Flute acoustics: measurement, modelling and design - School of ...

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30 CHAPTER 2. THEORY AND LITERATURE REVIEW Strong (1979) with a half-dozen empirical parameters to model the modern flute. These parameters are machine-learned from a training set of impedance spectra for all standard fingerings and some alternative fingerings. The model is accessed through a user-friendly web page. The software in its current form does not allow geometrical changes to the flute model, as it is intended primarily for use by flute players rather than makers. This work extends the model used in The Virtual Flute, making it accurate for flutes of varying geometry. While the idea of a flute model itself is not novel, its close association with a highly accurate and extensive database of flute impedance spectra should provide the accuracy and reliability required by instrument makers. Furthermore, a great deal of effort was put into the design of the user interface to the model. The use of a simple graphical interface widens significantly the pool of potential users of the software, making the work of musical acousticians much more widely available.
31 Chapter III Measuring acoustic impedance ∗ Resonances and/or singularities during measurement and calibration often limit the precision of acoustic impedance spectra. This chapter reviews and compares several established techniques, and describes a technique that incorporates three features that considerably improve precision. The first feature is to minimise problems due to resonances by calibrating the instrument using up to three different acoustic reference impedances that do not themselves exhibit resonances. The second involves using multiple pressure transducers to reduce the effects of measurement singularities. The third involves iteratively tailoring the spectrum of the stimulus signal to control the distribution of errors across the particular measured impedance spectrum. Examples are given of the performance of the technique on simple cylindrical waveguides. 3.1 INTRODUCTION The input impedance of any one-dimensional waveguide is defined as the complex ratio of pressure to volume flow at the input. This quantity is used to describe the linear acoustics of automotive mufflers, air-conditioning ducts and the passive elements of wind instruments and the vocal tract. For a musical instrument, the input impedance usefully displays important characteristics of the instrument in the absence of a player, and indicates how the instrument will respond when excited at any frequency. In this case, high resolution in magnitude and frequency are particularly important. If pressure and volume flow are measured at different points in a system, their ratio gives a transfer impedance, which is particularly useful in characterising multi-port systems. In this paper, we review the various approaches to measuring acoustic impedance and calibrating impedance heads and propose a general calibration technique for heads with multiple transducers. We consider the effect of transducer errors on impedance measurements and present a technique for distributing any measurement errors over the frequency range. To demonstrate the technique we use an impedance head with three microphones to measure the input impedance of simple cylindrical waveguides. The effects of calibration and optimisation on these measurements are presented and discussed. ∗ An abridged version of this chapter has been published as Dickens, P., Smith, J. & Wolfe, J. (2007), ‘Improved precision in measurements of acoustic impedance spectra using resonance-free calibration loads and controlled error distribution’, J. Acoust. Soc. Am. 121(3), 1471–81.
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340 REFERENCES Botros, A., Smith, J
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342 REFERENCES Kob, M. & Neuschaefe
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