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

CHAPTER 2. THEORY AND LITERATURE REVIEW 28
2.2.13 The embouchure hole and stopper
For our purposes, it is important to note that flutes have a small volume of air between the
embouchure hole and stopper. The stopper is usually set at 19.0 mm from the embouchure
in the case of classical flutes and 17.0 mm for modern flutes but it may be adjusted to suit
individual playing styles and intonations. The purpose of this upstream air volume (together
with the bore taper) is to compensate for the frequency-dependent impedance at the far end
of the flute, and thereby to bring the octaves into tune. Benade (1976) discusses the effect
of the bore profile and the upstream volume, and Wolfe et al. (2003) show the effect of the
stopper position on the input impedance of transverse flutes. The volume of air between the
embouchure hole and stopper also limits the range of the flute, since at high frequencies the
air acts as the compliant element in a Helmholtz oscillator (the mass of air in the embouchure
hole riser acts as the inertance). At the resonant frequency of this oscillator (approx. 7 kHz, well
above the playing range) the acoustic fields do not propagate substantially into the body of the
flute and the flute does not respond to changes in fingerings.
2.3 COMPUTER MODELS
Plitnik & Strong (1979) applied transmission line theory to the oboe and calculated the input
impedance for various fingerings. The authors compare the predicted impedance spectra with
measurements made by A. H. Benade. Although the results may not be accurate enough for
precise prediction of the tuning and playing qualities of oboes, the model provides a reasonably
good fit to experiment, and allows validation of the assumptions made. Strong et al. (1985)
used a numerical model to calculate impedances and standing wave patterns of the modern
flute. The results are compared to experiment and discrepancies in resonance frequencies are
discussed.
The numerical model of woodwind instruments developed by Keefe (1990) is very similar
to that used in this work. Keefe applies the model to the air column of a flute and finds good
agreement with experiment. However, no examples are given of the degree of accuracy of the
model in predicting the tuning of particular notes on the flute.
Several attempts have been made to produce a stand-alone computer program to predict
the playing qualities of woodwinds based on input geometrical parameters. Flutekey (Coltman
1998) is one such program, made by John Coltman. Flutekey is a MS-DOS based program that
calculates the tuning of notes on the modern (Boehm) flute with different hole parameters.
Resonans ∗ is a software package developed jointly by Le Mans University and IRCAM (Institut
de Recherche et Coordination Acoustique/Musique), Paris, allowing computer aided design
of wind instruments. The particular details of this software package are not readily available,
although the software is said to have been used successfully by several instrument makers.
The Virtual Flute (Botros et al. 2006) uses a transmission line model like that of Plitnik &
∗ Some information about Resonans may be found at .