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Simulation of the Ondes Martenot Ribbon-Controlled Oscillator Using Energy-Balanced Modeling of Nonlinear Time-Varying Electronic Components

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Even though digital technology now dominates the audio industry, there is still the need to preserve historic analog machines and instruments. The Onde Martenot, invented in 1928, is an example of a classic electronic musical instrument based on heterodyne processing. This paper describes a simulation of that instrument. In the Onde Martenot, two oscillators generate high-frequency quasi-sinusoidal signals, one of which is fixed and other is controlled by a player using a sliding ribbon. The sum of these two oscillators is an amplitude-modulated signal whose envelope is detected using a triode vacuum tube. That produces an audible sound with a frequency that is the difference of the two oscillators. The triode vacuum tube in the detector is a nonlinear component that adds harmonics to the signal. This paper focuses on using a power-balanced simulation of its ribbon-controlled oscillator, composed of linear, nonlinear, as well as time-varying components. Numerical experiments on the nonlinear time-varying circuit lead to expected observations: (1) the combination of the triode amplification and the LC-resonator produces a quasi-sinusoidal oscillation with a stable amplitude for a static configuration; (2) the mechanical force produced by the variable capacitor due to the ribbon displacement is undetectable by the musician for over-speed movement; and (3) the latency between the instantaneous frequency and the ribbon position is also undetectable. This corroborates that the Martenot s ribbon-controlled circuit is close to an ideal oscillator.

JAES Volume 67 Issue 12 pp. 961-971; December 2019
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