A Quantitative Study of Violin Geometry Using Contour Lines

It took around 200 years for the violin family, which dates back to the end of the sixteenth century in Italy, to adopt standard dimensions. Before about 1750, the size of instruments and their names differed from one country to another and from one luthier to another. Once the new standards had been imposed (namely the violin, viola and cello, which are still the current references), luthiers reduced the majority of instruments which stand between two sizes in order to make them fit a smaller size. An important question that arises in musicology nowadays is to determine whether or not an instrument has been reduced, and if so, to quantify how. Testimonies about violin reduction are scarce or imprecise. To our knowledge, very few recent studies have been carried out and were almost only qualitative, which leads us to study the instruments quantitatively. One possible type of reduction consists of removing a wooden slice in the main axis of the instrument and gluing the two halves back together. This reduction has a direct impact on the contour lines. In fact, whereas they are rather circular for an unreduced instrument, they become much sharper and discontinuous at their summit for an instrument reduced at its centre. In this research, we fit contour lines of 38 violins, violas and cellos with parametric equations and attempt to observe quantitative differences between (un)reduced instruments. We aim at developing an AI/classification/visualisation tool to process automatically our data and to observe differences between the two categories. This is not straightforward because the features of the instruments are not unified. A whole spectrum of more or less transformed violins exists for which it is more difficult to quantify the reduction. Some have not been reduced, but simply show deformations caused by the age (the wood warps with time, some instruments have cracked, etc.).