How Do They Work?The Arbutus tailpiece features an adjustable weight system which can be used as part of the instrument set-up process. Violin makers have understood for centuries that the tailpiece affects the tone of the instrument. The tailpiece interacts with the bridge and strings at very specific frequencies. This effect is called impedence matching by physicists. Below 1000 Hz there are five principal frequencies at which this effect occurs.  These correspond to five different ways the tailpiece can move within the constraints of the string after-lengths and the tail cord. The motions can be roughly characterized as swinging or rotating. You can imagine a swing mode by regarding the tailpiece as the seat of a child's swing. As it swings from side to side, both ends of the tailpiece move in the same direction. A rotational mode is more like a child's seesaw; the tailpiece rotates around an axis back and forth, with each end of the tailpiece moving in the opposite direction. The first three modes are swing modes and have frequencies normally below the open G (196 Hz) and are therefore unlikely to affect the tone of the instrument. The last two modes are rotational modes and have their frequencies very close to two very important violin body modes. (Fig. 1) Adjustment of these last modes can have a strong effect on the tone of the instrument.
One rotational mode acts about a vertical axis. When the front of the tailpiece moves toward the bass side the tail cord end moves toward the treble side and vice versa. The other rotational mode acts through a horizontal axis so that, as the front goes up, the end goes down, and vice versa. The frequency of the horizontal mode tends to be little higher than that of the vertical mode. The exact frequencies of the various modes depend on the instrument, the choice of strings, the choice of tail cord, the length of the after lengths and tail cord and, of course, the weight of the tailpiece. In addition, the distribution of the weight of the tailpiece is important. (Fig. 2)
The Arbutus tailpiece has a precisely milled groove in its underside to hold an adjusting weight. Also, the front underside has been carefully milled to improve the fit of fine tuners and to reduce unnecessary weight close to the bridge. The pocket where the tail gut end adjusters would lie has been enlarged for ease of installation. The saddle is made of anodized titanium for both strength and light weight.
The easiest method to install the weight is to insert it into the open end at the bridge end of the tailpiece. Its position can be adjusted by sliding forwards and backwards. The weights can be removed by sliding them forward toward the bridge end until they exit the groove. The tailpiece comes with a 3.0 gram weight. Additional weights are available. These weights can be used individually or together. If the weights are too stiff to slide easily, lubricate them and the groove with little hard soap. If the weight slides a little too freely try using a little beeswax instead.
The easiest way to install weights is before the tailpiece is installed on the instrument. Adjustment can be done by pushing the weight with a small ruler or straight edge laid flat under the tailpiece engaged with the exposed edge of the weight. Use a thin piece of wood to protect the instrument from inadvertent slips.
Violins have several modes that they tend to vibrate most strongly in. There are three modes which are often called the "signature" modes of the instrument. These are:
- A0 - the air cavity mode, around 280 Hz or a little above C# on the G string
- B1- - a strong body mode, around 460 Hz or a little below A# on the A string
- B1+ - a strong body mode, around 550 Hz or a little below C# on the A string
On violins the B1+ mode can cause a wolf note if it lies too close to a playable note. Many of the adjustment strategies makers use are either attempts to shift the resonate frequency of the B1+ mode by structural changes to the instrument; re-graduating, re-barring, etc. or adding damping by attaching weights at various places on the instrument. (So-called "wolf eliminators" for example) Interestingly enough, the natural resonance (in the horizontal rotational mode) of many high quality tailpieces is very close to the B1+ frequency. Since we have to have a tailpiece on the instrument for obvious reasons, it makes sense to take advantage of this fact and design a tailpiece which can be tuned to help reduce or eliminate problems with the wolf.
On an average setup, adjusting the weight will permit about a semitone of adjustment of the rotational tailpiece modes. The best method to do the adjustment is to start with the weight all the way forward towards the bridge. The graph below shows the B1- and B1+ violin modes (in brown) of a real violin and the two rotational modes of the tailpiece (in green) as installed on the instrument with the weight all the way forward.
The violin peak just above 550 Hz is the B1+ mode and the one around 460 Hz is the B1- mode. The tailpiece peak at 630 Hz is the horizontal rotational mode.
If we shift the weight half way along the groove towards the tail cord end we see the following results:
The violin is in magenta and the tailpiece is in red. Notice that the tailpiece resonance is moving downwards in frequency while the violin remains constant. In addition, the horizontal tailpiece mode is now split into two peaks.
If we move the weight further toward the end then we see the following:
In this case the tailpiece is in blue and the violin is in dark blue. The tailpiece horizontal mode has moved even farther downwards and the something very interesting has happened to the violin; the B1+ mode has split into two modes approximately +/- 25 Hz away from the original mode. This pushed the wolf away from C# where it was a problem reduced it to two smaller resonances away from playable notes. The instrument became much more even on the A string with no noticeable wolf.
The modes discussed so far are the motions that the tailpiece makes as a ridged body. At higher frequencies the tailpiece begins to flex in much the same way that the violin flexes. These flexural modes start occurring above 1000 Hz. The graph below shows the weight adjusted in the same three positions as the above examples.
The brown line is the weight forward, the green is the midpoint and the blue is toward the tail cord. The corresponding result for the violin is as follows:
The green line is the weight forward, the magenta is the midpoint and the blue is aft. These effects are subtle but audible to some listeners. Since they generally lie in a region of the response of the violin which has been called "nasal" the possibility exists that, assuming no wolf problems, adjusting the weight may improve the timbre of the instrument by affecting the resonances in this "nasal" region; more work needs to be done in this area.
This work was supported in part by the Natural Sciences and Engineering Research Council of the National Research Council of Canada.
 Stough, B., The Lower Violin Tailpiece Resonances. CASJ Vol. 3, No. 1 (Series II), May 1996.