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

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Chapter VII
The embouchure hole and player corrections
So far, this thesis has been concerned only with the flute as a resonator—the measured impedance
is passive and the interaction of the flute with the player has not been considered.
Fortunately, and in contrast with the clarinet (Fritz & Wolfe 2005), the flute is largely decoupled
from the player’s vocal tract, and so it seems likely that changes in the latter do not affect
much the resonances of the former. However, the interaction of the jet and player’s face with
the passive flute impedance needs to be considered, which is the subject of this chapter.
7.1 PLAYER IMPEDANCE CORRECTIONS
The flute impedance measured in Chapter 5 is the input impedance at the embouchure hole
for the flute at room temperature as measured through a 7.8 mm diameter impedance head.
However the impedance with which the jet interacts (and the impedance that should be modelled
in order to derive meaningful tuning predictions) differs from the measured impedance
in the following ways:
• the temperature of the air in the played flute is higher than room temperature and the
temperature varies along the flute
• the humidity and CO 2 content of the air in the played flute are both higher than ambient
air
• the player’s lip covers part of the embouchure hole, changing the entry diameter. To first
order, this is accounted for by the choice of impedance head. However, it varies among
players and over the range
• the player’s face shades the embouchure hole
• the acoustic wave can travel through the mouth into the vocal tract and thus the mouth
impedance should be taken into account.
These effects can be measured or modelled (Thwaites & Fletcher 1983, Fabre & Hirschberg
2000, Vergez et al. 2005) but the physics is complex. For the current application it suffices to
bundle these effects into a single impedance Z face . In reality, these effects are not equivalent
to a simple impedance, but this is an empirical model and such an approach is sufficient for
the goals of this thesis. Fletcher (1976, see also Fletcher & Rossing (1998)) examines the jetdrive
mechanism in organ pipes and shows that the radiation impedance from the mouth of
an organ pipe (approximately equivalent to the partly-open embouchure hole of a flute) is in
series with the ‘internal’ impedance. The jet itself contributes an active drive mechanism with
both ‘volume-flow’ and ‘pressure-drive’ terms.