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Systèmes dynamiques non-stationnaires : application aux instruments de musique à vent – SDNS-AIMV

Note attacks, endings and other transients : how are they mastered by musicians?

Understand the behaviour of self-sustained musical instruments for rapid changes in the musician's control on his instrument. Observe and quantify the action of the musician for note attacks, endings and transitions in musical contexts.

Tranisent regimes in a music instrument with self sustained oscillations: a domain in birth

Musical sounds cam be seen as having a “life”: they are born (attack phase), they go through a period of stability (sustain phase) and then disappear (extinction phase). During the sustain, the characteristics of the sound, such as loudness, frequency and colour undergo little or slow variations. During the rather quick phases of attack and extinction, and in note transition between two legato notes, the same characteristics of the sound can have big and fast variations. Perceptual tests show that these phases of quick variation, the attack in particular, have an importance to the ear that is rather important, even if their short duration would lead to different conclusions. <br />In self-sustained instruments, like clarinets or saxophones (and also flutes and bowed strings), musicians can control the sound during the whole duration of the note (as opposed to when the vibration is created, for example in the guitar or the piano). Scientists have a good understanding of the sustained part of the note in self-sustained instruments, as the musician’s control is rather stable. The same is not true for the attack or for other transients. In fact, the mathematical methods used for the sustain are not valid when fast variations of the parameters take place. <br />The general aim of SDNS-AIMV project is to understand the behavior of self-sustained musical instruments, and the role of the musician in note transients. The project will focus primarily on the attack of the note in a reed instrument (clarinet or saxophone). It may also cover other transients in other instruments if judged interesting or possible. <br />

Methods employed in the project cover the range of usual methods in physical sciences. There are two major axis in this project: one is fundamental, in the sense that it aims at understanding the behavior of simple models of the instrument, either mathematical or real instruments played by blowing machines, where part of the instruments’ elements are simplified to better fit mathematical models. In this axis, the aim is to understand in detail the role of each parameter in the sound that the model produces. Other than some obvious tools used in mathematical studies (bibliographic studies, computer simulations, analytical studies), this axis will use an “robotized artificial mouth” in order to impose simplified musician actions to a real instrument.
The second axis (“in vivo”) is somewhat opposite to the previous one. Given the complexity of an instrument played by a human, it is impractical to know in detail every parameter at play (in general they are in much bigger number than the ones used in simplified models). We propose to understand firtly which sound characteristics are sought by musicians (in particular, which characteristics of the attack), and what actions the use to produce these results. An important question is whether all musicians use similar actions for a same sound result, or if different actions are possible or required for different musicians. Modified instruments with integrated sensors will be conceived for this axis, and they will be optimized in order to reduce their intrusiveness in musical contexts. Methods for signal acquisition and analysis will be developed when necessary in order to compare actions of different musicians, and to compare real actions to results from the first axis.

Given that this subject is somewhat new in music acoustics, this project has unquestionably provided the music acoustics community with a theoretical framework to analyze note transients, when musician’s parameters have strong variations. Dynamic bifurcation theory has been identified as the most promising mathematical tool to understand the phenomena at play during the transient. Applying it to clarinet models has enlightened on the role of different parameters of the instrument: for instance, wind noise generated by turbulence when blowing into the instrument is determinant in almost every note beginning. The start of the note is triggered shortly after a static threshold in pressure is reached, and models can predict ho long after this event the periodic oscillation will be heard.
For simplified models predictions provide quite good results. In real conditions, though, musicians use far more complex variations of parameters then those studied in models. As a consequence, the delay between the crossing of the threshold and the beginning of the note can be much shorter than that obtained in artificially blown instruments. The reason for this is probably the complex pattern of parameter variations observed in musician’s recordings: rather than simply increasing gradually the blowing pressure, the pressure is increased to an almost constant level above threshold, and then the tongue is released from the read. Tongue movements are for now difficult to measure. Musicians seem to use blowing pressure to fine-tune the buildup of the sound. Sound levels are often seen to increase quicker in the mouth cavity than in the instrument.

As an exploratory project, SDNS-AIMV opens many new questions, in particular on the rather exceptional behavior that musicians can impose on their instruments. Indeed, they are able to produce faster attacks than “in vitro” models. One of the problems is that sensor-fitted instruments are yet unable of measuring the entire action of the musician on the instrument. A particular aspect that is missing from these measurements is the action of the tongue.
Nevertheless, these devices show a strong potential for pedagogical applications, in particular by improving communication between student and teacher when demonstrating technical aspects of instrument playing.
Within the fundamental axis, several short-term perspectives are foreseen, for instance extending the study to more complex time profiles on single parameter evolutions, and studying the combined variation of several parameters simultaneously. These will allow the comparison of different gestures, and possibly an automatic search for optimized parameter profiles in terms of the delay of the attack. Other effects may be explained with slightly different approaches, such as using continuous-time models to explain the possibility (wanted or unwanted) of starting a note on different registers.

The main contribution to scientific results comes from the PhD of Baptiste Bergeot, financed entirely on this project. A significant number of articles in peer-reviewed journals were obtained (J. Acoust Soc. Am., Acta Acustica united with Acustica and Non-linear Dynamics) and communications to international conferences in which music acoustic sessions were well represented. Simultaneously, internships and student projects have brought significant contributions, mostly represented in Acoustics conferences.

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The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

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