Ircam - Centre Georges-Pompidou Equipe Analyse/Synthèse

Comparison of real trumpet playing, rubber model of lips and computer model: benefits for a real-time computer instrument

Vergez Christophe vergez@ircam.fr

to appear in ICMC97, Thessaloniki, Grece, September 1997

Abstract

For several years, we have been developing and studying computer simulated models of brass instruments including the player's lips. The recent improvements concern the simulation of the bore, lip movements and dynamics, air flow through the lips, computation of noise-components and real-time playing interface. Moreover, to better understand the physics of real lips, we have built a rubber model of the lips and analysed its behavior when air pressure is applied as in trumpet playing conditions. The study of the rubber model has inspired some of the new developments of our computer model. We present all of these developments and demonstrate the new real-time model thus obtained. Interesting theoretical results, as well as remarkable sonic results, have been obtained with the rubber and the simulated models. The simulated model consists of one mass, representing the upper lip, which is nonlinearly coupled to a linear model of bore. We represent the bore by its reflection function. In order to obtain such a reflection function, we have carried out measurements of complex input impedances of trumpets in a full anechoic room. Obtaining the reflection function from the input impedance is not as simple as the definition would suggest. The complete numerical procedure includes reconstruction of the whole hermitian symmetrical spectrum, parasitic oscillation minimisation, phase rotation and fulfillment of continuity and causality conditions. The reflection functions thus obtained are processed to be used in the real-time model accounting for different valves positions. We present a low-cost implementation of bore length changes induced by valve position changes. Concerning the lips, the details of aeroacoustic and acoustic phenomena are not well understood. To introduce significant improvements in these domains, we felt the need for precise experiments and measurements on a real instrument. Therefore we have built a rubber model of the lips blown by a plexiglass mouth and coupled with a real trumpet. The mouth pressure, the mouthpiece pressure and the pressure in the instrument have been measured as well as the lip aperture. From these measures, we estimate the nonlinear coupling between the lips, the air flow and the mouthpiece pressure and compare the results with the coupling implemented in our model. We have also studied the question of the point where the flow separates from the lips. We include this feature in the real-time model and study its consequences. To better reproduce attack transients, we have recorded trumpet players and analysed their attack transients. The real-time model has been optimised, including a more realistic lip collision model. Furthermore, we found some interesting features related to the basic behavior of brass instruments, in particular to the role of the various forces acting upon the lips. Recordings also show a periodic component and a non-periodic component which can be considered as a random signal heard as "noise". A study of turbulent noise signals generated by air flow through a slit has been undertaken in our team. They exhibit noise spectral densities with characteristic shapes and amplitudes as predicted from theoretical considerations. Similar noise spectral densities are observed in our trumpet recordings. According to these findings, we have included a turbulent noise component in our model with successful results. An important aim of our work is the understanding of the behavior of the models and the control of this behavior for musical applications. In previous works we have shown that the Hopf theorem can be applied on a simplified model to prove that the system possesses a unique stable periodic orbit when the fixed point becomes unstable and that the characteristics of the oscillating solution are predictable. We show how the conditions required to apply the Hopf theorem are fulfilled in the improved models. This means that the improved models can be kept under control. Finally, we have developed a user interface and worked towards improving the ease of use, expressivity and flexibility which are essential from a musical point of view. The player can modify many parameters by using a MIDI saxophone, three foot pedals, a keyboard, as well as a graphic user interface. The real-time implementation will be presented and demonstrated.