Complete 3D Finite-Difference Time Domain Model of the Classical Guitar

taking different kinds of vibration and couplings between guitar parts into consideration

simulates the sound of a guitar, where all parameters, like geometry, material constants, couplings, etc. can be freely changed.

While the eigenmodes of the guitar are present when the body is vibrating for itself and when the guitar is not plucked

the forced oscillation patterns appear when the guitar is plucked. They are much more complicated, as measured with a microphone array show

The forced oscillation patterns of the same frequency do also depent on the driving point, so on the plucked string

The different guitar parts have different roles in the overall sound of the instrument. This is true for the steady-state as well as for the initial transient.

Digital Guitar Workshop is a free software developed during a project funded by the Deutsche Forschungsgemeinschaft (DFG). It shows geometries and microphone array measurements of many classical guitars, allows to built a new guitar and uses a simplified Finite-Difference model to calculate the resulting sound when plucking strings.

The calculated radiation of classical guitars in the surrounding space are complex and can be calculated from measurements of the vibrating body

Papers and Books on this and much more

Bader, R.: Computational Mechanics of the Classical Guitar. Springer, Heidelberg 2005.

Computational Mechanics of the Classical Guitar

Bader, R..: Nonlinearities and Synchronization in Musical Acoustics and Music Psychology. Springer Series Current Research in Systematic Musicology, Vol. 2, Springer Heidelberg , 2013.

Nonlinearities and Synchronization in Musical Acoustics and Music Psychology

 

Bader, R.: Radiation characteristics of multiple and single sound hole vihuelas and a classical guitar. J. Acoust. Soc. Am. 131 (1), 819-828, 2012.

Bader, R.: Characterization of guitars through fractal correlation dimensions of initial transients. In: J. of New Music Research, 35 (4), 323-32, 2008.

Bader, R.: Characterizing Classical Guitars Using Top Plate Radiation Patterns Measured by a Microphone Array. Acta Acustica united with Acustica 97, 830-839, 2011.

Bader, R.,  Richter, J., Münster, M. and Pfeifle, F.: Digital Guitar Workshop – A Physical Modeling Software for Instrument Builders. In Proceedings of the Third Vienna Talk on Music Acoustics, edited by Alexander Mayer, Vasileios Chatziioannou, and Werner Goebl, 266–266, 2015.

Richter, J., Münster, M., Bader, R.: Calculating guitar sound radiation by forward-propagating measured forced-oscillation patterns, Proc. Mtgs. Acoust. 19, 035002, 2013.

Münster, M., Richter, J., Bader, R.: Eigenvalue shapes compared to forced oscillation patterns of guitars, Proc. Mtgs. Acoust. 19, 035001, 2013.

Bader, R.: Real-time guitar radiation sound synthesis of forced string and body eigenfrequency vibrations using microphone array techniques. JASA 125, 2515, 2009.

Bader, R.: Fine tuning of guitar sounds with changed top plate, back plate and rim geometry using a whole body 3D Finite-Difference model. In: Forum Acusticum joined with American Acoustical Society Paris 08, 5039-5044, 2008.

Bader, R.: Complete Geometric Computer Simulation of a Classical Guitar. Lay-Language paper of the American Acoustical Society 05,  2005.

Bader, R.: Nonlinearities in the sound production of the classical guitar. In: Proceedings of the Forum Acusticum 2005, 685-689, 2005.

Bader, R.: Physical model of a complete classical guitar body. In: Proceedings of the Stockholm Music Acoustics Conference 2003, R. Bresin (ed.) Vol. 1, 21-124, 2003.

Bader, R.: Physical model of a complete classical guitar body. In: Proceedings of the Stockholm Music Acoustics Conference 2003, R. Bresin (ed.) Vol. 1, 21-124, 2003.