The musician’s ability to modify the pitch of his instrument is a common feature for most instruments from the flute family. Musicians can alter a given note by adjusting the airjet velocity or by changing the resonator impedance through the modification of the embouchure (opening or closing the open end of the resonator where the embouchure is). A trained musician can adapt to a wide variety of instruments and even correct the pitch of poorly built instruments. Flute makers, on the other hand, propose a pitch structure (diapason) by placing the tone holes, adapting their size and height and by choosing the bore’s internal geometry. The choices made by the maker take into account the musician’s evaluation, creating a loop that through centuries of iterations has produced optimal instruments following a range of cultural and technological constraints. Throughout this article, the relationship between flute manufacture and the musician’s control will be discussed and analyzed. Identifying, modeling and quantifying the possibilities the musician has to control the instrument as well as the parameters the flute maker can modify to close this optimization loop, we propose a methodology to determine the geometry of the instrument for a given control strategy and vice versa.
To play a transverse or notch flute, musicians place their mouth near an open end of the instrument where a sharp edge or labium is the target of the air-jet blown by the musicians. The jet/labium interaction is responsible for generating sound. Musicians can control the geometry of the air-jet during their performance. They can, for example, decrease the distance from their lips to the labium when increasing the pitch. The presence of the musician and the variation of his position while playing modifies the boundary conditions at the opening which, in turn, impacts the passive resonances of the instrument/player system. Flute manufacture adapted empirically to take into account this effect but, until now, it was never systematically quantified. The main goal of this study is to quantify and model the influence of the musician’s presence and his movements as a modification on the radiation impedance of the instrument. Finite element simulations and experimental mockups are implemented and described in order to fit experimental models. Such models are useful as a complement to physical models of flutes as well as to understand the choices made in flute manufacture.
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