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

CHAPTER 7. THE EMBOUCHURE HOLE AND PLAYER CORRECTIONS 103
Figure 7.3: The pitch correction used by Botros et al. (2006).
tuning as the scale is ascended, and the tuning of some notes does not match the general trend
(especially C♯5 and A♯6). The errant tuning of individual notes is easily explained: the placement
and size of the holes on a flute is always a compromise and some tuning anomalies are
tolerated in favour of keeping the flute design relatively simple and not too unwieldy. In particular
the C♯ hole doubles as tone hole for C♯5 and C♯6, and register hole for D5, D♯5 and D6.
This requires a compromise between position (higher than desired for C♯5/6) and size (therefore
smaller than desired for C♯5/6). This compromise works better for C♯6 than C♯5 which is
understandable—the pitch of C♯5 is more easily adjusted by the player.
A player can always correct the tuning of individual notes with her embouchure. The trend
towards sharper tuning over the scale is largely a function of the stopper position. The stopper
position of 17.5 mm used here is a general guide—flute players adjust this parameter to correct
the tuning—and there may well be a different optimum for the flute in question. Moveover,
studies have shown that musicians actually like slightly wide octaves when not played simultaneously
(Ward 1954) and this may explain the increase in tuning error with pitch of note.
Incidentally, most of the notes in Figure 7.2 are sharp. This is due to the relatively short tuning
slide position used in experiments. When informally playing the laboratory flute at A 440 our
resident flutist, Jane Cavanagh, routinely set the slide closer to 8 mm than the 4 mm used here.
Jane also has a fairly open blowhole (hers is the embouchure pictured in Figure 7.1).
For the Virtual Flute Botros et al. (2006) used a pitch correction to adjust the tuning derived
from the impedance minima of measured spectra in order to match the data of Figure 7.2. The
correction used by Botros et al. is shown in Figure 7.3.
7.3 CORRECTION FACTOR
In this thesis, Z face is allowed to vary with played frequency in order to adjust the tuning. The input
impedance of the flute is calculated with the temperature gradient given in §2.2.1 through