The first part of the project focused on developing fast, reliable numerical schemes for the solution of nonlinear vibrating systems. This work is a necessary building block for the rest of the project since developing and understanding virtual, mathematical copies of the instruments cannot be done efficiently without such schemes. For the musical instruments of interest here (such as harpsichords), nonlinearities take many forms. When plucked at higher forces, the string undergoes tension modulation, entailing a range of phenomena not accounted for by linear theory alone. The tension modulation is due to geometric effects and results in relevant perceptual phenomena that must be considered for realistic synthesis. Some previous models (most notably, the Kirchhoff-Carrier model) do consider such tension modulation effects, and reliable schemes existed before the beginning of the project. However, this model was shown to be inaccurate since it neglects the transfer of energy from the transverse to the longitudinal motion. During NEMUS, new, fast schemes have been developed to treat various cases of interest, including that of the vibrating string with geometrically exact nonlinearity (i.e. not approximate, as is the case for Kirchhoff-Carrier) by means of a newly developed technique based on energy quadratisation. These schemes can treat many nonlinearities of interest in acoustics when the nonlinearity is a function of the displacement. Further schemes have been studied during this first part of the project, for which the nonlinearity is a function of the velocity instead. Audio circuits yield a direct application for such schemes, though the bowed string also belongs to this case. This part of the work was done by the P.I. and one of the PhD students. Parallel to the numerical schemes, the PI and the second PhD student have undertaken some preliminary experimental work. A reliable measurement chain is fundamental for the success of NEMUS since the acoustic properties of the soundboards will be measured and assessed. More important work was done to build a network of experts in organology and museum conservation practices, as well as builders, to work more specifically on two case studies. The first will consider a harpsichord built in the ``Ruckers’’ style. While design changes are noticeable in the four generations of the Ruckers lineage, the soundboard design is remarkably similar across builders in this family. The second project intends to investigate more closely a recent acquisition of a non-sounding harpsichord attributed to Alessandro Trasuntino and stored in the San Colombano Museum here in Bologna.
