Quantifying Vowel Space Using
Recordings of the IPA Vowels
Bob Shackleton
Congressional Budget Office
Quantitative Linguistics and Dialectology
University of Groningen
June 29, 2012
Introduction
• Quantifying relative distances between different sounds is a key requirement of
dialectometry – for impressionistic records and modern acoustic analysis
• Proposal: analyze multiple experts’ recordings of cardinal vowels from the
International Phonetic Alphabet to characterize vowel space (extending work
by Heeringa, Leinonen, and others)
• Recordings by Jones, Ladefoged, Esling, Wells, House, and others
• Use Praat software to develop cochleagrams of each recorded vowel
• Calculate Euclidean distances between cochleagrams and apply 3D
multidimensional scaling (MDS) to the distance matrix
• Apply (rotated) factor analysis (FA) directly to cochleagrams to develop 3D
characterization of vowel space
• Use a simple characterization of factors to explore characterization
• Basic Result: Analysis yields intuitively sensible 3-dimensional quantification of
vowel space and distances among vowels
Cochleagrams
• 28 cochleagrams per recording per speaker (values in tenths of Barks)
• Cochleagrams are variable for each recording and across speakers – total ~5,500
Bark/10
11
21
31
41
51
61
71
81
91
101
111
121
131
141
151
161
171
181
191
Hertz
103
198
297
403
517
641
778
931
1104
1298
1520
1773
2062
2392
2772
3209
3711
4289
4955
Multidimensional Scaling
• Average together all speakers’ cochleagrams for each of the 28 IPA vowels; calculate a matrix of
Euclidean distances between all the averages; apply MDS to averages, specifying 3 dimensions
• Rotate and normalize MDS results so that [a] is at [0.0,0.0,0.0], [ɑ] is at [3.0,0.0,0.0], and [i] is on the
x,y plane (i.e., open unrounded front to back distance = 3.0 and open unrounded front is directly
“above,” as in traditional vowel diagram)
• MDS dimensions 1 and 2 mainly characterize backing and height, respectively, dimension 3 mainly
rounding (shape is basically a rectangular box with the closed back unrounded corner “smooshed in”)
• Blue through green diamonds are front to back unrounded vowels; red through yellow circles are front
to back rounded vowels
Multidimensional Scaling
• Dimension 3 mainly characterizes rounding: all unrounded vowels except for [ɤ] and [ɯ]
take positive or near-positive values; rounded values uniformly non-positive
• Matrix of Euclidean distances among vowels nearly perfectly correlated with matrix of
Euclidean distances between average cochleagrams; that is, the MDS is replicating the
relative distances among the original average cardinal vowels
• Limitation of MDS: results cannot be easily applied to new data
Multidimensional Scaling
Multidimensional Scaling
Multidimensional Scaling
Where is Rounding?
Rounding is characterized mainly as a deviation from unrounded intensities in the second
formant – roughly Barks 9 through 14 or 1100 Hz through 2600 Hz)
Factor Analysis: Factors
• Perform factor analysis with varimax rotation on all 5000+ cochleagrams, specifying 2 or 3
factors
• For 2 factors, loadings on cochleagrram intensities closely replicate Leinonen’s (2010) barkfilter
results for Swedish speakers; if a 3rd factor is specified, it appears between the first two
• Factor 1 captures variation mainly in Barks 14 through 20 (Formant 3 values – ~2400 Hz +)
• Factor 2 captures variation mainly in Barks 5 through 9 (Formant 1 values – ~500 to 1100 Hz)
• Factor 3 captures variation in Barks 10 through 13 (Formant 2 values – ~1100 to 2400 Hz), right
where rounding differences appear
Factor Analysis: Loadings
• Again, average together all speakers’ scores for each vowel; normalize and rotate so that [a] is at
[0.0,0.0,0.0], [ɑ] is at [3.0,0.0,0.0], and [i] is on the x,y plane
• Reasonably good replication of original distances, but not as good as MDS: correlations with
original data & with MDS distances are both about 0.9 (still get the same “smooshed box” shape)
• Oblique rotation of factors yields almost exactly the same results, suggesting that factors are
indeed essentially orthogonal
• Factors can be applied to any new data to place it in the same grid
A VERY Simple Characterization of Factors
• Simplify the factors: calculate a Factor 2 /Formant 1 value that is just the average of
cochleagram values 41 to 90; a Factor 3 / Formant 2 value that is the average of values 91 to 130;
and a Factor 1 /Formant 3 that is the average of values 131 to 200
• Average together all speakers’ scores for each vowel; e.g. CFU [i] = 29.2, 25.2, 43.0
A VERY Simple Characterization of Factors
• Again, rotate and normalize the values so that [a] is at [0.0,0.0,0.0], [ɑ] is at [3.0,0.0,0.0], and [i] is
on the x,y plane
• Better replication of original Euclidean distances than the factor analysis: correlation with data
and with MDS distances = 0.97, correlation with factors = 0.85
• Can still be applied to any new data
• Variance among speakers: the average standard deviations are 1.0 for Factor 1 / Formant 3, 0.5
for Factor 2 / Formant 1, and 0.9 for Factor 3 / Formant 2
Three-Dimensional Dispersion
Three-Dimensional Dispersion
Three-Dimensional Dispersion
Conclusions
• Can apply MDS, factor analysis, or even simpler calculations to cochleagrams
of recordings of cardinal vowels to characterize vowel space
• Each analysis yields intuitively sensible 3-dimensional characterization of
vowel space and distances among vowels
• Approaches yield closely correlated results, and are essentially consistent with
formant analysis
Data
MDS
Factors
Simple
Data
1.000
0.998
0.898
0.958
MDS
0.998
1.000
0.902
0.960
Factors Simple
0.898
0.958
0.902
0.960
1.000
0.850
0.850
1.000
• Results suggest that:
• the entire spectrum is important, not just the formants, and
• relative average intensities across a few broad ranges of frequencies
contain most of the important information needed to process vowels
• Factor results can be applied to any recording