Electro-acoustic control of radiation impedance for brass instrument timbre shaping: design of a vocalizing mute

The application of active control to musical instruments brings many benefits to composers and performers, by expanding their sound possibilities. This paper addresses the active control of a brass instrument to design a vocalizing mute. To this end, a sensor (pressure transducer) and an actuator (loudspeaker) with a feedback loop are placed at the bell extremity. A single-input single-output controller is designed to simulate the insertion of a flow-to-flow vocal filter, upstream of the natural radiation impedance load. The vocal transfer function with its target resonances is basically derived using the transfer matrix method for a vocal tract composed of concatenated acoustic cylinders. The loudspeaker model is based on the Thiele and Small description. Numerical experiments are presented on the controller, for a simplified trombone model that admits a Kelly-Lochbaum structure (mouthpiece, bore, bell and radiation are cascaded using the transfer matrix method). Finally, the sensitivity of the control to air temperature, bell opening angle and loudspeakers parameters is studied.