Towards an Explanation of Shape of the Violin
Stanisław Krupowicz · 2017
Skalmierski's theory of stretched violin plates [6] is briefly described.In the course of developing a computer model for the theory, it was necessary to address the geometry of violin plates.Following Skalmierski's theory, various methods of inducing tensions into violin plates were considered.One of the most obvious, assumes that violin ribs are bent "cold", and therefore, preserve their elastic properties.The differential equations governing the large deflection of a bent beam were solved [4] and the resulting deflection curves were scaled up to match the overall dimensions of the original Stradivari violin from 1716, known as "Messiah" [2].Three curves corresponding to the tail, middle and neck parts of the body have been assembled into half of the violin plate outline.The "Messiah" plate outline was sampled and digitized.The two curves were then compared, using various statistical tools.It was found that these two shapes were strikingly similar.The similarity is even greater, if the regions of the side blocks are omitted.The results obtained strongly support the hypothesis that Stradivari bent his violins' ribs "cold", which is in contradiction to the commonly used method in modem violin building.This confirms Skalmierski's theory, since elastically bent ribs produce counteracting forces to the compression forces of the strings.It also offers an explanation of the violin's particular shape -it is the only possible shape yielded by elastically bent ribs.