What's next to do?It ought to be of considerable scientific interest to carry out further experimental investigations into the influence of this special, geometrically defined shell upon its mechanical function, especially after the plates have been glued to the rib and the sound post is put into the instrument stretching all those "elements", like laths in an umbrella distributing tension to the surface. The tension on the umbrella laths are easy to predict, it should be equal in each one and sector surface. The violin shell is much more complicated. Besides the complex shape we have to deal with isotropic material.
Comparing the shape of geometrically defined shells to those made by intuition, I have found no measurable difference using the "Ghladni method" for the "tuning process" on free plates. The euphonious result of my own completed instruments, however, clearly favours shells constructed according to the geometric model. This advantage may well depend upon extremely subtle differences, which are more easily achieved within the disipline imposed by the geometric model.
I have been fortunate in having access to a milling technique which allows isolines to be cut with an accuracy of 0.1 mm (X,Y,Z). The first result resembles a telescope shaped model, which can be adjusted to any desirable height and arched shaped cross section. The surface of the shell is finished using flexible scrapers, and will conform to the geometric model as close as possible.
I strongly suggest that the amount of circumstantial evidence in favour of the model is sufficiently imposing to justify its further analysis using scientifically rigorous methods as are possible by "Finit Element Method" calculations. If this geometric model is the origin accomplished by Leonardo da Vinci it should interest a lot of people to go forward looking for evidence that its function is of vital importance for the quality of sound. The model is extremely amenable both to computerization and to modern milling machinery. I would very much like to be involved in any project and I will answer any proposal or question as well as any point of view to come forward.
References. (1#) Simone F.Sacconi; Die "geheimnisse" Stradivarius, 1981 (2#) Otto Möckel; Die Kunst des Geigenbaues, 1967. (3#) Robert L J Zuger; Violinen, redovisning av en studie av samband mellan geometri, design och funktion, 1987.