Digital Culture & AudioVisual Challenges

Summary
Scope of this research is to construct a virtual musical instrument using physical modelling techniques, while input data are provided by the simulation of the mechanical behaviour of the instrument. A musical instrument is a mechanical structure, which behaviour is simulated using finite elements method (FEM). FEM simulation can be applied for every different way of playing the instrument in order to produce a musical note. The simulation results include the modes of vibration of the sound-generating parts that characterise the instrument timbre. Timbre is generally depicted by the sound spectrogram that contains fundamental and harmonic frequencies as well as their amplitude. This data is inserted into a physical modelling algorithm and the result is the musical note that corresponds to the FEM data. Repeating this procedure the complete instrument playing length can be recorded for further application; for example somebody could “play” the instrument using a MIDI keyboard of a ICT application.

Objective
Musical Instruments are maybe the most ancient if not the most significant interface between arts and engineering. They appeared in human communities even from primitive establishments and continue to be present importantly until nowadays. Artistically they play dominant role in music composition and performance. Technically they represent one of the most complicated and poly-parametric mechanical structures ever made.
The aim of the present work is to construct a virtual musical instrument that simulates a physical one. The motivations that triggered this are mainly two: First the necessity to reproduce the sound of important musical instruments that are nowadays kept in museums or collections in a so-called static way, i.e. nobody could actually hear their sound. Secondly, to give the possibility to everyone that wants to obtain a special and/or specific musical instrument to build it taking decisions about the materials selection and geometrical design and listen to the sound that the instrument can generate. Thus, the desired instrument can be manufactured following the final design decision, ensuring that the result is quite near to the desirable and at the same time by decreasing the manufacturing costs and time as well as the materials wasted. Above motivations are added to the initial one that is the hunger of musicians, composers and any other concerns with electronic musical instruments, for better digital instruments.

Method
A two-steps procedure is followed in order to achieve the above mentioned aim, structural analysis and physical modelling. In order to simulate the structural behaviour of a musical instrument, finite elements method (FEM) is chosen. FEM solves numerically the partial differential equations describing structural problems. In our case the problem to be solved is the sound generation from either vibrating strings-plates systems in addition to a Helmholtz resonator, or from vibrating air columns inside a mostly cylindrical tube. The first system corresponds to a string instrument, while the second to a wind instrument. Applying FEM the results include the vibration modes (eigenmodes) and frequencies (eigenfrequencies) of the vibrating systems. Eigenfrequencies calculations include the magnitude in which they appear in the simulated vibration. The next step is to use the FEM results as input data in a sound synthesis algorithm to generate sound.
“The motto of physical modelling synthesis is that when a model has been designed properly, so that it behaves much like the actual acoustic instrument, the synthetic sound will automatically be natural in response to performance”[1]. Trying to comply with this motto, it was concluded that the best way to design properly a musical instrument is to follow the above mentioned FEM simulation. Having completed the structural analysis resulting in the instrument spectrogram, the last is introduced into any sound synthesis algorithm. The result is the sound of the individual musical note that corresponds to the structural analysis data.
In this case the above described method was applied in a flute in order to synthesize a set of musical notes. Results are compared to the experimentally measured ones.

Conclusions
Design and construction of a virtual musical instrument with maximum correspondence to an acoustical one has been described. FEM numerical method was applied in order to build the instrument spectrogram for each musical note of a set of notes produced by a flute. Then those spectrograms become the input for physical modelling algorithms sound synthesis and the sound results are compared to experimentally measured data.

Reference
1. Välimäki, V., Pakarinen, J., Erkut, C. and Karjalainen, M., “Discrete-Time Modelling of Musical Instruments”, Rep. Prog. Phys., vol. 69, no. 1, 2006, pp. 1-78