What actually defines the shape of a violin
At first glance the violin may give the impression that its body consists simply of three parts; an "upper" part near the neck, a "waist" and a "lower" part, all of which fit together in some remarkable way to form a mechanical and aesthetic unit.
It is not easy to precisely describe this shape in words, either in terms of the design of the; "outline", or in terms of the design of the acoustical sufaces; "shape of the shell". It is even more difficult to attempt a rational explanation of this complicated structure. Many authorities have already described the instrument geometrically by a definition of the outline. This is of course one possible approach, but the great number of different outlines fails to bring us any closer to one underlying concept of design and physical function. I assumed that if there are fundamental geometric properties hidden in the instruments original construction, then these would be discernable through a study of the shallow arching of the shell. The shells are the basic primary acoustical surfaces; their arching should therefore reflect any fundamental properties of design, geometrical or physical.
I have found no previous analysis in the literature relating the geometry of the shell to a fundamental and unifying concept of design. If the structure of the violin is based upon a geometric concept then it must be limited only to such primary forms as the circular arc, the square, and the equilateral triangle in order to be practicable to the violin maker.
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