ‘parasitic’ – it drains energy from the instrument without contributing to the overall sound output. Moreover, if it falls near the fundamental of a note between the open G and D strings, the response of that note is hampered by the slow rise of the tailpiece resonance. All this can be avoided by dropping the tailpiece resonance frequency below the open G – by using a heavier tailpiece, for example, or by simply adding mass under the existing tailpiece near the G-string slot using tungsten putty.

Figure 3 shows the spectrum of an instrument which, in its initial state, had two peaks on the bass slope of A0. When a 2g mass was added near the G-string slot in the tailpiece, the lowfrequency peak dropped out of the picture, and the A0 peak rose about one decibel. The second split turned out to be a resonance of the chinrest. After a 3g mass was stuck to its underside, A0 jumped up about 3.5dB – a total gain of about 4.5dB.

This kind of parasitic resonance can be used to advantage in suppressing a wolf note – indeed, this is just how most wolf note eliminators work. There is a resonance of the suspended tailpiece lies in the appropriate frequency range, but without specialised equipment there is no easy way to identify and tune it. Faced with a recalcitrant wolf note, however, it’s worth sticking a bit of modelling clay at the centre of the tailpiece (see Making Matters, August 2019), and adjusting it position up or down to see if it helps. White manufactures a tailpiece with a moveable mass on its underside for just this purpose.

FIGURE 3 Violin in its original state (3a); with 2g on the bass corner of the tailpiece (3b), and with an additional 3g underneath the chin rest (3c). These two interventions raise the AO peak more than 4 decibels.

To get a quick sense of the relative importance of the mass of the tailpiece itself, measurements were taken before and after 40g of modelling clay were spread out over the entire tailpiece. This both quintupled the suspended mass (the tailpiece weighed about 10g) and severely damped the tailpiece modes. Figure 4 shows only modest changes to the spectrum. A0 amplitude is increased slightly (presumably because the lowest tailpiece mode has moved well down in frequency), while the B1 modes (two of the so-called ‘signature’ modes) show a slight drop in amplitude. As these modes often cause wolf notes, this could be advantageous to playability.

All the above suggests that it is not the absolute mass or material properties of the tailpiece that are important, but rather the frequencies of the suspended tailpiece modes, and how they interact with the instrument body. A well-adjusted tailpiece is, I believe, one that stays out of the way of A0; leaves sufficient space between bridge and tailpiece to avoid muting; and ensures that any ringing of the afterlengths is musically unobtrusive. If it also manages to suppress a wolf note, that is a bonus.

FINGERBOARDS

The acoustics of the fingerboard seem relatively straightforward compared with the tailpiece. Once it is glued in place, the modes of the free fingerboard are subsumed into those of the assembled instrument. Many of the resulting modes involve at least some fingerboard motion – if just a slight flexing along the neck. But a number involve vigorous activity at the free end. The lowest in frequency is known as ‘B0’, typically falling between 200 and 350Hz. When B0 is excited, the end of the fingerboard flaps up and down like the end of a diving board.

Although the fingerboard (like the tailpiece) is too small to radiate sound at low frequencies, it can do so indirectly by distorting the violin body very slightly during each vibrational cycle. To the extent that these distortions induce a fluctuation in the overall volume of the body, sound will be radiated. This creates a small peak in the radiation spectrum. Its frequency can be shifted (intentionally or otherwise) by changing the mass and/or stiffness of the overhanging portion of the fingerboard, and to a lesser extent by changes to the stiffness of the neck and the mass of the scroll.

THE FINGERBOARD CAN RADIATE SOUND INDIRECTLY BY DISTORTING THE VIOLIN BODY SLIGHTLY DURING EACH VIBRATIONAL CYCLE

FIGURE 4 Sound radiation of a violin with (red) and without (black) 40g of modelling clay blanketing its tailpiece

In the 1990s the American violin researcher Carleen Hutchins proposed tuning B0 to the same frequency as A0, thus splitting the radiation peak. Although the total sound output remains about the same, Hutchins believed that the match lends the instrument a special ‘liveliness’ that players enjoy. German maker Martin Schleske describes instruments with an A0–B0 match as ‘very popular among musicians due to their enhanced playability’ (bit.ly/2ZANfQ2).

Other makers, myself among them, try to keep B0 well away from A0. Thomas Croen of Eugene, OR, US, spent many years refining A0–B0 matching procedures, and wrote an article on the subject in the VSA Journal. Croen finally concluded that his instruments work best with B0 tuned well below A0. Maker Boris Haug, whose interest in fingerboard tuning was spurred by a search for alternative materials, also deliberately avoids matching A0 and B0, but he places B0 above A0 in frequency. Both approaches avoid splitting A0, and effectively relegate the B0 peak to the spectral valleys to either side. Note that there is no published research showing that players prefer either an A0–B0 match or mismatch, or indeed that they can tell the difference either way. Blind testing may one day sort this out.

Violin makers routinely use the tap tones of the top and back as a reference during graduation. Could the lowest mode of the free fingerboard be useful in a similar way? The box (left) shows how to measure this. Schleske found that dividing this frequency by 1.68 gives a reasonably good estimate of the B0 frequency. But whatever your interest in B0, adjusting a fingerboard’s lowest modes also affect the higher ones. In the assembled violin, there are eight modes below 2.5kHz that involve significant fingerboard motion. More research is needed to understand how much the properties of the fingerboard affect the instrument’s playing qualities over a broad frequency range. The need for such research has become pressing as supplies of high-quality ebony dwindle, and makers look for alternative materials.

While judicious adjustments to a tailpiece or fingerboard can sometimes make a notable difference to an instrument, these two elements of an instrument’s set-up cannot be described as sensitive to modification. That is all for the best: it means a fingerboard can be planed, or a mute stowed at the end of the tailpiece, with little risk to the instrument’s tonal balance. The same cannot be said for the bridge. Recent research has underscored its extraordinary role in shaping an instrument’s sound, and this will be the focus of next month’s article.