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The axes are marked in Hertz, but scaled on the Bark scale, which reflects the
ear’s sensitivity to differences in pitch (cf. Ladefoged 1996: 80). The equation for
calculating bark units from Hertz (Zwicker & Terhardt 1980) is:
(3) B = 13 arctan (0.76 f) + 3.5 arctan (f/7.5) 2
B – critical band value in Bark
f – frequency in kHz, arctan in radians
The ellipses are centered on the mean for each vowel and have radii of two
standard deviations “along the first two principal components of the distribution”
(Maddieson & Anderson 1994). There is reasonable separation between the vowels
indicating that the values of F1 and F2 are sufficient acoustic properties for distinguishing
the vowels. However, some overlap exists between E and A, E and , and , and K and ,
which indicates that other factors may assist in distinguishing these pairs of vowels.
Concerning E and A, there is a large difference in bandwidth between the F1 values
of the two vowels, which may be an additional cue for distinguishing the sounds. The
vowel E has a mean bandwidth of 9.7 Hz (SD = 1.9), whereas the vowel A has a mean
bandwidth of 23.5 Hz (SD = 7.2).
Concerning E and , there is a difference in the value of F3 between the two
vowels, as is evident from the plot of F1 versus F3 shown in Figure 8.30. Since F2' takes
into account the influence of F3, a plot of F1 vs. F2' also shows this separation between E
and , as seen in Figure 8.31. Concerning and , and K and , I found no parameter
resulting in an absolute separation between the two respective values in each pair.
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