Simulation of an Ondes Martenot Circuit

Authors

Judy Najnudel, Thomas Helie, David Roze, Henri Boutin

Abstract

The ondes Martenot is a classic electronic musical instrument based on heterodyning processing. This article proposes a power-balanced simulation of its circuit, in order to synthesize the sound it produces. To this end, the proposed approach consists in formulating the circuit as a Port-Hamiltonian System, for which power-balanced numerical methods are available. Observations on numerical experiments based upon this formulation allow simplifications of the circuit in order to achieve real-time computation in home-studio conditions.

Citation

• Journal: IEEE/ACM Transactions on Audio, Speech, and Language Processing
• Year: 2020
• Volume: 28
• Issue:
• Pages: 2651–2660
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/taslp.2020.3019643

BibTeX

@article{Najnudel_2020,
  title={{Simulation of an Ondes Martenot Circuit}},
  volume={28},
  ISSN={2329-9304},
  DOI={10.1109/taslp.2020.3019643},
  journal={IEEE/ACM Transactions on Audio, Speech, and Language Processing},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Najnudel, Judy and Helie, Thomas and Roze, David and Boutin, Henri},
  year={2020},
  pages={2651--2660}
}

Download the bib file

References

• Belrose, J. S. Reginald Aubrey Fessenden and the birth of wireless telephony. IEEE Antennas and Propagation Magazine vol. 44 38–47 (2002) – 10.1109/map.2002.1003633
• Quartier, L., Meurisse, T., Colmars, J., Frelat, J. & Vaiedelich, S. Intensity Key of the Ondes Martenot: An Early Mechanical Haptic Device. Acta Acustica united with Acustica vol. 101 421–428 (2015) – 10.3813/aaa.918837
• laurendeau, Maurice Martenot luthier de l’électronique (1990)
• Najnudel, J., Hélie, T. & Roze, D. Simulation of the Ondes Martenot Ribbon-Controlled Oscillator Using Energy-Balanced Modeling of Nonlinear Time-Varying Electronic Components. Journal of the Audio Engineering Society vol. 67 961–971 (2019) – 10.17743/jaes.2019.0040
• Falaize, A. & Hélie, T. Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano. Journal of Sound and Vibration vol. 390 289–309 (2017) – 10.1016/j.jsv.2016.11.008
• Falaize, A. & Hélie, T. Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach. Applied Sciences vol. 6 273 (2016) – 10.3390/app6100273
• couprie, Oskar sala. Observatoire Leonardo des Arts et Techno-sciences (2002)
• glinsky, Theremin Ether music and espionage (2000)
• courrier, Analyse de fonctionnement onde 169. 2012 unpublished document Musée de la Musique (0)
• RAMEL, S. Conservation and restoration of electroacoustic musical instruments at the Musée de la Musique, Paris. Organised Sound vol. 9 87–90 (2004) – 10.1017/s1355771804000111
• Lopes, N., Hélie, T. & Falaize, A. Explicit second-order accurate method for the passive guaranteed simulation of port-Hamiltonian systems. IFAC-PapersOnLine vol. 48 223–228 (2015) – 10.1016/j.ifacol.2015.10.243
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• Lopes, N. & Hélie, T. Energy Balanced Model of a Jet Interacting With a Brass Player’s Lip. Acta Acustica united with Acustica vol. 102 141–154 (2016) – 10.3813/aaa.918931
• Bonardi, A. & Barthélemy, J. The preservation, emulation, migration, and virtualization of live electronics for performing arts. Journal on Computing and Cultural Heritage vol. 1 1–16 (2008) – 10.1145/1367080.1367086
• Davies, H. The Preservation of Electronic Musical Instruments. Journal of New Music Research vol. 30 295–302 (2001) – 10.1076/jnmr.30.4.295.7492
• D’Angelo, S., Pakarinen, J. & Valimaki, V. New Family of Wave-Digital Triode Models. IEEE Transactions on Audio, Speech, and Language Processing vol. 21 313–321 (2013) – 10.1109/tasl.2012.2224340
• dempwolf, Discretization of parametric analog circuits for real-time simulations. Proc 13th Int Conf Digital Audio Effects (DAFx-10) (0)
• pakarinen, Wave digital modeling of the output chain of a vacuum-tube amplifier. Proc 12th Int Conf Digital Audio Effects (DAFx-09) (0)
• cohen, Real-time simulation of a guitar power amplifier. Proc 13th Int Conf Digital Audio Effects (DAFx-10) (0)
• Fontana, F. & Civolani, M. Modeling of the EMS VCS3 Voltage-Controlled Filter as a Nonlinear Filter Network. IEEE Transactions on Audio, Speech, and Language Processing vol. 18 760–772 (2010) – 10.1109/tasl.2010.2046287
• Maschke, B. M., Van Der Schaft, A. J. & Breedveld, P. C. An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. Journal of the Franklin Institute vol. 329 923–966 (1992) – 10.1016/s0016-0032(92)90049-m
• macak, Simulation of Fender type guitar preamp using approximation and state space model. Proc 10th Int Conf Digital Audio Effects (DAFx) (0)
• Llewellyn, F. B. A Study of Noise in Vacuum Tubes and Attached Circuits. Proceedings of the IRE vol. 18 243–265 (1930) – 10.1109/jrproc.1930.221993
• Pearson, G. L. Fluctuation Noise in Vacuum Tubes*. Bell System Technical Journal vol. 13 634–653 (1934) – 10.1002/j.1538-7305.1934.tb04441.x
• muller, Trajectory anti-aliasing on guaranteed-passive simulation of nonlinear physical systems. Proc Int Conf Digital Audio Effects (0)
• deuflhard, Newton Methods for Nonlinear Problems Affine Invariance and Adaptive Algorithms (2011)
• muller, Power-balanced modelling of circuits as skew gradient systems. Proc 21 st Int Conf Digit Audio Effects (0)
• Itoh, T. & Abe, K. Hamiltonian-conserving discrete canonical equations based on variational difference quotients. Journal of Computational Physics vol. 76 85–102 (1988) – 10.1016/0021-9991(88)90132-5
• falaize, PyPHS: Passive modeling and simulation in python. (2016)
• rocard, Dynamique générale des vibrations (1971)
• Edson, W. Noise in Oscillators. Proceedings of the IRE vol. 48 1454–1466 (1960) – 10.1109/jrproc.1960.287573
• Yeh, D. T., Abel, J. S. & Smith, J. O. Automated Physical Modeling of Nonlinear Audio Circuits For Real-Time Audio Effects—Part I: Theoretical Development. IEEE Transactions on Audio, Speech, and Language Processing vol. 18 728–737 (2010) – 10.1109/tasl.2009.2033978
• Yeh, D. T. Automated Physical Modeling of Nonlinear Audio Circuits for Real-Time Audio Effects—Part II: BJT and Vacuum Tube Examples. IEEE Transactions on Audio, Speech, and Language Processing vol. 20 1207–1216 (2012) – 10.1109/tasl.2011.2173677
• cohen, Modélisation, analyse et identification de circuits non linéaires: Application aux amplificateurs guitare à lampes pour la simulation en temps réel. Ph D dissertation Informatique Télécommunications et Électronique Université Pierre & Marie Curie-Paris 6 (2012)
• Fettweis, A. Wave digital filters: Theory and practice. Proceedings of the IEEE vol. 74 270–327 (1986) – 10.1109/proc.1986.13458
• Bilbao, S. Wave and Scattering Methods for Numerical Simulation. (2004) doi:10.1002/0470870192 – 10.1002/0470870192
• Werner, K. J., Dunkel, W. R., Rest, M., Olsen, M. J. & Smith, J. O. Wave digital filter modeling of circuits with operational amplifiers. 2016 24th European Signal Processing Conference (EUSIPCO) 1033–1037 (2016) doi:10.1109/eusipco.2016.7760405 – 10.1109/eusipco.2016.7760405
• Werner, K. J., Bernardini, A., Smith, J. O. & Sarti, A. Modeling Circuits With Arbitrary Topologies and Active Linear Multiports Using Wave Digital Filters. IEEE Transactions on Circuits and Systems I: Regular Papers vol. 65 4233–4246 (2018) – 10.1109/tcsi.2018.2837912
• olsen, Resolving grouped nonlinearities in wave digital filters using iterative techniques. Proc 19th Int Conf Digital Audio Effects (DAFx-16) (0)
• Bernardini, A., Maffezzoni, P. & Sarti, A. Linear Multistep Discretization Methods With Variable Step-Size in Nonlinear Wave Digital Structures for Virtual Analog Modeling. IEEE/ACM Transactions on Audio, Speech, and Language Processing vol. 27 1763–1776 (2019) – 10.1109/taslp.2019.2931759
• Bernardini, A., Vergani, A. E. & Sarti, A. Wave Digital Modeling of Nonlinear 3-terminal Devices for Virtual Analog Applications. Circuits, Systems, and Signal Processing vol. 39 3289–3319 (2020) – 10.1007/s00034-019-01331-7
• bogason, Modeling time-varying reactances using wave digital filters. Proc 21st Int Conf Digit Audio Effects (DAFx-18) (0)
• Pakarinen, J. & Yeh, D. T. A Review of Digital Techniques for Modeling Vacuum-Tube Guitar Amplifiers. Computer Music Journal vol. 33 85–100 (2009) – 10.1162/comj.2009.33.2.85
• leipp, Les ondes Martenot ” Bulletin Du GAM No 60 (1972)
• Välimäki, V. et al. Virtual Analog Effects. DAFX: Digital Audio Effects 473–522 (2011) doi:10.1002/9781119991298.ch12 – 10.1002/9781119991298.ch12
• De Sanctis, G. & Sarti, A. Virtual Analog Modeling in the Wave-Digital Domain. IEEE Transactions on Audio, Speech, and Language Processing vol. 18 715–727 (2010) – 10.1109/tasl.2009.2033637
• Wedepohl, L. M. & Jackson, L. Modified nodal analysis: an essential addition to electrical circuit theory and analysis. Engineering Science & Education Journal vol. 11 84–92 (2002) – 10.1049/esej:20020301
• Chung-Wen Ho, Ruehli, A. & Brennan, P. The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems vol. 22 504–509 (1975) – 10.1109/tcs.1975.1084079
• (0)
• holters, Physical modelling of a Wah-Wah effect pedal as a case study for application of the nodal DK method to circuits with variable parts. Proc 11th Int Conf Digital Audio Effects (DAFx) (0)
• cohen, Measures and parameter estimation of triodes, for the real-time simulation of a multi-stage guitar preamplifier. (0)
• koren, Improved vacuum tube models for Spice simulations. Glass Audio (1996)
• (0)
• 6F5 typical operating conditions and characteristics. (0)
• van der Schaft, A. J. A Realization Procedure for Systems of Nonlinear Higher-order Differential Equations. IFAC Proceedings Volumes vol. 20 85–90 (1987) – 10.1016/s1474-6670(17)55069-7
• Brockett, R. W. Finite Dimensional Linear Systems. (2015) doi:10.1137/1.9781611973884 – 10.1137/1.9781611973884
• Cardarilli, G. C., Re, M. & Di Carlo, L. Improved large-signal model for vacuum triodes. 2009 IEEE International Symposium on Circuits and Systems 3006–3009 (2009) doi:10.1109/iscas.2009.5118435 – 10.1109/iscas.2009.5118435
• leach jr, Spice models for vacuum-tube amplifiers. J Audio Eng Soc (1995)