A crosslinguistic analysis of vowel inventory size influence on vowel dispersion

Miao Zhang

University of Zurich

Eleanor Chodroff

University of Zurich

Background

Phonological and phonetic typology

• Considerable research on phonological typology (Maddieson 1984; Gordon 2016).
• Phonetic typology, however, is less well-studied (Becker-Kristal 2010; Chodroff 2024), and the relationship between phonological typology and phonetic realization is not well understood.
• Due to the increase in computational power and the availability of large-scale multilingual corpora, we can now investigate phonetic typology questions in a more systematic and crosslinguistically comparable way (Salesky et al. 2020; Paschen, Fuchs, and Seifart 2022; Blum et al. 2024).

A phonetic typological question

• Vowel inventories vary widely in size across languages, from as few as 2 vowel qualities (Ubykh, Abkhaz) to 14 (German) (Maddieson 1984; Maddieson 2013).
• Inventory Size Hypothesis (ISH): As the number of vowels in a language increases, the phonetic realization of vowels may be influenced to maintain distinctiveness.
• Two possible strategies:
  • Global dispersion: the overall vowel space may expand to accommodate more contrasts.
  • Local precision: individual vowel categories may become more precise and less variable to reduce confusability.

Theories on optimal vowel systems

Quantal Theory (QT)

• Point vowels occupy stable “quantal regions.” They tolerate continuous articulatory variation with minimal acoustic change, requiring less articulatory precision (Stevens 1972, 1989).

Adaptive Dispersion Theory (ADT)

• Point vowels occupy the extremes of the acoustic space. They maximize global dispersion to enhance perceptual contrast and minimize confusability (Liljencrants and Lindblom 1972; Lindblom 1986, 1990; Vaux and Samuels 2015).

Dispersion-Focalization Theory (DFT)

• Point vowels optimize two competing pressures. They maximize global dispersion (inter-vowel distance) and local focalization (converging formants that create highly salient spectral peaks) (Schwartz et al. 1997a, 1997b).

Theoretical predictions

Prediction 1 (QT):

• Point vowels are located in intrinsically stable articulatory-acoustic plateaus. Neither global dispersion nor local precision should change systematically with the inventory size.

Prediction 2 (ADT):

• Point vowels must maximize perceptual contrast. As inventory size increases, global dispersion expands, and local precision increases.

Prediction 3 (DFT):

• Point vowels optimize both perceptual distance and salience. As inventory size increases, global dispersion expands, but local precision remains stable, anchored by inherent characteristics of focal salience (formant convergence).

Schematic illustration of ISH

Measures of dispersion in previous work

Global	Local
Convex hull area (Al-Tamimi and Ferragne 2005); mean distance to vowel space center (Engstrand and Krull 1991); maximal F1/F2 ranges (Recasens and Espinosa 2009)	Standard deviation/variance (Heeringa and Schoormann 2015); acoustic ellipses (Recasens and Espinosa 2009); inter-token distances (Engstrand and Krull 1991)

Negative evidence

The majority of previous work did NOT find supportive evidence for ISH, either in global dispersion or local precision.

• Global Dispersion:
  • Engstrand and Krull (1991); Livijn (2000); Meunier et al. (2003); Recasens and Espinosa (2006); Recasens and Espinosa (2009); Gendrot and Adda-Decker (2007); Lee (2012); Heeringa and Schoormann (2015); Salesky et al. (2020); Hutin and Allassonnière-Tang (2022).
• Local Precision:
  • Bradlow (1995); Livijn (2000); Meunier et al. (2003); Recasens and Espinosa (2006); Recasens and Espinosa (2009); Lee (2012); Heeringa and Schoormann (2015); Salesky et al. (2020); Hutin and Allassonnière-Tang (2022).

Positive evidence

Some studies did find supportive evidence for ISH.

• Global dispersion:
  • Flege (1989); Jongman, Fourakis, and Sereno (1989); Bradlow (1995); Guion (2003); Al-Tamimi and Ferragne (2005); Peters, Heeringa, and Schoormann (2017); Larouche and Steffann (2018).
• Local precision: Found some evidence (Larouche and Steffann 2018).

Methodological limitations in prior work

Limited Language Sampling

• Most experimental studies investigate very few languages (Range: 2-7; Median: 3; Mean: 3.67).

Restricted Speaker Pools

• Speaker sample sizes are often remarkably small, ranging from 1 to 20 speakers per language, with a median of 5, and a mean of 7.2.

This introduces substantial bias, yet the exact magnitude of the bias remains unclear.

Research questions

We investigate the effect of vowel inventory size on vowel dispersion (global dispersion and local precision) across 67 languages using a large-scale multilingual phonetic corpus, VoxCommunis (Ahn and Chodroff 2022), using the point vowels /i, a, u/.

Research Questions:

1. Do larger vowel inventories show greater global dispersion?

2. Do larger vowel inventories show increased local precision?

Metrics to quantify vowel dispersion

1. Global dispersion: Mean distance to the vowel space center of each speaker × vowel group.

2. Local precision 1: Mean distance to the vowel centroids of each speaker × vowel group.

3. Local precision 2: 95% confidence ellipse area of each speaker × vowel group.

4. Overall confusability: Joint conditional entropy of the vowel system of each speaker in each language.

Global dispersion

Mean distance to the vowel space center of each speaker × vowel group.

Local precision 1

Mean distance to the vowel centroids of each speaker × vowel group.

Local precision 2

95% confidence ellipse area of each vowel category of each speaker.

\[\text{Area} = \pi \cdot \chi^2_{0.95, 2} \cdot \sqrt{|\mathbf{\Sigma}|}\]

Where \(\mathbf{\Sigma}\) is the covariance matrix of (F1, F2) within each speaker × vowel group.

Overall confusibility

Joint conditional entropy of the vowel system of each language. Lower entropy = less distributional uncertainty and confusability.

\[H(F1,F2|V)=\sum_{v}p(v)H(F1,F2|V=v)\]

Where \(H(F1, F2 \mid V=v)\) is the entropy of the 2D Gaussian distribution of vowel \(v\) computed from its covariance matrix \(\mathbf{\Sigma}_v\):

\[H(F1, F2 \mid V=v) = \frac{1}{2} \ln \det(2\pi e \mathbf{\Sigma}_v)\]

Joint conditional entropy

Entropy is computed from the full 2D covariance structure and reflects the overall confusability of the vowel system at the language level.

Methods

The dataset

Our dataset consists of speech from across 67 languages in 18 language families, produced by 59,658 speakers. The number of speakers per language ranges from 10 to 17,293, with a mean of 890 and a median of 160.

Corpus: Common voice

Speech comes from Mozilla Common Voice (Ardila et al. 2019) with phone- and word-level alignments from VoxCommunis (Ahn and Chodroff 2022).

Common Voice: an open-source, crowd-sourced multilingual dataset created by Mozilla, consisting of scripted read speech, and currently contains over 20,000 hours of speech in 120+ languages.

• The language should have at least 2 hours of validated recordings.
  • Validated recordings = recordings that have at least two upvotes.
• The language should either have a working G2P model or a pronunciation dictionary with a good coverage of the lexicon in Common Voice.

Corpus: VoxCommunis

VoxCommunis is a phonetic corpus derived from the Common Voice dataset, specifically curated to support large-scale cross-linguistic acoustic analysis and laboratory phonetics research.

• Forced alignment with the Montreal Forced Aligner (McAuliffe et al. 2017).
• For languages that lack an existing pronunciation dictionary with a good coverage of the lexicon in Common Voice, we created a new dictionary using either rule-based or neural network-based grapheme-to-phoneme (G2P) conversion.
• We performed speaker verification to ensure that each client ID in Common Voice includes only voices from one speaker. For details, see Zhang et al. (2025).

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Formant extraction and processing

From all monophthongal vowel tokens (regardless of length or stress contrast) in VoxCommunis, we extracted the first two formants at the vowel midpoint using Parselmouth (Jadoul, Thompson, and de Boer 2018).

Formant tracking parameters for different pitch ranges:

Pitch Range	F0 Threshold	Frequency Range	Number of Formants	Window length
High	≥ 160 Hz	0–5500 Hz	5	0.025s
Low	< 160 Hz	0–4500 Hz	4	0.040s

Outliers were removed within each language \(\times\) vowel \(\times\) pitch range using a 95% Mahalanobis distance threshold (\(\text{df} = 2\)).

Formants were speaker-normalized with the ΔF method (Johnson 2020) using all tokens for each speaker.

ΔF method normalization

The ΔF method models the vocal tract as a uniform tube to calculate a speaker-specific formant spacing parameter (\(\Delta F\)). Scaling raw formants by \(\Delta F\) removes anatomical variance, centering the normalized vowel space on (0.5, 1.5).

\[ \Delta F = \frac{1}{mn} \sum_{j=1}^{m} \sum_{i=1}^{n} \left[ \frac{F_{ij}}{i - 0.5} \right] \]

\[ F_i' = \frac{F_i}{\Delta F} \]

Where:

• \(n = 2\) (calculated over F1 and F2).
• \(F_{ij}\): \(i\)-th raw formant of the \(j\)-th token.
• \(F_i'\): normalized, scale-invariant formant value.

Filtering on speaker and language

Speakers and languages:

• Each speaker should have produced no less than 20 tokens of each point vowel (/i, a, u/), and each language should have at least 10 speakers after filtering.

Special cases of vowels:

• The Abkhaz schwa (/ə/) is retained as a special case for /i/.
• Japanese /ɯ/ is retained as the dominant high back vowel for /u/.

Vowel quality counts:

• Inventory sizes count vowel-quality contrasts, not length or nasality, following Whalen and Levitt (1995).

Statistical modeling

For each vowel-level metric (Metrics 1-3):

\[ \text{metric} \sim \text{vowel} * \text{inventory size} + (1 + \text{vowel} \mid \text{language}) \]

• Vowel is sum-coded such that the intercept in the model corresponds to the grand mean of the three point vowels.

For the joint conditional entropy metric (Metric 4):

\[ \text{entropy} \sim \text{inventory size} + (1 | \text{language}) \]

Modeling Results

Result 1: No reliable evidence for global dispersion

Inventory-size effect:
\(\beta = 0.005\), \(SE = 0.003\), \(p = 0.109\)

No reliable evidence that larger inventories push point vowels farther from the vowel space center.

Result 2: Local precision increases

Distance to centroid
\(\beta = -0.008\), \(SE = 0.002\), \(p = 0.001\)

Ellipse area
\(\beta = -0.018\), \(SE = 0.008\), \(p = 0.039\)

Larger inventories show tighter, more compact vowel categories across both metrics.

Result 3: Overall confusability decreases

Inventory-size effect:
\(\beta = -0.060\), \(SE = 0.020\), \(p = 0.003\)

Lower entropy indicates less distributional uncertainty within vowel categories.

Discussion

Interpretation

Inventory pressure appears to affect local precision more clearly than global dispersion.

• Larger inventories do not show a reliable increase in distance to the vowel space center.
• The local-precision metrics decrease with inventory size as well as joint conditional entropy of each language, which quantifies the uncertainty across vowel categories.
• The evidence supports the precision side of the inventory size hypothesis.

Interpretation

These are mixed results that partially support the phonetic predictions of Quantal Theory (QT) and Adaptive Dispersion Theory (ADT), but not that of Dispersion-Focalization Theory (DFT).

Dispersion is constrained

According to QT, the point vowels are already in the most stable region of the articulatory-acoustic space, so they cannot be pushed farther apart without sacrificing acoustic-perceptual stability.

Precision is flexible

However, languages can reduce the acoustic spread of the vowels to enhance the perceptual distinctiveness when the entire vowel space becomes more crowded.

Probing the bias in previous work

• Previous research has not shown a consistent relationship between vowel inventory size and vowel dispersion, potentially due to bias in sampling.

• The mean number of language examined in previous experimental study was less than 4, and the average number of speakers per language was only 7.

• To evaluate the bias due to small samples, and to estimate the probable minimum number of languages needed to make a reliable typological inference, we ran a two-step resampling simulation based on our dataset.

Resampling simulation

1. Bias Evaluation

• 5000 iterations of randomly sampling \(N = 3\) languages of different inventory size.
• Fit a regression model (joint conditional entropy ~ inventory size) for each sample.
• Distribution of slopes (Sig. Negative/Positive vs. Not Sig., \(\alpha = 0.05\)).

2. Power Analysis via Resampling

• Sweep \(N = 3 \to 40\) languages (2,000 iterations per step).
  • When \(N\) is not more than the number of unique inventory sizes, the languages have to differ in inventory size. When \(N\) is larger than the number of unique inventory sizes, each inventory size should have at least one language.
• Fit a regression model (joint conditional entropy ~ inventory size) for each sample.
• Threshold: The exact \(N\) where error rate stabilizes \(< 5\%\).
  • Error rate \(=\) proportion of Not Sig. or Sig. Positive results in 2000 samples.

Results of bias evaluation

• 3-language samples are highly biased, with over 25% of the samples showing an effect that does not support ISH.

Example of a highly biased sample

Results of empirical power analysis

A minimum of 8, preferably 28 languages are needed to reduce sampling bias to an acceptable level.

Benefit of large-scale corpus analysis

• Large-scale corpus analysis allows us to test the hypothesis across a large number of languages, which reduces the sampling bias and increases the reliability of the results.
• All languages can be analyzed under the same pipeline, which reduces the variability introduced by different experimental designs and analysis methods.

Limitations

• Does the pattern of no global dispersion hold for non-point vowels?
• The quality of corpus phonetic data depends on various sources: the recording, the acoustic model, the G2P conversion, the description of its inventory size, and other preprocessing steps. E.g.,
  • G2P transcriptions of some languages are more narrow than others.
  • The acoustic model is of better quality for languages with more training data.
  • More than half of the languages in our corpus are Indo-European, which may limit the generalizability of the results.
• The analysis tests association, not a causal mechanism.

Next steps

• Add finer vowel categories where alignments and inventories support them.
• Compare production precision with perceptual precision. The two may be differently affected by inventory size.
• Include more non-Indo-European languages to further reduce sampling bias and increase the generalizability of the results.

Conclusion

• Across 67 languages, larger vowel inventories show vowel production with greater local precision, but not reliably greater global vowel dispersion.

• For a crosslinguistic phonetic typological claim like the inventory size hypothesis, low numbers of sampled languages can easily lead to biased results.

• Corpus phonetic studies allowing for large-scale crosslinguistic analysis can help reduce sampling bias and increase the reliability of the typological inference.

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