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

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130 CHAPTER 9. APPLICATIONS AND FURTHER DIRECTIONS 50 40 30 Tuning (cents) 20 10 0 -10 -20 -1 octave loco +1 octave +2 octaves + 3 octaves -30 D4 Eb4 E4 F4 F#4 G4 G#4 A4 Bb4 B4 C5 C#5 Note Figure 9.4: The predicted tuning of the Pearl modern flute after moving and resizing the C♯ hole and closing the hole for all notes except C♯5 and C♯6. as an acoustic short circuit.) The nodal positions for these notes are shown in Figure 9.5. The average nodal position was 253.2 mm from the embouchure hole, almost exactly the position of the new larger C♯ key. As discussed above, however, the ‘register hole’ also serves to sharpen the notes G♯6andC♯7, and must be placed somewhat higher than the new ‘acoustically correct’ C♯ key in order to fulfil this function. 9.1.3 Adding a separate register hole I next added a vent hole at 239.5 mm from the embouchure hole. The hole was made 4.0 mm in diameter with similar key dimensions to the original C♯ key. The fingerings for all notes previously using the C♯ key except for C♯5 and C♯6 were changed to use this vent key instead. The resulting tuning is shown in Figure 9.6. The use of this vent hole brings G♯6 andC♯7 back into tune, without adversely affecting the tuning of the other notes that use this key. D7 is still sharp, but this note was sharp in the original flute and none of the modifications made brought this note into tune. This note is near the top of the range on the modern flute and at such a high frequency the register hole has little effect. This note is insensitive to changes in the register hole and may need to be dealt with separately (The Virtual Flute may be used to search for other fingerings). The exact size of this vent hole is not critical, although in general a smaller vent hole is preferred since it perturbs the tuning of notes less when not at an optimal position. The size of 4.0 mm was chosen by examining the relevant impedance spectra and ensuring sure that any lower resonances are detuned and weakened sufficiently by opening the vent hole. Compare Figure 9.6 with Figure 9.1 to see the improvements in tuning achieved as a result of the minor changes made in this section. 9.1.4 Remaining tuning problems The tuning shown in Figure 9.6 shows some octave stretching, with the notes in the range D6 to C♯7 being more than 10 cents sharper than the range two octaves lower. As discussed in
9.1. ADDING A NEW HOLE TO THE MODERN FLUTE 131 position from embouchure (mm) 280 270 260 250 240 230 220 D5 D#5 D6 G#6 A6 C#7 D7 Note Figure 9.5: Position of pressure nodes nearest the C♯ hole (measured from the centre of the embouchure hole) for all notes that use the C♯ hole other than C♯5 andC♯6. The C♯ hole was closed for this calculation. 50 40 30 Tuning (cents) 20 10 0 -10 -20 -1 octave loco +1 octave +2 octaves + 3 octaves -30 D4 Eb4 E4 F4 F#4 G4 G#4 A4 Bb4 B4 C5 C#5 Note Figure 9.6: The predicted tuning of the Pearl modern flute after moving and resizing the C♯ hole and adding a new register hole.
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Flute acoustics: measurement, model
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To Renée iii
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vi I am grateful to my parents, Ros
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x 4.4 Conclusions and further direc
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2 CHAPTER 1. INTRODUCTION and the p
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4 CHAPTER 1. INTRODUCTION Figure 1.
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6 CHAPTER 1. INTRODUCTION 1.5 ACOUS
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10 CHAPTER 1. INTRODUCTION
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12 CHAPTER 2. THEORY AND LITERATURE
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k = ω c and pressure given by p(x,
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32 CHAPTER 3. MEASURING ACOUSTIC IM
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54 CHAPTER 4. FINGER HOLE IMPEDANCE
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180 APPENDIX A. IMPEDANCE SPECTRA C
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192 APPENDIX A. IMPEDANCE SPECTRA D
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194 APPENDIX A. IMPEDANCE SPECTRA
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196 APPENDIX B. PROGRAM LISTINGS /*
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338 APPENDIX C. QUANTIFYING MUSIC s
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340 REFERENCES Botros, A., Smith, J
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342 REFERENCES Kob, M. & Neuschaefe
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