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EVALUATION OF A TECHNIQUE FOR IMPROVING THE MAPPING OF
MULTIPLE SPEAKERS’ VOWEL SPACES IN THE F1 ~ F2 PLANE1
Dominic Watt & Anne Fabricius
Abstract
We evaluate a vowel formant normalisation technique that allows direct visual and
statistical comparison of vowel triangles for multiple speakers of different sexes, by
calculating for each speaker a ‘centre of gravity’ S in the F1 ~ F2 plane. S is calculated
on the basis of formant frequency measurements taken for the so-called ‘point’ vowel
[i], the average F1 and F2 for the vowel category with the highest average F1 (for
English, usually the vowel of the TRAP or START lexical sets), and hypothetical
minimal F1 and F2 values (coordinates we label [uÈ]) extrapolated from the other two
points. Expression of individual F1 and F2 measurements as ratios of the value of S for
that formant permits direct mapping of different speakers’ vowel triangles onto one
another, resulting in marked improvements in agreement in vowel triangle (a) area and
(b) overlap, as compared to similar mappings attempted using linear Hz scales and the
z (Bark) scale.
1. Introduction
For some considerable time it has been commonplace in phonetic and
sociolinguistic research to represent spoken vowels by means of the frequencies of
their two lowest formants, F1 and F2. The method has been adopted in order, among
other things, to allow greater objectivity and replicability when classifying individual
vowels than is possible using impressionistic auditory analysis alone. F1 has been
shown to correlate inversely with the position of the highest part of the tongue body in
the height dimension (open vowels have higher F1 values than close vowels do), while
F2 is correlated with tongue frontness (front vowels have higher F2 values than back
vowels do, especially if back vowels are also rounded). Vowels are frequently
represented using straightforward measurements in linear Hz, or by expressing the
relationship between the two parameters in some way (e.g. by plotting F1 against F2 –
F1 for a given vowel, as per Ladefoged & Maddieson 1990, Iivonen 1994), or by using
some transform or ‘warping’ of the Hz scale so as to reflect the non-linear mapping of
the acoustic parameter Hz to its perceptual correlates (e.g. through use of log(Hz)
transforms, or the Mel, Koenig, Bark, or Equivalent Rectangular Bandwidth (ERB)
scales). Some models also take account of higher formants such as F3, or of the
fundamental frequency (F0; see e.g. Hindle 1978, Disner 1980, Lobanov 1980, Moore
& Glasberg 1983, Deterding 1990, Rosner & Pickering 1994, Labov 2001, or Adank
et al. 2001 for evaluations of competing algorithms). In the case of the use of non-
linear transforms, the intention is to minimise as far as possible the influence of non-
linguistic factors on those properties in the acoustic signal which the researcher
1 We are grateful to the following people for their input, comments and other feedback: Patti Adank,
Paul Carter, Bernhard Fabricius, Paul Foulkes, Rob Hagiwara, Ghada Khattab, John Local, Richard
Ogden, Peter Patrick, Jane Stuart-Smith, and an anonymous reviewer.
Nelson, D. (ed.) Leeds Working Papers in Linguistics and Phonetics 9 (2002), pp. 159-173.
Evaluation of a technique for mapping
perceives to be important. Listeners appear capable of automatically factoring out
certain aspects of the acoustic signal, such that they can, for example, understand
natural speech produced by men, women and children with more or less equal
proficiency, despite large differences in the acoustic signatures of ‘equivalent’ sounds
produced by each type of speaker chiefly as a consequence of vocal tract length (VTL;
e.g. Stevens 1998). A central concern in the acoustic analysis of vowels has therefore
been to attempt to eliminate the effect of VTL on the relative frequencies of the lower
formants for multiple speakers. By performing such ‘normalisation’ on speech signals,
the researcher is permitted to make more direct comparison of formant frequencies of
vowels spoken by speakers of different sexes and ages, and is also able to approximate
more closely the way in which listeners may perceive spoken vowels.
Figure 1. Frequency of second formant versus frequency of first formant for ten American
English vowels produced by 76 men, women and children (adapted from Peterson & Barney 1952
by Lieberman & Blumstein 1988).
An especially frequently used technique of visually assessing the similarities and
differences between F1 and F2 frequencies for vowels produced by different speakers
is one involving plotting unnormalised F1 and F2 against each other on x-y scatter
graphs (e.g. Peterson & Barney 1952, Hagiwara 1997, Watt & Tillotson 2001).2 This
method allows the researcher to superimpose one speaker’s vowel sample onto
another’s, and thereby to estimate whether or not, for example, Speaker A has on the
2 Hagiwara (1997) presents scatter plots in which the units are in Hz plotted on a Bark scale such that
higher frequencies are compressed relative to lower ones, but this is a matter of adjusting the scaling on
the axes of the plots rather than transforming the data themselves.
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Watt & Fabricius
whole a higher F2 for a given vowel category than does Speaker B; such an
observation might confirm a hypothesised process of vowel fronting. Data in this form
also permit straightforward statistical comparison of samples, but only if it is assumed
that VTL, and therefore the potential ranges of values for both F1 and F2, are
effectively constant across all the speakers sampled.
So as to minimise the potentially problematic influence of VTL-related variation
among speakers of different ages and sexes, some researchers have used only post-
pubertal male speakers as informants for investigations of vowel variation (e.g.
Eremeeva & Stuart-Smith 2003). Serious problems are encountered if samples more
representative of the population as a whole are used, because the F1 ~ F2 frequencies
for women tend to be significantly higher for adult females than for adult male
speakers, with children having formant frequencies which are still higher than those of
women. It is obviously not possible directly to compare (linear Hz) F1 ~ F2 scatter
plots for adult males and females, or for adults and children, because the F1 ~ F2
planes for women – and particularly young children – are considerably stretched in
both dimensions relative to those of male speakers (hence the elongation of the
envelopes drawn around tokens of the peripheral monophthongs in Figure 1).
As mentioned above, numerous techniques have been devised in an attempt to
reduce the discrepancies between the speech of men, women and children in this
respect. Some are designed to compress the higher frequency ranges used by women
and children relative to the lower ones; others work by expressing individual values in
terms of distance from a mean derived from the formant frequency measurements
themselves. An example of the first sort of transform is the Bark transform, which
involves conversion of Hz measurements into perceptual units based on the critical
bandwidth response of the ear (Zwicker & Feldtkeller 1967). We make no criticism of
the use of Bark-transformed data, nor the validity of the scale itself, except to say that
it does not in fact fully permit direct comparison of one speaker’s vowel sample with
another speaker’s vowel sample in the way we would wish. This is because the
influence of VTL is not actually wholly eliminated, since within the frequency range
in which F1 typically falls – between c. 200Hz and 1 kHz – the mapping between Hz
and Barks is effectively linear (see Traunmüller 1990; Adank et al. 2001). Within this
frequency range, higher Hz values correspond very closely to proportionately higher
Bark values, and it is only at frequencies well above those in which F1 is found that
there is significant divergence between the scales. Therefore the problem of cross-
speaker mapping persists, although the ‘compression’ of higher frequency ranges,
such as those in which F2 is commonly found for adult speakers, corrects this problem
to some degree. However, if our aim is to map one speaker’s vowel space onto
another’s for the purposes of comparing their vowel systems, in a way which removes
absolute differences in formant frequency further than Bark-transforming the data will
allow, we must follow another approach.
We evaluate in this paper a method for allowing direct visual and statistical
comparison of vowel spaces for different speakers which derives from measurements
in Hz of F1 and F2 at the midpoints of stressed spoken vowels. Our focus will be on an
assessment of the extent of reduction of speaker sex-related differences in samples of
vowel formant frequencies for two RP British English speakers (one male, one
female) where the frequency values are expressed on the following scales: (a) linear
Hz; (b) critical band rate z (in Barks) and (c) a so-called ‘S transform’. The last of
these is calibrated from the F1 ~ F2 plane’s ‘centre of gravity’ S by taking the grand
mean of the mean F1 and F2 frequencies for points at the apices of a triangular plane
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Evaluation of a technique for mapping
which are assumed to represent F1 and F2 maxima and minima for the speaker in
question (these being [i], [a] and [uÈ]; see below). The procedures for calculating z and
S values for individual speakers are outlined in detail in the next section. Our estimate
of the improvement in comparability between speaker samples is based on the
increase in mapping between one speaker’s vowel triangle and another’s along two
continuous parameters: (a) the ratio of the area of the female speaker’s vowel
triangle to that of the male speaker’s triangle and (b) the degree of overlap between
the two triangles, expressed in terms of that percentage of the male speaker’s triangle
which overlaps with the female speaker’s triangle, and vice versa. It is demonstrated
that on both counts the S transform performs much better than Bark-transformed
representations of the two speakers’ vowel triangles.
2. Methods
2.1 Procedure for calculating critical band rate z (in Barks)
The transform used here is that from Traunmüller (1990):
26.81 f
1960 + f
z = - 0.53
where f is frequency in Hz. According to Traunmüller, the values obtained using this
equation agree with the values tabulated by Zwicker (1961) to within ±0.05 Bark in
the frequency range 0.2 – 6.7 kHz.
For our present purposes, one advantage of converting all Hz measurements
using the above equation is that one can apply the same transform to all the formant
frequency measurements made for any number of speakers. The disadvantage, as
noted above (and as demonstrated below), is that one only marginally reduces the
effect of VTL, rather than eliminating it as far as possible. So while it is considerably
more time-consuming to convert Hz measurements into the S-transformed values used
for the comparison discussed in Section 3 below (because S values for each individual
speaker must be calculated for F1 and F2), the latter technique, as we shall see, allows
a much higher degree of mapping between samples for speakers whose VTLs are very
different from each other.
2.2 Procedure for calculating S
Our procedure for determining the F1 and F2 values of S for an individual
speaker is discussed in this section. For clarity, we follow Wells (1982) in assigning
the keywords FLEECE and TRAP to the lexical sets containing the vowels labelled /iù/
and /a/ in other descriptions of British English phonology, since we believe the use of
phonetic symbols to represent vowel categories which are highly variable in British
English (to the extent that, for example, the TRAP vowel can be realised as anything
from [Q] to [], depending upon accent) to be potentially confusing.
2.2.1 Step One
· Assume that for a given speaker’s sample the average F1 and the average F2
for the vowels of words of the FLEECE set represent that speaker’s minimum
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F1 and maximum F2. This seems a reasonable assumption, if no
observations are made to the contrary (but see below).
· Assume that for a given speaker’s sample the average F1 for the vowels of
words of the TRAP set represents that speaker’s maximum F1. Depending
upon the accent, one might wish to select words of the START set instead,
since in certain accents of British English the TRAP vowel is generally
produced with a somewhat raised quality. The influence of post-vocalic
rhoticity in certain accents might present problems if START is used,
however, because of the influence of a following rhotic on the formants of
vowels in words like start, car, farm, etc. The point is to obtain an estimate
of the region in which a speaker’s maximum F1 is located, but clearly it is
sensible to be consistent within a given sample (i.e. choosing either TRAP or
START for all the informants concerned).
By definition, there will be individual formant frequency values higher and
lower than the average F1 and F2 values we take to be maxima and minima for these
formants. It might therefore be said that because F1 and F2 values for a given vowel
category are generally somewhat - indeed often highly - variable, taking the mean
values for F1 and F2 runs the risk of giving a false picture of the extremes of a
speaker’s vowel plane. However, averaging the F1 and F2 values for a given vowel
category eliminates (or at least reduces) the potential of inaccurate individual formant
frequency measurements to distort the geometry of an individual speaker’s vowel
triangle.
It might also be objected that this routine assumes that each speaker’s FLEECE
and TRAP vowels are more or less invariant, when it is clear from many previous
studies that they are not, even in highly controlled speech elicited using artificial
means. We must assume for the time being that FLEECE is rather less variable in
accents of British English than other vowels, and that TRAP (or START) is likely to be
the most open vowel speakers of British varieties will use. Again, it should be stressed
that if the researcher is satisfied that FLEECE is relatively stable across a sample of
speakers, that if he/she is circumspect about the choice of open vowel to use as the F1
maximum, and that if formant measurement is done as consistently as possible, we
should be able to arrive at optimally comparable samples for speakers of different
sexes and ages.3
2.2.2 Step Two
The next step is to arrive at an estimate of the F1 and F2 minima for a given
speaker. In a very large number of studies of vowel variation in English, this limit is
taken to be represented by the average F1 and F2 values for the vowel /u/, which we
label here GOOSE. We take the view, however, that in many accents of English GOOSE
is only rarely fully back, fully close, and fully rounded (see e.g. Hagiwara 1997;
Watson et al. 1998; Labov 2001: 475ff), and that the average formant frequencies for
this vowel produced by the average British English speaker are not a good reflection
of the minimum possible F1 and F2 frequencies that such a speaker could achieve.
3 There is no reason why other vowel categories such as KIT and/or FACE could not be used to represent
F1 minima and F2 maxima, should it be anticipated or observed that the average formant values for
FLEECE do not in fact provide a reliable estimate of these limits in the accent(s) under scrutiny.
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Evaluation of a technique for mapping
Instead, we advocate the use of hypothetical lower limits on F1 and F2 which, though
almost certainly not attested in a sample of informant’s speech, are nonetheless
arrived at in a principled way. These minimal values (or rather coordinates on the F1 ~
F2 plane) we label [uÈ]. They are arrived at as follows:
· It will be recalled from Section 2.2.1 that the average F1 for FLEECE was
assumed to represent the minimum F1 for a given speaker. Therefore, we
may assume that the F1 of [uÈ] is equivalent to that for FLEECE, since we
have no evidence to suggest that it is any lower.
· Since - by definition - F2 cannot have a lower frequency than F1, but often
has a frequency so close to it that the spectral peaks cannot reliably be
distinguished from one another using instrumental analysis, we can
justifiably assume for present purposes that the speaker’s closest, backest
possible vowel has an F2 exactly equivalent to its F1 frequency. Thus, F1
and F2 of [uÈ] are (a) equal to the average F1 value for FLEECE for a given
speaker, and therefore (b) exactly equal to one another.
The result of these calculations is a triangular area on the F1 ~ F2 plane, as
shown in Figure 2. Note that the axes are reversed, as is conventional in x-y plots
representing vowel systems.
Figure 2. Schematised representation of the ‘vowel triangle’ used for the calculation of S. i = min.
F1, max. F2 (average F1 ~ F2 for FLEECE); a = max. F1 (average F1 ~ F2 for TRAP); uÈ = min. F1,
min. F2, where F1 (uÈ) and F2 (uÈ) = F1 (i).
F2
uÈi
F1
a
2.2.3 Step Three
The next step is to calculate for the individual speaker in question the Fn
frequencies of the centre of gravity or ‘centroid’ S (following Koopmans-van Beinum
1980), which is quite simply the grand mean of Fn for i, a and uÈ (a worked example is
provided in Appendix 2). We then divide all the observed measurements of Fn by the
S value for that formant, and express all resulting figures as values on scales Fn/S(Fn),
i.e. as ratios of S. Because S(Fn) divided by S(Fn) is always equal to 1 (with the
coordinates of S therefore always being (1,1) in any speaker’s vowel triangle), vowel
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Watt & Fabricius
tokens with low Fn values on the Hz scale will have Fn/S(Fn) values between 0 and 1,
while vowels with Fn values greater than the S value for that formant will have
Fn/S(Fn) values higher than 1. Since all speakers’ vowel triangles will be defined
relative to S, we can compare samples for different speakers, both statistically and
visually, directly with another. Plotting average or individual F1 ~ F2 measurements
for phonologically ‘back’ vowels such as GOOSE and GOAT on the F1/S(F1) ~ F2/S(F2)
plane is thus straightforward, regardless of how phonetically back or front these
vowels are.
2.3 Materials
We turn now to compare vowel samples for the two British English RP speakers
referred to in Section 1. The data are drawn from formant frequency measurements
made by Deterding (1997) from recordings of BBC broadcasts held in the MARSEC
(Machine Readable Spoken English Corpus) database (Roach et al. 1993).4 The
programmes in question were broadcast in the 1980s, and according to Roach et al.,
‘the accent of all the speakers is RP or close to it’ (Roach et al. 1993:48). From the ten
speakers (5 male, 5 female), we selected a male speaker and a female speaker at
random. The speakers in question are A (female) and C (male); speaker A’s sample is
drawn from a religious affairs programme, while C’s is based on a radio lecture on
economics (see Deterding 1997:48). Because our intention here is to assess the
relative effectiveness of z-transforming and S-transforming the linear Hz data in terms
of mapping one speaker’s FLEECE ~ TRAP ~ GOOSE triangle onto another’s, it is
sufficient to use two speakers whose formant frequencies in the Hz domain for
‘equivalent’ vowels are markedly mismatched, though of course any number of
speakers could be compared using this technique.
Details of how the original formant measurements themselves were made can be
found in Deterding (1997:48-50); the source figures can be downloaded directly from
the Internet.5
3. Results
3.1 Triangles plotted using Hz scale
The relative shapes, sizes and and degree of overlap between the triangles
generated from the raw Hz data for speakers A and C are shown in Figure 3.
Agreement of the areas of the two triangles is poor: that for the female speaker
A (DA) is almost four times larger than that for the male speaker C (DC) at a DC : DA
ratio of 1 : 3.93 (see Table 1 below for the full results in tabular form). The degree of
overlap is also low: the proportion of DC overlapping DA is just 46.1%. That is, more
than half of DC lies in an area of the vowel plane which is unoccupied by DA, as we
would expect given the significantly lower average F1 ~ F2 frequencies for adult male
speakers. The proportion of the vowel plane occupied by DA which lies outside DC
approaches 90% (86.3%). We can say, therefore, that the mapping of the samples for
these two speakers is overall very poor.
4 See http://www.rdg.ac.uk/AcaDepts/ll/speechlab/marsec/.
5 http://www.arts.nie.edu.sg/ell/davidd/data/jipa-vowels/index.htm. Note that the URL provided in the
appendix of Deterding (1997) is no longer active.
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Evaluation of a technique for mapping
3.2 Triangles plotted using z (Bark) scale
Figure 4 shows the same data z-transformed using Traunmüller’s equation
discussed in Section 2.1.
Figure 3. Comparison of FLEECE ~ TRAP ~ GOOSE vowel triangles for Speakers A and C (linear
Hz).
FLEECE GOOSE
TRAP
FLEECE
GOOSE
TRAP
200
300
400
500
600
700
800
900
1000
1100
1200
10001500200025003000
F2 (Hz)
F1 (Hz)
Speaker A (Female) Speaker C (Male)
Figure 4. Comparison of FLEECE ~ TRAP ~ GOOSE vowel triangles for Speakers A and C
(Barks).
FLEECE
GOOSE
TRAP
FLEECE GOOSE
TRAP
2
3
4
5
6
7
8
9
10
1010.51111.51212.51313.51414.51515.5
F2 (Bark)
F
1
(Bark)
Speaker A (Female) Speaker C (Male)
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Watt & Fabricius
There is a noticeable improvement here in terms of area ratio, the ratio of DC to
DA now being 1 : 2.76. This means that there is an improvement in agreement in area
ratio of 29.8% over the equivalent triangles on an F1 (Hz) ~ F2 (Hz) plane if we
transform the Hz measurements into Bark units. However, the extent to which the two
triangles overlap is not greatly improved: the portion of DC which overlaps DA still
accounts for just under half (49.9%) of the total area of DC, while the overlapping area
occupies a mere 18.1% of DA.
3.3 Triangles plotted using S units
If the Hz figures are transformed using the S-transform described in Section 2.2
above, however, we see dramatic improvements in both area ratio and degree of
overlap. Figure 5 shows that all but a tiny fraction of DC overlaps with DA, and that
there is a substantial improvement in the match between the areas for the two
triangles.
Figure 5. Comparison of FLEECE ~ TRAP ~ GOOSE vowel triangles for Speakers A and C
(Fn/S(Fn)).
TRAP
GOOSE
FLEECE
FLEECE
TRAP
GOOSE
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.7511.251.51.752
F2/S(F2)
F1/S(F1)
Speaker A (Female) Speaker C (Male)
Although there is still clearly a fair degree of mismatch between the areas of the
two triangles – particularly in terms of F1 differences for each of the three vowel
categories – at a DC : DA ratio of 1 : 2.16 the agreement in area is nonetheless
improved relative both to Hz (45% improvement) and to the Bark-transformed data
(21.7% improvement). Degree of overlap expressed in terms of the proportion of DC
overlapping with DA approaches complete overlap, at 99.2%. That portion of DA
overlapping DC is 45.8% of the overall area of DA.
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Evaluation of a technique for mapping
3.4 Summary
To summarise the marked improvements in area and overlap agreement
resulting from S-transforming the original Hz data, the figures discussed in the
preceding paragraphs above are shown in tabular form in Table 1.
Table 1. Improvements in area ratio and degree of overlap between FLEECE ~ TRAP ~ GOOSE
triangles for Speakers A (female) and C (male).
Hz Bark S
area ratio (DC : DA) 1 : 3.93 1 : 2.76 1 : 2.16
% improvement over Hz - 29.8 45
% improvement over Bark - - 21.7
% overlap (DC : DA) 46.1 49.9 99.2
% improvement over Hz - 8.2 115.2
% improvement over Bark - - 98.8
% overlap (DA : DC) 13.7 18.1 45.8
% improvement over Hz - 32.1 234.3
% improvement over Bark - - 153
It may be noted from Figure 5, incidentally, that the Fn/S(Fn) values for Speaker
C’s GOOSE vowel approach (1,1). That is, his GOOSE vowel is on average very close to
the centre of gravity calculated for his vowel space on the basis of the actual and
extrapolated F1 ~ F2 values in his sample. This can be seen as a demonstration of the
advantages of not using the average F1 and F2 values for GOOSE in the calculation of
S, since if C’s GOOSE vowel has average F1 and F2 values in the central region of his
vowel space it would be unwise to treat it as a ‘back’ vowel from a phonetic point of
view. If we were to use it to represent the F1 ~ F2 minima for this speaker because we
assume it to be the closest and backest vowel that speaker could produce, we run the
risk of distorting the overall shape and underestimating the extent of Speaker C’s
maximal triangle on the F1 ~ F2 plane. Furthermore, by plotting a speaker’s actual
average F1 ~ F2 values for GOOSE and other phonologically back vowels within the
triangle whose rearward boundary is defined by the extrapolated coordinates [uÈ], we
gain an impression of the location of these back vowels relative to this rearward limit.
For example, we can assess whether one English speaker is in the habit of using on
average a fronter pronunciation of the GOOSE or GOAT vowels than another, and we
can, moreover, be confident that if differences of this sort are in evidence when the
relevant formant frequency values are expressed in terms of Fn/S(Fn), they will also be
found in the original Hz measurements (i.e., that they are not artefacts of the S-
transform algorithm but reflect real inter-speaker differences which are not
attributable simply to difference in VTL).
It is perhaps trivial to point out that individual vowels can be plotted on the
F1/S(F1) ~ F2/S(F2) space as easily as averaged Fn/S(Fn) values for vowel categories
can. By way of illustration, Figure 6 in Appendix 1 shows Hz and Fn/S(Fn) plots for all
the individual vowel tokens for Speaker A. We feel, however, that it is important to
note that the absence of warping of the vowel space of the sort inherent in Bark-
transformed data means that one can inspect vowel plots plotted on axes using the
Fn/S(Fn) scale as though they were plotted using Hz scales, while simultaneously
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Watt & Fabricius
being able to map multiple plots onto one another more fully than is possible using
either the Hz or the Bark scale.
4. Conclusion
We may see from Table 1 that the S-transform allows much closer mapping of
samples for different speakers onto one another than do the original measurements in
linear Hz, and their equivalent values on the Bark scale. It outperforms the z-transform
on both criteria, and more particularly on the overlap criterion, in which
improvements are on the order of 100 – 150%.
We do not intend the above evaluation as a criticism of the Bark scale in any
other respect, however: we propose the S-transform only as a means of allowing
enhanced visual and statistical comparisons between vowel formant data sets collected
for different speakers, and do not claim it has any psychoperceptual validity (e.g. that
it mimics the normalisation process assumed to exist for the auditory processing of
speech signals, or such like). Instead, we see it solely as a useful tool for researchers
wishing to reduce inter-speaker differences resulting from variations in VTL when
performing analyses of vowel samples in, for instance, instrumental studies of vowel
variation and change.
Although it has been demonstrated using only very limited amounts of data
drawn from recordings of two English speakers, we do not expect that the
effectiveness of the S-transform on the area ratio/overlap criteria will be diminished
much, if at all, if applied to data from other languages, or from larger numbers of
speakers. Although it is a relatively cumbersome algorithm to use on large samples of
vowel formant data (especially compared to converting Hz values into Bark units)
there are clear advantages - at least according to the criteria chosen for this evaluation
- to the S transform over Hz measurements or their equivalents on the Bark scale.
There are obviously great improvements that could be made, for example by finding
some means of correcting the discrepancy between male and female speakers with
respect to F1/S(F1), or perhaps by running the S-transform on z-transformed data.
There are also many other normalisation algorithms that the S-transform can be
evaluated against on the area ratio and overlap parameters used as criteria in the
present study; comparisons will be reported on in due course.
References
Adank, P., van Hout, R. & Smits, R. (2001). A comparison between human vowel
normalization strategies and acoustic vowel transformation techniques.
Proceedings of the 7th International Conference on Speech Communication and
Technology (Eurospeech 2001) Aalborg, Vol. I. pp. 481-4.
Deterding, D. (1990). Speaker normalization for automatic speech recognition.
Unpublished PhD thesis, University of Cambridge.
Deterding, D. (1997). The formants of monophthong vowels in Standard Southern
British English pronunciation. Journal of the International Phonetic Association
27. 47-55.
Disner, S.F. (1980). Evaluation of vowel normalization procedures. Journal of the
Acoustical Society of America 67(1). 253-61.
Eremeeva, V. & Stuart-Smith, J. (2003, forthcoming). A sociophonetic investigation
of the vowels OUT and BIT in Glaswegian. Proceedings of the 15th International
Congress of Phonetic Sciences, Barcelona.
169
Evaluation of a technique for mapping
Hagiwara, R. (1997). Dialect variation and formant frequency: the American English
vowels revisited. Journal of the Acoustical Society of America 102(1). 655-8.
Hindle, D. (1978). Approaches to vowel normalization in the study of natural speech.
In Sankoff, D. (ed.) Linguistic Variation: Models and Methods. New York:
Academic Press. pp. 161-72.
Iivonen, A. (1994). A psychoacoustical explanation for the number of major IPA
vowels. Journal of the International Phonetic Association 24(2). 73-90.
Koopmans-van Beinum, F.J. (1980). Vowel contrast reduction: an acoustical and
perceptual study of Dutch vowels in various speech conditions. PhD thesis,
University of Amsterdam.
Labov, W. (2001). Principles of Linguistic Change, vol. II: Social Factors. Oxford:
Blackwell.
Ladefoged, P. & Maddieson, I. (1990). Vowels of the world’s languages. Journal of
Phonetics 18. 93-122.
Lieberman, P. & Blumstein, S.E. (1988). Speech Physiology, Speech Perception, and
Acoustic Phonetics. Cambridge: Cambridge University Press.
Lobanov, B.M. (1980). Classification of Russian vowels spoken by different speakers.
Journal of the Acoustical Society of America 67. 253-61.
Moore, B.C.J. & Glasberg, B.R. (1983). Suggested formulae for calculating auditory-
filter bandwidths and excitation patterns. Journal of the Acoustical Society of
America 74. 750-3.
Peterson, G.E. & Barney, H.L. (1952). Control methods used in a study of the vowels.
Journal of the Acoustical Society of America 32. 693-702.
Roach, P., Knowles, G., Varadi, T. & Arnfield, S. (1993). MARSEC: a machine-
readable spoken English corpus. Journal of the International Phonetic
Association 23. 47-54.
Rosner, B.S. & Pickering, J.B. (1994). Vowel Perception and Production. Oxford:
Oxford University Press.
Stevens, K.N. (1998). Acoustic Phonetics. Cambridge, Mass.: MIT Press.
Traunmüller, H. (1990). Analytical expressions for the tonotopic sensory scale.
Journal of the Acoustical Society of America 88(1). 97-100.
Watson, C.I., Harrington, J. & Evans, Z. (1998). An acoustic comparison between
New Zealand and Australian English vowels. Australian Journal of Linguistics
18(2). 185-207.
Watt, D.J.L. & Tillotson, J. (2001). A spectrographic analysis of vowel fronting in
Bradford English. English World-Wide 22(2). 269-302.
Wells, J.C. (1982). Accents of English (3 vols). Cambridge: Cambridge University
Press.
Zwicker, E. (1961). Subdivision of the audible frequency range into critical bands
(Frequenzgruppen). Journal of the Acoustical Society of America 33. 248.
Zwicker, E. & Feldtkeller, R. (1967). Das Ohr als Nachrichtenempfänger. Stuttgart:
S. Hirtzel Verlag.
170
Watt & Fabricius
Dominic Watt Anne Fabricius
Department of English English Section
University of Aberdeen Department of Language & Culture
Taylor Building Roskilde University
Old Aberdeen PO Box 260
Aberdeen AB24 3UB DK-4000 Roskilde
Scotland Denmark
d.j.l.watt@abdn.ac.uk fabri@ruc.dk
171
Evaluation of a technique for mapping
Appendix 1
Figure 6. Vowel plots for Speaker A (data from Deterding 1997). Scales are in Hz (upper pane)
and in Fn/S(Fn) units (lower pane).
200
400
600
800
1000
1200
1400
50010001500200025003000
F2 (Hz)
F1 (Hz)
FLEECE
KIT
DRESS
TRAP
STRUT
START
LOT
THOUGHT
FOOT
GOOSE
NURSE
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
0.250.751.251.75
F2/S(F2)
F1/S(F1)
FLEECE
KIT
DRESS
TRAP
STRUT
START
LOT
THOUGHT
FOOT
GOOSE
NURSE
172
Watt & Fabricius
173
Appendix 2
Calculation of S: worked example (figures for Speaker A).
Mean F1 and F2 for [i a uÈ], derived from Deterding’s (1997) data
Vowel F1 (Hz) F2 (Hz)
i 304 2664
a 1067 1690
uÈ 304 304 (i.e. both values equal to F1 for [i])
ß
Mean F1 and F2 for S
304 + 1067 + 304 1675
S(F1) = = = 558.3
3 3
2664 + 1690 + 304 4658
S(F2) = = = 1552.7
3 3
ß
Speaker A’s FLEECE, TRAP and GOOSE means (Hz) converted into S units
304 2664
1067 ¸ 558.3 1690 ¸ 1552.7
333 1529
ß
Vowel F1/S(F1) F2/S(F2)
FLEECE 0.545 1.716
TRAP 1.911 1.088
GOOSE 0.596 0.985
