362 Renée van Bezooijen and Vincent J. van Heuven
800 Hz for a low (open) vowel /a/. The second formant frequency (or F2)
reÀ ects the place of maximal constriction during the production of the vowel,
i.e., the front vs. back dimension, such that the F2 values range from roughly
2200 Hz for front /i/ down to some 600 Hz for back /u/.
The relationship between the formant frequencies and the correspond-
ing perceived vowel quality is not linear. For instance, a change in F1 from
200 to 300 Hz brings about a much larger change in perceived vowel quality
(height) than a numerically equal change from 700 to 800 Hz. Over the past
decades an empirical formula has been developed that adequately maps the
differences in Hertz-values onto the perceptual vowel quality domain, using
the so-called Bark transformation (for a summary of positions, see Hayward
2000). Using this transformation, the perceptual distance between any two
vowel qualities can be computed from acoustic measurements. We used the
Bark formula as given by Traunmüller (1990):
Bark = [(26.81 × F) / (1960 + F)] - 0.53
where F represents the measured formant frequency in Hertz. Given that the
¿ rst and last portions of any vowel, monophthongs and diphthongs alike, are
strongly inÀ uenced by (the articulation place of) the neigh boring consonants,
it is customary to sample the formant values for the starting point of the diph-
thong at one-quarter of the time-course of the diphthong, and to measure the
formants for the endpoint of the diphthong at 75% of its duration. The degree of
diphthongization is then expressed as the distance in Barks between the onset
and the offset vowel quality. In terms of the traditional vowel diagrams used
by impressionistic linguists and phoneticians, this procedure is the equivalent
of measuring the length of the arrow that represents the diphthong.
3.2 Acoustic processing
The audio recordings were digitally sampled (16 kHz, 16 bits) and stored on
computer disk. Using the Praat speech processing software (Boersma and
Weenink 1996) the beginnings and end points of the target vowels were
located in oscillographic and/or spectro graphic displays. Formant tracks for
the lowest two formants (F1, F2) were then computed at 25, 50, and 75% of the
duration of the target vowel (for details see Van Heuven et al. 2005).
Figure 15.3 illustrates the measurements. It shows the wide-band spec-
trogram of a target diphthong /͑i/ with the formant tracks drawn through the
lowest two formants as white lines. The duration of this diphthong token was