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

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