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

128 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 9.1: The predicted tuning of the unmodified Pearl modern flute.
due to the C♯ hole are immediately apparent—both C♯5 and C♯7 are over 20 cents sharp. Interestingly,
C♯6 is no sharper than its adjacent notes; this was also seen in the played pitch
measurements of Chapter 7. On the unmodified flute the C♯ key is 7.0 mm in diameter and is
238.4 mm from the embouchure hole.
The following sections describe the effects on tuning of simple changes to the software
model of the flute.
9.1.2 An ‘acoustically correct’ C♯ hole
The first change I made was to increase the size of the C♯ hole and to place it at its ‘acoustically
correct’ position. The advantage of this change is that the notes made with this hole have
timbre more similar to other notes in the scale. The hole diameter was changed from 7.0 to
13.2 mm and the key diameter was changed from 13.0 to 19.0 mm (these values were chosen
so as to match the properties of the next few holes). The height of the key above the hole was
changed from 1.9 to 2.4 mm and the thickness of the key was changed from 3.6 to 4.0 mm (these
are average values for the next few holes). The hole was moved 15 mm down the flute, making
it 253.4 mm from the embouchure hole (at this position the consecutive distances between
the first few holes form a geometric series). The resulting tuning is shown in Figure 9.2. Small
changes in tuning can be seen for notes made with the C♯ hole closed: most notes are flattened,
but the change is at most 4 cents. A few such notes are sharpened, but by no more than 1 cent.
This change is consistent with an increase in the size of the cavity formed by the closed C♯ hole.
For notes made with the C♯ hole open, C♯5, C♯6andC♯7 are more in tune, although the spread
in tuning between the three notes is nearly 20 cents. The tuning of D5 and D6 is acceptable, but
E♭5 is over 40 cents sharp and D7 is out of range. These notes use the C♯ hole as a register hole
and for this purpose the hole is too big and rather inefficient. The remaining notes that use the
open C♯ hole (G♯6 and A6) are within a few cents in tuning compared to the adjacent notes).
D♯5 and A6 have low playability compared to adjacent notes—likely due to the inefficiency of