MAKING MATTERS

Points of interest to violin and bow makers

Steve Sirr and John R. Waddle use CT scans to examine the internal air volume of 20 Cremonese violins, and make a surprising discovery about the soundpost position

FIGURE 2 The area beneath the curve represents the internal air volume for the ‘Betts’ violin. Note the ‘soundpost notch’, which exactly divides the violin’s internal air volume into two equal parts.

Since we performed the first CT scan of a violin in 1987, the non-invasive procedure has become standard practice in the study of bowed stringed instruments. In our previous articles we have used CT scans to examine various instrument properties such as the wood density, mass and volume. Others have written about the possible design of the parts of the instruments, including geometric and proportional systems. Now we turn our attention to air.

One could say that a violin has no measurable air volume, as the f-holes form openings in the top. However, if we ignore that for study purposes and pretend that there are no f-holes, we can find a value for the interior air volume.

This is done by making CT ‘slices’ showing an instrument’s lateral crosssection, each of which has a thickness of 0.5mm (figure 1). We then calculate the area of each slice, subtracting everything but the air: the front and black plates, ribs, blocks, linings, soundpost, bass-bar and any repair work. We then multiply the remainder by the slice thickness to find the internal air volume of each slice in cubic centimetres.

THE ‘SOUNDPOST NOTCH’ APPEARS AT THE EXACT MIDPOINT OF THE INTERNAL AIR VOLUME

Figure 2 shows a typical profile curve for a violin’s internal air volume, in this case the 1704 ‘Betts’ Stradivari. CT slice number 1 was taken from the bottom of the violin, while number 683 was taken from the top. Making graphs such as this allows us to compare instruments in terms of the amount of air volume and its internal distribution: interior features such as the bass-bar and corner-blocks can all be detected in the curves of the graph. Then the instrument’s internal air volume can be determined by measuring the area beneath the curve, which in the case of the ‘Betts’ works out at 1,991cm 3 .

3.2cm³

FIGURE 1A Internal air area measurement for the widest upper bout of the 1704 ‘Betts’ Stradivari (64.3cm 2 ). The CT slice thickness is 0.5mm and hence the CT slice volume is 3.2cm³.

2.3cm³

FIGURE 1B The air area of the narrowest middle bout is 45.4cm², so the slice volume is 2.3cm³.

4.1cm³

FIGURE 1C The air area of the widest lower bout is 82.3cm², so the slice volume is 4.1cm³.

Table 1 shows the internal air volumes of 20 old Italian violins, ordered by date. The average internal air volume for violins crafted by the Amati family is 1,819cm 3 +/-138. For Antonio Stradivari the figure is 1,972cm +/-71, while for ‘del Gesù’ it is 1,882cm +/-83. The violins with the greatest internal air volumes are both Stradivaris: the 1714 ‘Jackson’ (2,062cm 3 ) and 1734 ‘Willemotte’ (2,060cm 3 ). Conversely, the violins with the smallest internal air volumes are both by the Amati family: the 1609 Girolamo Amati (1,586cm ) and the 1574 Andrea Amati (1,673cm )

Many, if not most, old Italian instruments will have changed in the past 300 years. Rib structures may not be exactly as they were when new. Blocks may not be original, bass-bars may have been replaced, and plate thicknesses may have been altered.

Nevertheless, having created internal air volume graphs for each of the violins in Table 1, we noticed a curious feature that seems to be consistent. Each graph contains a ‘notch’, a small dip in volume caused by excluding the wood of the soundpost. On figure 2 this can be seen between slices 287 and 297. What is interesting is that this ‘notch’ appears at the exact midpoint of the internal air volume: the area of the graph to the left is precisely equal to that of the right. This location also corresponds to what Andrew Dipper calls the ‘focal axis’ in his analysis of Cremonese archings (see The Strad, October 2020). Not only is this phenomenon true of all the violins included in this study, but we have also noticed the same feature in violas and cellos. We believe that this feature may have been intentional.

TABLE 1 Internal air volumes of 20 Cremonese violins crafted by the Amati family, Antonio Stradivari and Guarneri ‘del Gesù’ between 1560 and 1742

What is the practical impact of this new information? We believe the unique relationship between the focal axis and the internal air volume played an important role in the construction of early Cremonese violins. We also hope that acoustical scientists studying bowed stringed instruments will reveal more information regarding this relationship. The effect it may or may not have had on the way an instrument functions, practically or tonally, is a very complex issue and we will leave those questions for further study.