The field of vibration and modal analysis is a fairly mature engineering field. There are many complex manufactured products which have undergone an enormous amount of vibrational and modal research. Musical instruments could easily be likewise researched and understood, IF, there was the funding. The technology certainly exists as does an understanding of what research would have to be done. It all comes down to there not being any financing for such "scientific" projects.
Many people refer to a process as being scientific if it employs a dogmatic empirical process. However, true science goes beyond carefully controlled empirical observations and experiments and submitts the results to a group of peers for review. I believe that many good luthiers engage in a very well controlled empirical process not unlike a scientist, however, they are generally not involved in peer review etc. and so you can't really call it "scientific".
Many of the accounts I've read on the practices and personalities of succesful luthiers indicates to me that they are dogmatic and empirical in their building process, they carefully controll as many variables as possible and observe specific experiments in a controlled way. It's not science but it is intelligent empiricism.
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