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

CHAPTER 9. APPLICATIONS AND FURTHER DIRECTIONS 124
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 9.2: The predicted tuning of the Pearl modern flute after moving and resizing the C♯
hole.
normalised magnitude
pressure flow
1
0
-50 0 50 100 150 200 250 300 350 400 450 500 550 600 650
x (mm)
Figure 9.3: Normalised magnitude of pressure and volume flow along the flute for the note E♭5.
the C♯ hole acting as a register hole.
The pressure and flow profiles along the flute for the note E♭5 are shown in Figure 9.3. For
this note the strongest resonance in the flute is a half-wave resonance between the open C♯ hole
at 253.4 mm and the open E♭ hole at 494.3 mm. The C♯ hole is not strictly acting as a register
hole, since a register hole should detune the lower resonance (E♭5 in this case) and leave the
desired resonance unchanged. The hole is too big and too far down the flute to satisfy this
second requirement.
The modified C♯ hole is evidently not a very good register hole. So perhaps we could do
without it. If the C♯ hole is closed for all fingerings except C♯5 and C♯6, the tuning shown in
Figure 9.4 results. Now G♯6 and C♯7 are approx. 25 cents flat (relative to adjacent notes) and
the other notes that ordinarily use the C♯ hole as a register hole are in tune. The C♯ hole acts as
more than just a register key for the notes G♯6 and C♯7: it also sharpens them. This role must
be taken into account in deciding on the placement of a new ‘register’ hole.
All of the fingerings that use the C♯ key as a ‘register hole’ or a ‘vent hole’ were analysed
for their pressure node nearest the C♯ key position. (The terms ‘register hole’ and ‘vent hole’
are rather loose, but are understood here to refer to any open hole that does not act primarily