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

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CHAPTER 1. INTRODUCTION 6 1.5 ACOUSTIC IMPEDANCE: PREDICTING THE PLAYING QUALITIES OF A FLUTE Many of the acoustical characteristics of a flute may be quantified by its acoustic impedance spectrum. Acoustic impedance is the ratio of pressure to flow at the input to the instrument and describes how the flute will ‘respond’ to exciation at a particular frequency. The magnitude of the acoustic impedance of a flute varies over the frequency range of the instrument and has many maxima and minima. Because the flute is open to the air at the embouchure, the minima correspond to the possible standing waves, and the notes the flute can play are close in frequency to these minima. The impedance spectrum can also tell us about the tonal characteristics and playability of a note. Generally, if for some fingering there are many impedance minima with frequencies in a harmonic relationship to each other, then the note produced will be harmonically rich (bright); if not the note will be more pure (or dull sounding). Playability of a note depends upon many factors, such as how deep its impedance minima are, and whether or not there are other minima nearby. Each fingering for the flute produces a different impedance curve, with different possible standing waves. Many methods may be used to measure the acoustic impedance of woodwind instruments. At the least, some source of acoustic energy is needed (such as a loudspeaker) along with a means of measuring or inferring both the pressure and the flow. A review of many methods that have been used is provided in Chapter 3, which also documents the development of a novel, high-precision measurement and calibration technique. The acoustic impedance of a flute can be modelled by treating the flute as a one-dimensional network of cylinders and cones. We may then calculate the impedance properties of each element and derive the impedance of the entire flute. Figure 1.4 illustrates such an approach. Starting at the downstream end of the flute, the impedance of the last cylindrical segment is calculated (Z 1 ), as is the impedance of the last tone hole (Z 2 ). These impedances are combined in parallel and the result used in the calculation of the impedance at the next section. The impedance is calculated in an iterative manner until the entire flute is modelled. If the geometrical lengths of the flute segments are used without correction to calculate the impedance, it will not be accurate. This is because of various effects that are not adequately modelled by the one-dimensional network described above. However, adequate results can be achieved if measured length corrections are used. The tone hole segments (but not the bore) in Figure 1.4 are shown with length corrections added. 1.6 TUNING, TRADITION AND THE ‘STANDARD FLUTIST’ Musicians can be (understandably) resistant to people meddling with their instruments, and a flute judged to be perfectly in tune by one person may be out of tune to another. Musical instruments usually evolve, as instrument makers adapt to changing musical tastes and playing styles. Musicians are taught to compensate for their instrument’s peculiarities, and with years of practice they do this remarkably well. For this reason it is often difficult to convince musicians that a new design is better than the existing one, since adopting the ‘improved’ instrument will entail ‘un-learning’ some of their technique. Furthermore, the concept of an
CHAPTER 1. INTRODUCTION 7 Figure 1.4: The footjoint of a modern flute showing one closed hole and one open hole (a). The impedance of the flute is modelled by dividing the flute into cylindrical and conical segments (b) and adding length corrections (c).
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CHAPTER 5. IMPEDANCE SPECTRA OF THE
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CHAPTER 6. MATERIAL AND SURFACE EFF
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CHAPTER 7. THE EMBOUCHURE HOLE AND
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107 Chapter VIII Software implement
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CHAPTER 8. SOFTWARE IMPLEMENTATION
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CHAPTER 9. APPLICATIONS AND FURTHER
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Tuning (cents) CHAPTER 9. APPLICATI
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189 Appendix B Program listings B.1
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333 References Åbom, M. & Bodén,
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REFERENCES 335 Dubos, V., Kergomard
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REFERENCES 337 Strong, W. J., Fletc
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