Real-Time FPGA and GUI-driven Auralization of Geometry and Material Variations of the Piano
Final Report Abstract
A Finite-Difference Time Domain (FDTD) model of the Grand D piano was implemented on an FPGA device. Additionally, on a Linux system a AGMP software was developed as a Graphical User Interface (GUI) which imports CAD files of piano soundboards or bridges, visualizes them and makes it possible to change all material parameters, like Young’s modulus, density, thickness, internal damping, etc., as well as listening position of the radiated sounds. Also analyzing tools were implemented like the visualization of forced oscillation patterns and eigenmodes, spectra, spectral centroid and other parameters. The system was implemented at the Steinway & Sons R&D department and the users there were instructed how to use the software. They can import new soundboard geometries and use different kind of woods, varnishes, etc. This can be done in single cases as well as calculating a parameter space of varying one parameter in a systematic way. The user can then listen to the sounds at different listening positions, freely chosen by the listener, where typical positions (player, microphones, audience) are implemented as templates. Two Steinway Grand D pianos were measured in the anechoic chamber of the Institute during seven production stages over its frequency range. The two pianos had different material properties as the plancks of the spruce soundboard were different, resulting in considerable different vibration patterns. The recordings were analyzed using different methods, reconstructing transient impulse responses, calculating eigenvalues, calculating forced oscillation patterns, propagating the measurements to the soundboard surface using the Minimum Energy Method (MEM) and calculating sound properties like brightness, Interaural Cross-Correlation, initial transient inharmonicity, etc. Futhermore, after the end of the project the two pianos were compared after one year of playing, considering the differences. The results are partly presented at conferences, still the collected data are so huge that they are still under investigation and part of the PhD of Niko Plath, how was employed on the project doing the measurements. Additionally, a viscoelastic Finite-Difference Time Domain damping model was developed and implemented first in C++ and then on a GPU to test its validity. As damping was considered to be more complex than expected and need to be modeled as a frequencydependent parameter in the future, this model enables to perform such a complex damping behavior as found in wood. Still implementing this model on the FPGA was not part of the application and too complex to also be performed within the time span on the project. Still the results for simple geometries, like a drum and a plain Steinway Grand D piano soundboard showed that the method is valid and should be implemented on an FPGA in the future. To investigate internal damping of wood further in a cooperation with the Thünen Institute of Wood Research in Hamburg, a vacuum tube measurement of piano soundboard wood was performed showing the complexity of internal damping.
