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

CHAPTER 7. THE EMBOUCHURE HOLE AND PLAYER CORRECTIONS 101
The impedance of the played flute is then
Z played flute = Z face + Z flute , (7.1)
where Z flute is the input impedance of the flute with a temperature gradient and CO 2 and H 2 O
partial pressures in air equal to those in a played flute, as seen through an orifice with radius
somewhat smaller than the input radius of the embouchure hole. The exact size of the orifice
to use is difficult to determine, since the excitation of a played flute is not at all like the excitation
used in Chapter 5, where the flute was excited with plane waves from the end of a 7.8 mm
diameter impedance head. To get an idea of the extent to which the embouchure hole is covered
by the player’s lower lip, a flutist was asked to ‘mime’ several notes over the range of the
flute. Miming should give representative results, since flutists are trained to regularly set their
embouchure before playing, so that the initial transient of a note is strong and in tune. (The
face impedance was measured simultaneously, but the results are erratic and do not show the
expected variation with frequency.) Photographs of the embouchure for these notes are shown
in Figure 7.1. It is clear from these photographs that the lower lip covers approximately 25% of
the embouchure hole, and the upper lip protrudes somewhat further than the lower lip. The
jet length appears to shorten slightly for higher notes. The jet length was estimated from the
photographs to be 7.3 mm for C4 and 6.7 mm for F7—a decrease of 8%. For a more detailed
study of the lip configuration of flute players see Fletcher (1975).
As was seen in §5.3.3, reducing the input radius of the embouchure hole lowers the frequency
of impedance minima. Given the difficulty in determining the exact size of the input
radius, a radius of 3.9 mm was used. This corresponds to the size of the impedance head used
in Chapter 5, which in an earlier study was chosen to simulate the amount of the embouchure
hole which remained uncovered by the player’s lip (Wolfe et al. 2001a).
7.2 MODERN FLUTE TUNING
We choose to determine Z face empirically based on tuning data. Three experienced flutists
were asked to play each standard fingering on the same flute that was used for impedance
measurements (Botros et al. 2006). The stopper and tuning slide of the flute were set at the
same position as for measurements (i.e. 17.5 and 4 mm respectively). The flutists were asked to
avoid correcting the pitch for notes that were out of tune; rather the goal was to achieve the best
tone. As discussed in §2.2.12, the frequency of any note on the flute varies with the amplitude of
excitation. For this reason the players were asked to play each note mezzo forte. The resulting
pitch correction is then only strictly valid when the flute is played at this level; but a single
pitch correction for each note is needed for flute design purposes, and the correction derived
at mezzo forte is in my view most appropriate. The test notes were ordered so as to minimise
the effect of pitch memory: the intervals between successive notes were large and mostly not
simple consonances. Each note was repeated four times and the pitch was measured on a
tuning meter with a resolution of 5 cents. The results are shown in Figure 7.2.
It is immediately obvious from Figure 7.2 that this modern flute in this configuration does
not have perfect tuning, at least, not for these players. There is a general trend towards sharper