An Unsuspected Function of the Violin's Pegbox.

​

 

In the process of making a violin, when the time comes to position the pegs, the luthier refers to old models and ways. However, how exactly was their placement originally calculated?

 

Of course, one must take into consideration the practical use of the tuning pegs: they should allow the player to have enough room to tune the instrument comfortably. But is this the only criteria on which we should base their positioning?

​

Proportions

​

The violin maker usually calculates the afterlength (the distance between the bridge and the tailpiece) to 1/6 of the vibrating string length in order to optimize the overall timbre.

​

I realised that the distance from the D peg to the top nut is the same as that of the afterlength, i.e., also equal to 1/6 of the vibrating string. Harmonic relations between the vibrating string section and the peg-box section can also be found for the other strings, see Figure 1, in which the relations for the Stradivari “Messiah” are shown. The G string peg-box section shows a 1/20 relation, the A string slightly longer than 1/5, and the E string 1/10.

 

The length from the A peg to the top nut is often slightly longer than 1/5 of the vibrating string. It is likely that the usual measurement has been modified in order to accommodate more space for the player to manipulate both the A and the D pegs.

But here is another observation: when the placement of the A peg is low and the string touches the D peg, the latter acts as a nut. The distance between the A string touching on the D peg and the top nut again equals to 1/6 of the vibrating string length.

 

Even if the Baroque string length is taken as reference, the proportions are still approximately the same, as the length of the pegbox string section should vary from 0,5 to 1 mm compared with the modern string length .

 

The idea to build a string instrument in such a way that the unused string sections are in a harmonic relation to the main section is also realized in the Steinway grand pianos, for example, see the study of Öberg and Askenfelt*. In Steinways, this is called “duplex stringing”.

 

* Öberg, F. und Askenfelt, A.: Acoustical and perceptual influence of duplex stringing

in grand pianos. Journal of the Acoustical Society of America, 131:856–871, 2010.

​

From the present discoveries, it seems that the violin used a very similar approach to stringing already at the beginning of its conception.

​

The positioning of the pegs, however, varies slightly depending on the individual instrument. Moreover, when this concept is applied, the G peg might look abnormally high in the pegbox. Some have been bushed and placed lower.

​

In any case, on the well-preserved Amati and Stradivari instruments, it is quite clear that the positioning of the pegs follows the described principle of proportions.

 

 

​