The design of the instruments "outline"
At this point the outline of the instrument is not yet defined. In order to do so, some solid geometry is required, where the whole idea of construction with dually equal elements between upper and lower part started from. The distance between the baselines at the centre defines the size of an equilateral triangle. The length of the sides of this triangle become a radius, defining the height of the arch. The next step is to construct the longitudinal arc, which is determined by the length of the instrument and the height of the arch at the centre. When this has been carried out, any desired cross section can be constructed as well as the templates for the actual building process, since the height and width between the "base lines" are known at each single point on the longitudinal centreline.
When lower isoline approaches the vicinity of the zero level their outline widens. If 4.5 mm above zero level is chosen as the lowest isoline, this level is almost equal to the thickness of the edge between the C-bouts, the cross-sectional shape of the scoop is determined by the thickness of the edge and the intersecting arch. It is therefore possible for the thickness of the scoop at that particular point to be less than about 3.5 mm (see figure 13). This thickness can, if desired, be slowly decreased to about 1.8 mm att the widest "upper" and "lower" widths, but will at the same time somewhat influence the position of the deepest point of the scoop, the edge and the outline of the instrument. This is shown on the drawing pages, step D, where the geometrically defined arch remaines unchanged. It is up to the violin maker to decide the shape of the scoop, the edge, the form of the C-bout and corners and thus the shape of the outline, all of which can be arranged to suit the violin maker's aesthtic taste. Three different designs for the scoop are shown, demonstration possible variants for the given cross section.
It is obvious that a wider scoop relieves the tension on the intersection point and the possibility to act upon the vibrations of the bridge. This gives the violin maker another possibility to compromise for the properties of the wood in order to accomplish the best possible result. Portions of the outline can be parallel to to the lowest chosen isoline, a line drawn from the end-button and the neck to the widest "lower" and "upper" parts. It is consequently possible for the violin maker to influence these factors, while designing an outline within the strictures of the geometrical model. It is possible to follow an even lower isoline at the "upper" and "lower" parts where the outline of the isoline becomes more square-shaped, because the isoline tends to go in the direction of the baseline,which lies partly outside the outline of the instrument. The more square-like outline of some cellos can therefore be seen as a consequence of these factors, since the edge is proportionately thinner than the violin, and the lowest isoline must assume a more sqare-like shape. These factors also explain why the cello generally has a proportionately narrower scoop than the violin.