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

CHAPTER 9. APPLICATIONS AND FURTHER DIRECTIONS 134
In order to model tone holes drilled directly through the wall of a woodwind instrument
and stopped by the player’s fingers, the lumped-element impedances for such holes were measured
over a wide range of parameters, and fit-formulae were derived for the associated lengthcorrections
(i.e. for the reactive part of each measured impedance) (Chapter 4). Such formulae
for closed finger holes were not found in an extensive literature search, but they are important
since the player’s finger can have a large impact on the length corrections for closed tone
holes. The measurements were subject to some systematic errors (discussed in §4.4). These
did not materially affect the determination of the length corrections, but did compromise the
measurement of the resistive part of each tone hole impedance. In future, it may be beneficial
to determine these equivalent-circuit impedances to a higher degree of precision, and to measure
the resistance at tone-hole junctions. Some suggestions for how to improve these measurements
are given in Chapter 4. It would also be of interest to investigate non-linear effects
at finger holes. This has been done for open tone holes such as are found on the modern flute
(Dalmont et al. 2002). The range of tone hole geometries studied does not include all tone hole
types found on woodwind instruments, such as the long sloped holes found on bassoons or the
holes on the clarinet lined with a metal pipe that protrudes into the bore. Undercut tone holes
were also not measured. In future work, it is hoped that the database of tone hole impedances
will be extended to encompass many of these geometries.
Further work is needed on the timber used to make classical flutes. In Chapter 6 the effects
of humidity and oiling on pipes made from radiata pine were investigated. This study could be
expanded to include typical flute timbers and to examine changes in the acoustic impedance
and playing characteristics of a new flute over time. Players and makers speak of improvement
in the performance of a new flute over time, as the flute is ‘played in’. Is this due to gradual polishing
of the bore with repeated oiling and swabbing? Do the sharp edges at the embouchure
hole and tone holes slowly wear away, and could this improve the flute’s performance? Or are
there no appreciable changes at all in the acoustic properties of a flute in its first weeks and
months of playing? Could it be the flutist, and not the flute, that adapts (plays in) over the first
few weeks? Answers to some of these questions could lead to more informed methods of oiling
for both makers and players. In this thesis the standard viscothermal theory for wall losses was
used. It is noted that there has been no conclusive experimental validation of this theory, and
in most practical situations the wall losses appear to be somewhat greater than predicted. It
would thus also be interesting to use the impedance spectrometer to gauge the validity of the
viscothermal model for wall losses. Deviations from theory may result for timber pipes, even
those with dense grain and a well-sealed surface. A clearer understanding of wall losses would
lead to more accurate impedance modelling.
In Chapter 7 the effect of the player on flute tuning is investigated and an empirical correction
is derived and included in the impedance model of a played flute. No attempt was made to
incorporate a physical model of the jet excitation, since the main goal of the thesis was to predict
flute tunings which are largely determined by the frequency of the (empirically corrected)
impedance minima. Further work in this area is warranted, for several reasons. Firstly, by combining
the impedance model with a physical model of the jet excitation, one may synthesise