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 JS (2002) Reginald Aubrey Fessenden and the birth of wireless telephony. IEEE Antennas Propag Mag 44(2):38–47. https://doi.org/10.1109/map.2002.1003633 – 10.1109/map.2002.1003633
• Quartier L, Meurisse T, Colmars J, Frelat J, Vaiedelich S (2015) Intensity Key of the Ondes Martenot: An Early Mechanical Haptic Device. Acta Acustica united with Acustica 101(2):421–428. https://doi.org/10.3813/aaa.918837 – 10.3813/aaa.918837
• laurendeau, Maurice Martenot luthier de l’électronique (1990)
• Najnudel J, Hélie T, Roze D (2019) Simulation of the Ondes Martenot Ribbon-Controlled Oscillator Using Energy-Balanced Modeling of Nonlinear Time-Varying Electronic Components. J Audio Eng Soc 67(12):961–971. https://doi.org/10.17743/jaes.2019.0040 – 10.17743/jaes.2019.0040
• Falaize A, Hélie T (2017) Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano. Journal of Sound and Vibration 390:289–309. https://doi.org/10.1016/j.jsv.2016.11.008 – 10.1016/j.jsv.2016.11.008
• Falaize A, Hélie T (2016) Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach. Applied Sciences 6(10):273. https://doi.org/10.3390/app6100273 – 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 (2004) Conservation and restoration of electroacoustic musical instruments at the Musée de la Musique, Paris. Org Sound 9(1):87–90. https://doi.org/10.1017/s1355771804000111 – 10.1017/s1355771804000111
• Lopes N, Hélie T, Falaize A (2015) Explicit second-order accurate method for the passive guaranteed simulation of port-Hamiltonian systems. IFAC-PapersOnLine 48(13):223–228. https://doi.org/10.1016/j.ifacol.2015.10.243 – 10.1016/j.ifacol.2015.10.243
• van der Schaft A, Jeltsema D (2014) Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control 1(2-3):173–378. https://doi.org/10.1561/2600000002 – 10.1561/2600000002
• Lopes N, Hélie T (2016) Energy Balanced Model of a Jet Interacting With a Brass Player’s Lip. Acta Acustica united with Acustica 102(1):141–154. https://doi.org/10.3813/aaa.918931 – 10.3813/aaa.918931
• Bonardi A, Barthélemy J (2008) The preservation, emulation, migration, and virtualization of live electronics for performing arts. J Comput Cult Herit 1(1):1–16. https://doi.org/10.1145/1367080.1367086 – 10.1145/1367080.1367086
• Davies H (2001) The Preservation of Electronic Musical Instruments. Journal of New Music Research 30(4):295–302. https://doi.org/10.1076/jnmr.30.4.295.7492 – 10.1076/jnmr.30.4.295.7492
• D’Angelo S, Pakarinen J, Valimaki V (2013) New Family of Wave-Digital Triode Models. IEEE Trans Audio Speech Lang Process 21(2):313–321. https://doi.org/10.1109/tasl.2012.2224340 – 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 (2010) Modeling of the EMS VCS3 Voltage-Controlled Filter as a Nonlinear Filter Network. IEEE Trans Audio Speech Lang Process 18(4):760–772. https://doi.org/10.1109/tasl.2010.2046287 – 10.1109/tasl.2010.2046287
• Maschke BM, Van Der Schaft AJ, Breedveld PC (1992) An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. Journal of the Franklin Institute 329(5):923–966. https://doi.org/10.1016/s0016-0032(92)90049-m – 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 FB (1930) A Study of Noise in Vacuum Tubes and Attached Circuits. Proc IRE 18(2):243–265. https://doi.org/10.1109/jrproc.1930.221993 – 10.1109/jrproc.1930.221993
• Pearson GL (1934) Fluctuation Noise in Vacuum Tubes*. Bell System Technical Journal 13(4):634–653. https://doi.org/10.1002/j.1538-7305.1934.tb04441.x – 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 (1988) Hamiltonian-conserving discrete canonical equations based on variational difference quotients. Journal of Computational Physics 76(1):85–102. https://doi.org/10.1016/0021-9991(88)90132-5 – 10.1016/0021-9991(88)90132-5
• falaize, PyPHS: Passive modeling and simulation in python. (2016)
• rocard, Dynamique générale des vibrations (1971)
• Edson W (1960) Noise in Oscillators. Proc IRE 48(8):1454–1466. https://doi.org/10.1109/jrproc.1960.287573 – 10.1109/jrproc.1960.287573
• Yeh DT, Abel JS, Smith JO (2010) Automated Physical Modeling of Nonlinear Audio Circuits For Real-Time Audio Effects—Part I: Theoretical Development. IEEE Trans Audio Speech Lang Process 18(4):728–737. https://doi.org/10.1109/tasl.2009.2033978 – 10.1109/tasl.2009.2033978
• Yeh DT (2012) Automated Physical Modeling of Nonlinear Audio Circuits for Real-Time Audio Effects—Part II: BJT and Vacuum Tube Examples. IEEE Trans Audio Speech Lang Process 20(4):1207–1216. https://doi.org/10.1109/tasl.2011.2173677 – 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 (1986) Wave digital filters: Theory and practice. Proc IEEE 74(2):270–327. https://doi.org/10.1109/proc.1986.13458 – 10.1109/proc.1986.13458
• Bilbao S (2004) Wave and Scattering Methods for Numerical Simulation. Wiley – 10.1002/0470870192
• Werner KJ, Dunkel WR, Rest M, Olsen MJ, Smith JO (2016) Wave digital filter modeling of circuits with operational amplifiers. In: 2016 24th European Signal Processing Conference (EUSIPCO). IEEE, pp 1033–1037 – 10.1109/eusipco.2016.7760405
• Werner KJ, Bernardini A, Smith JO, Sarti A (2018) Modeling Circuits With Arbitrary Topologies and Active Linear Multiports Using Wave Digital Filters. IEEE Trans Circuits Syst I 65(12):4233–4246. https://doi.org/10.1109/tcsi.2018.2837912 – 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 (2019) Linear Multistep Discretization Methods With Variable Step-Size in Nonlinear Wave Digital Structures for Virtual Analog Modeling. IEEE/ACM Trans Audio Speech Lang Process 27(11):1763–1776. https://doi.org/10.1109/taslp.2019.2931759 – 10.1109/taslp.2019.2931759
• Bernardini A, Vergani AE, Sarti A (2020) Wave Digital Modeling of Nonlinear 3-terminal Devices for Virtual Analog Applications. Circuits Syst Signal Process 39(7):3289–3319. https://doi.org/10.1007/s00034-019-01331-7 – 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 DT (2009) A Review of Digital Techniques for Modeling Vacuum-Tube Guitar Amplifiers. Computer Music Journal 33(2):85–100. https://doi.org/10.1162/comj.2009.33.2.85 – 10.1162/comj.2009.33.2.85
• leipp, Les ondes Martenot ” Bulletin Du GAM No 60 (1972)
• Välimäki V, Bilbao S, Smith JO, Abel JS, Pakarinen J, Berners D (2011) Virtual Analog Effects. DAFX: Digital Audio Effects 473–522 – 10.1002/9781119991298.ch12
• De Sanctis G, Sarti A (2010) Virtual Analog Modeling in the Wave-Digital Domain. IEEE Trans Audio Speech Lang Process 18(4):715–727. https://doi.org/10.1109/tasl.2009.2033637 – 10.1109/tasl.2009.2033637
• Wedepohl LM, Jackson L (2002) Modified nodal analysis: an essential addition to electrical circuit theory and analysis. Engineering Science & Education Journal 11(3):84–92. https://doi.org/10.1049/esej:20020301 – 10.1049/esej:20020301
• Chung-Wen Ho, Ruehli A, Brennan P (1975) The modified nodal approach to network analysis. IEEE Trans Circuits Syst 22(6):504–509. https://doi.org/10.1109/tcs.1975.1084079 – 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 AJ (1987) A Realization Procedure for Systems of Nonlinear Higher-order Differential Equations. IFAC Proceedings Volumes 20(5):85–90. https://doi.org/10.1016/s1474-6670(17)55069-7 – 10.1016/s1474-6670(17)55069-7
• Brockett RW (2015) Finite Dimensional Linear Systems. Society for Industrial and Applied Mathematics, Philadelphia, PA – 10.1137/1.9781611973884
• Cardarilli GC, Re M, Di Carlo L (2009) Improved large-signal model for vacuum triodes. In: 2009 IEEE International Symposium on Circuits and Systems. IEEE, pp 3006–3009 – 10.1109/iscas.2009.5118435
• leach jr, Spice models for vacuum-tube amplifiers. J Audio Eng Soc (1995)