Software to calculate periodic solutions using the harmonic-balance method
Harmbal is a software for computation of periodic solutions by
the harmonic-balance method. It was developed for the study of musical
instruments, and the project was initiated during the post-doctorate
of Snorre Farner at LMA in 2002.
Harmbal is implemented in C with a nongraphical user interface
and should compile on most platforms. It is distributed under CeCILL
(a Gnu GPL-compatible license), which allows anyone to modify and
improve the code for research purposes.
Example of result obtained with Harmbal (via Gnuplot)
The result of computation of the periodic solution of a (nearly)
lossless clarinet model by considering successively 3, 10, 50, and 300
acoustic modes. The result (plotted by Gnuplot) is presented in the
frequency domain (left), and in time domain (right) and compared to
the analytical solution (known in this particular case and called the
The code is available as a compressed "tar" archive:
HARMBAL latest version
- Decompress the archive
Under unix run tar -xvzf
archive.tgz, and under MS Windows, use the Winzip software
Installation in the
documentation describes the complete procedure.
Latest version of the user documentation is available at
Publications based on the use of Harmbal:
- S. Farner and C. Vergez and J. Kergomard and A. Lizée,
Contribution to harmonic balance calculations of periodic
oscillation for self-sustained musical instruments with focus on
single-reed instruments. J. Acoust. Soc. Am., Vol. 119 (3),
2006, pp. 1794-1804: Online version (HAL)
Keywords: harmonic balance principles for autonomous systems
/ structure of the software Harmbal / validation and illustration of
Harmbal capabilities with models of musical instruments.
- C. Fritz, S. Farner, and J. Kergomard. Some aspects of the
harmonic balance method applied to the clarinet. Applied
Acoustics, Vol. 65 (12), 2004, pp. 1155-1180: electronic preprint
Keywords: Harmonic balance method applied to study the
behaviour of the clarinet.
- We wish to thank
Joël Gilbert for his assistance from the beginning of the project,
through stimulating discussions and by giving us his own Matlab code for
harmonic balance computation. The starting point of the project was
the work he carried out in 1989 on harmonic balance method for self-sustained
J. Gilbert, J. Kergomard, E. Ngoya. Calculation of the
steady-state oscillations of a clarinet using the harmonic balance
technique. J. Acoust. Soc. Am. 86, 1989, pp. 35-41.
- The software has been realised with support from the MOSART IHP
network of the EU.
- Centre National de la Recherche Scientifique
- Snorre Farner, postdoc: farner (a) pvv.ntnu.no
- Christophe Vergez, researcher (CNRS, LMA): vergez (a) lma.cnrs-mrs.fr
- Jean Kergomard, researcher (CNRS, LMA): kergomard (a) lma.cnrs-mrs.fr