Regime change thresholds in flute-like instruments: influence of the mouth pressure dynamics

Since they correspond to a jump from a given note to another one, the mouth pressure thresholds leading to regime changes are particularly important quantities in flute-like instruments. In this paper, a comparison of such thresholds between an artificial mouth, an experienced flutist and a non player is provided. It highlights the ability of the experienced player to considerabily shift regime change thresholds, and thus to enlarge its control in terms of nuances and spectrum. Based on recent works on other wind instruments and on the theory of dynamic bifurcations, the hypothe- sis is tested experimentally and numerically that the dynamics of the blowing pressure influences regime change thresholds. The results highlight the strong influence of this parameter on thresholds, suggesting its wide use by experienced musicians. Starting from these observations and from an analysis of a physical model of flute-like instruments, involving numerical continuation methods and Floquet stability analysis, a phenomenological modelling of regime change is proposed and validated. It allows to predict the regime change thresholds in the dynamic case, in which time variations of the blowing pressure are taken into account

Is the jet-drive flute model able to produce modulated sounds like Flautas de Chinos ?

Flautas de chinos - prehispanic chilean flutes played during ritual celebrations in central Chile - are known to produce very particular beating sounds, the so-called sonido rajado. Some previous works have focused on the spectral analysis of these sounds, and on the input impedance of the complex resonator. However, the beating sounds origin remains to be investigated. Throughout this paper, a comparison is provided between the characteristics of both the sound produced by flautas de chinos and a synthesis sound obtained through time-domain simulation of the jet-drive model for flute-like instruments. Jet-drive model appears to be able to produce quasiperiodic sounds similar to sonido rajado. Finally, the analysis of the system dynamics through numerical continuation methods allows to explore the production mechanism of these quasiperiodic regimes.Comment: Stockholm Music Acoustics Conference, Stockholm : Sweden (2013

Flute-like musical instruments: a toy model investigated through numerical continuation

Self-sustained musical instruments (bowed string, woodwind and brass instruments) can be modeled by nonlinear lumped dynamical systems. Among these instruments, flutes and flue organ pipes present the particularity to be modeled as a delay dynamical system. In this paper, such a system, a toy model of flute-like instruments, is studied using numerical continuation. Equilibrium and periodic solutions are explored with respect to the blowing pressure, with focus on amplitude and frequency evolutions along the different solution branches, as well as "jumps" between periodic solution branches. The influence of a second model parameter (namely the inharmonicity) on the behaviour of the system is addressed. It is shown that harmonicity plays a key role in the presence of hysteresis or quasi-periodic regime. Throughout the paper, experimental results on a real instrument are presented to illustrate various phenomena, and allow some qualitative comparisons with numerical results

To what extent can a linear analysis predict the behaviour of a flute model ?

International audienceAlthough they have been widely studied for years, some aspects of the behaviour of flute-like musical instruments remain poorly understood. The study of a physical model of the instrument has demonstrated its interest in the understanding of various phenomena, such as the hysteresis related to regime changes or the variations of the frequency with the blowing pressure. As it involves both nonlinear and delayed terms, an indepth study of the state of the art flute model requires specific numerical methods, which are often computationally expensive. The simplification of the model through its linearisation around a non-oscillating trivial solution is thus particularly interesting, due to the simplicity of the calculations. The information provided by such an analysis in terms of oscillation frequency or oscillation thresholds of the different periodic solutions has been highlighted in previous work . Surprisingly enough, the present study shows that this simple linear analysis provides information about the stability zones of the different periodic solutions (i.e. the different registers), and allows to predict, in some cases, the register resulting from a transient of the mouth pressure. Such information can be obtained without solving the nonlinear equations and without computing the steady-state oscillations of the model

An acoustic model to control an experimental slide flute

International audienceWe consider the problem of modeling and control of a slide flute: a kind of recorder without finger holes but ended by a piston to modify the length of the resonator. To control dynamical systems, it is important to elaborate a realistic model, so that control laws can be tested efficiently before they are implemented on real size prototypes. The dynamical model we have elaborated takes into account the coupling effects between the jet and the pipe which is a linear acoustic resonator. The jet is obtained by blowing through a flue channel and formed by flow separation at the flue exit, and finally directed towards a sharp edge, called the labium. A modal analysis is then performed using the linearized boundary conditions to compute the suitable blowing pressure and the suitable pipe length to obtain a desired pitch. This will constitute the "feedforward" part of our control algorithm. The Proportional-Integral feedback term is then elaborated to regulate the system to the desired set point, using the length of the piston measured by an encoder and the blowing pressure measured by a pressure sensor. First experimental results, obtained on a "mechatronic" prototype developed at Mines ParisTech will be presented

An acoustic model for automatic control of a slide flute

International audienceIn this paper, we consider the problem of modeling and control of a slide flute : a kind of recorder without finger holes but which is ended by a piston mechanism to modify the length of the resonator. A previous study has been done (see [3]), but with a very simple boundary condition for the mouth, corresponding to an ideal situation assuming that the acoustic pressure is zero at the entrance of the resonator. In this work, we have taken into account a more realistic model, describing the coupling effects between the jet and the pipe. The jet is obtained by blowing through a flue channel and formed by flow separation at the flue exit, and finally directed towards a sharp edge, called the labium. The resulting structure can then be seen as a nonlinear oscillator coupled with the pipe which is a linear acoustic resonator. The pressure obtained through this model has been compared to the pressure measured on an actual instrument, a recorder closed at its end. A modal analysis is then performed using the linearized boundary conditions which can also be used to compute the suitable blowing pressure and the suitable pipe length to obtain a desired fundamental frequency or equivalently a desired pitch. This will constitute the basis of our control algorithm. A possible musical application of such a device is to build a flue instrument with a pitch independent of the dynamical level

Experimental Study of Attack Transients in Flute-like Instruments

International audienceThe stationary behavior of flute-like instruments is fairly well understood. Models and experimental studies allow to predict and to understand the influences of the principal parameters (flow velocity, position of the edge, etc) on the sound if these parameters stay constant in time. Depending on the instrument, these parameters can be fixed by the flute maker or by the musician. In musical playing, the musician plays on them to act on the sound. Some parameters can vary rapidly, like during the attack transients. The response of the instruments to these variations is crucial to determine their quality, in musical use. The target of this study is to understand the influences of these parameters on the characteristics of attack transients. The study presented is based on measurements on an actual recorder in musical context. Parameters of attack transient for acoustic and musician control are extracted from the data. Relations between these parameters are searched by taking into account the characteristics of the instruments. This study is a first step in the understanding of the possibilities of the musicians' control and of the physical limitations

Modelling the Evolutionary Dynamics of Viruses within Their Hosts: A Case Study Using High-Throughput Sequencing

Uncovering how natural selection and genetic drift shape the evolutionary dynamics of virus populations within their hosts can pave the way to a better understanding of virus emergence. Mathematical models already play a leading role in these studies and are intended to predict future emergences. Here, using high-throughput sequencing, we analyzed the within-host population dynamics of four Potato virus Y (PVY) variants differing at most by two substitutions involved in pathogenicity properties. Model selection procedures were used to compare experimental results to six hypotheses regarding competitiveness and intensity of genetic drift experienced by viruses during host plant colonization. Results indicated that the frequencies of variants were well described using Lotka-Volterra models where the competition coefficients βij exerted by variant j on variant i are equal to their fitness ratio, rj/ri. Statistical inference allowed the estimation of the effect of each mutation on fitness, revealing slight (s = −0.45%) and high (s = −13.2%) fitness costs and a negative epistasis between them. Results also indicated that only 1 to 4 infectious units initiated the population of one apical leaf. The between-host variances of the variant frequencies were described using Dirichlet-multinomial distributions whose scale parameters, closely related to the fixation index FST, were shown to vary with time. The genetic differentiation of virus populations among plants increased from 0 to 10 days post-inoculation and then decreased until 35 days. Overall, this study showed that mathematical models can accurately describe both selection and genetic drift processes shaping the evolutionary dynamics of viruses within their hosts

Direct generation of a multi-transverse mode non-classical state of light

Quantum computation and communication protocols require quantum resources which are in the continuous variable regime squeezed and/or quadrature entangled optical modes. To perform more and more complex and robust protocols, one needs sources that can produce in a controlled way highly multimode quantum states of light. One possibility is to mix different single mode quantum resources. Another is to directly use a multimode device, either in the spatial or in the frequency domain. We present here the first experimental demonstration of a device capable of producing simultanuously several squeezed transverse modes of the same frequency and which is potentially scalable. We show that this device, which is an Optical Parametric Oscillator using a self-imaging cavity, produces a multimode quantum resource made of three squeezed transverse modes