Quantifying Vowel Space Using Recordings of the IPA Vowels

Bob ShackletonCongressional Budget Office

Quantitative Linguistics and DialectologyUniversity of Groningen

June 29, 2012

• 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

Introduction

• 28 cochleagrams per recording per speaker (values in tenths of Barks)

• Cochleagrams are variable for each recording and across speakers – total ~5,500

Cochleagrams

Bark/10Hertz11 10321 19831 29741 40351 51761 64171 77881 93191 1104101 1298111 1520121 1773131 2062141 2392151 2772161 3209171 3711181 4289191 4955

• 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

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)

• 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: Factors

• 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

Factor Analysis: Loadings

• 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

A VERY Simple Characterization of Factors

Three-Dimensional Dispersion

Three-Dimensional Dispersion

Three-Dimensional Dispersion

• 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

• 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

Conclusions

Data MDS Factors SimpleData 1.000 0.998 0.898 0.958MDS 0.998 1.000 0.902 0.960Factors 0.898 0.902 1.000 0.850Simple 0.958 0.960 0.850 1.000