Periodic Reporting for period 1 - NEMUS (Numerical Restoration of Historical Musical Instruments)
Berichtszeitraum: 2021-07-01 bis 2022-12-31
The conservation and restoration of musical instruments presents multiple challenges. Above all, the need to preserve the documentary evidence of ancient instruments is often prioritised over playability. As a result, most ancient instruments have fallen out of playing condition and will remain so. To give an account of their sound, many museums have been promoting the construction of copies, which only partially solves the problem of preservation since the copies will eventually fall into disrepair if not adequately maintained. The objective of NEMUS – Numerical Restoration of Historical Musical Instruments is to build virtual copies of ancient museum instruments that are currently out of playing condition. The copies will be playable in real-time with a computer and designed using advanced physical modelling principles. The algorithms will solve the complicated system of wave equations describing sound production and propagation in musical instruments, thus offering realistic and sustainable technology to recreate the sound of instruments which will otherwise be lost. The project will also complement organological studies by offering scientific ground to relevant problems, such as the acoustics of harpsichord soundboards. Custom-built soundboards will be purchased and acoustically measured at various stages of construction. The builders will build the soundboards according to various paradigms which have tried to uncover the mystique surrounding antiques. However, no acoustical study has ever been performed to test the response and performance of the soundboards built according to such paradigms. Another important objective of NEMUS is to offer a viable, sustainable way of performing acoustical measurements and simulating harpsichord soundboards. By working directly with world-famous builders and museum curators, NEMUS intends to complement and advance the knowledge about antique keyboard instruments and to offer a digital solution to the problem of conservation of musical instruments. The results of NEMUS will benefit museum curators first, then musicians, museum attendees and whoever wishes to play and record music with the restored instruments. The digital copies will be packaged in plugin form using the most common plugin formats. Using a midi controller, they will be playable within the most common digital audio workstations.
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.
The most remarkable progress during this first part of the project is the efficiency of the new numerical schemes for nonlinear vibration. These allow speedups of over one hundred times compared to previously available schemes, though some properties relating to accuracy and convergence are still being investigated. Some preliminary tests allow to appreciate the goodness of the models produced so far. While the plectra and the soundboard are not considered, a network of strings alone gives a remarkably good-sounding realisation of a stringed instrument.