A Reanalysis of the Voicing Effect in English: With Implications for Featural Specification

2.1 Production

The above hypotheses encounter more problems when the voicing effect is examined more closely. Voicing effects occur even when voiced obstruents are phonetically devoiced (Chen, 1970; Fox & Terbeek, 1977; Walsh & Parker, 1981), ruling out an active articulation-based source that relies on actual vocal fold vibration (although such a source may have been active at some previous time, and the pattern subsequently phonologized). A universal basis for the effect is called into question by the apparent absence of a lengthening effect in certain languages (Flege, 1979; Hillenbrand et al., 1984; Keating, 1979, 1985). ¹ Even in English, with one of the most robust voicing effects measured, durational differences are not found in all contexts. Production studies typically consist of either word lists or brief sentences read by participants in a laboratory setting. In sentence contexts, the target words are often in utterance final position. Such words are also typically monosyllabic, which entails that the target vowel receives primary stress. When some or all of these factors are varied, the voicing effect can be significantly reduced, or disappear altogether: in phrase-medial position (vs. phrase-final) (Crystal & House, 1988; Luce & Charles-Luce, 1985; Smith, 2002; Umeda, 1975), ² polysyllabic words (vs. monosyllabic) (Klatt, 1973; Port, 1981; Umeda, 1975), ³ lax vowels (vs. tense) (Crystal & House, 1988; Luce & Charles-Luce, 1985; Peterson & Lehiste, 1960), ⁴ unstressed vowels (vs. stressed vowels) (de Jong, 2004; Van Summers, 1987), ⁵ and fast speaking rates (vs. slow speaking rates) (Ko, 2018; Port, 1976; Smith, 2002). ⁶

2.2 Compensation

Obstruent duration differences mirror vowel duration differences: they are small or non-existent in the contexts in which vowel duration differences are small or non-existent (Crystal & House, 1982; Luce & Charles-Luce, 1985; Miller et al., 1986), ⁷ and they are large where large vowel duration differences are found, and in the opposite direction (e.g., Chen, 1970; Klatt, 1976; Luce & Charles-Luce, 1985; Miller & Volaitis, 1989; Umeda, 1975). ⁸ The inverse correlation between differences in obstruent duration and differences in preceding vowel duration was noted early on (Catford, 1977; Kozhevnikov & Chistovich, 1965). However, temporal compensation as an explanation for the voicing effect has been explicitly considered and rejected on a number of separate occasions (Braunschweiler, 1997; Chen, 1970; Keating, 1985). These rejections are largely based on the assumption that temporal compensation should be total, or near total, with the consequence that all syllables would have the same length. ⁹

Although syllable-level isochrony was originally hypothesized to apply in so-called “syllable-timed” languages like English (e.g., Pike, 1945), and to be the source of a number of apparently compensatory effects, it has become clear that uniform timing for syllables is not consistently enforced in English ¹⁰ or in any other language that has been investigated (see Krivokapić, 2020 for a review).

2.3 Competition

More recent work on temporal compensation is situated within Articulatory Phonology (AP), which does not assume isochrony at any level. This is appealing for “compensatory” phenomena that range widely in their degree (e.g.,Elert, 1965; Kavitskaya, 2002; H. Kim & Cole, 2005; Kristoffersen, 2000; Munhall et al., 1992). In AP, articulatory units of various sizes are modeled as harmonic oscillators with different characteristic frequencies (e.g., Browman & Goldstein, 1988, 1990; Nam & Saltzman, 2003; O’Dell & Nieminen, 1999; Saltzman et al., 2008). Phasing relationships between such articulatory units are modeled as oscillator coupling, in which the system settles at a characteristic frequency intermediate between the frequencies of the individual units. The same result can be derived from a competing constraints model in which none of the individual constraints on preferred frequencies can be perfectly satisfied, and a “compromise” frequency is adopted. Our model of the voicing effect is based on this approach. ¹¹

2.4 Intrinsic duration

In our proposed model, it is preferred durations at the segment level that drive the voicing effect. We posit that something similar is at work in so-called prominence-based compensation, which occurs between two syllables of inherently different durations within the same word. Final lengthening associated with phrasal boundaries is typically strongest for the segment closest to the boundary, and extends only as far as the onset of the final syllable in most cases (Berkovits, 1993; Cambier-Langeveld, 1997; Campbell, 1992; Hofhuis et al., 1995; Port & Cummins, 1992; Turk & Shattuck-Hufnagel, 2007). However, Cambier-Langeveld (1997, 2000) show that, in Dutch, the penultimate syllable of the final word also sometimes experiences significant lengthening. This happens only when the final syllable is unstressed, or contains a schwa vowel (see also, Katsika, 2016; Turk & Shattuck-Hufnagel, 2007 for similar results).

In these studies, the characteristically shorter duration of unstressed vowels seems to prevent them from lengthening to a degree sufficient to satisfy the requirements of phrase-final lengthening. The voicing effect can be described in similar terms: lengthening (also often due to a phrase-final boundary) “shifts” to earlier segments (the vowel) when the final segment (the voiced obstruent) cannot be lengthened sufficiently. ¹²

2.5 Elasticity

Our model assigns a characteristic elasticity to each segment, which mediates the degree to which the segment resists pressures to lengthen or shorten from its preferred duration (see also Cambier-Langeveld, 2000; Miller, 1981). The concept of elasticity is related to the concept of spring stiffness in AP (e.g., Browman & Goldstein, 1986): a force of the same size will cause a greater perturbation to a spring with a smaller stiffness parameter, resulting in a longer duration. However, elasticity differs from spring stiffness in important ways: it applies to phonemes, which are not part of the inventory of timing units within AP, and not just to phonemes as a class, but to individual phonemes.

What is crucial in our model is that elasticity and duration determine the proportion of the syllable that each segment comprises (see Campbell, 1992). Our Expandability Hypothesis is defined in (1).

(1) The Expandability Hypothesis

All segments have a characteristic elasticity that determines their resistance to lengthening

Resistance to lengthening increases with increasing duration for all segments

Lower elasticity equates with a more rapid increase in resistance

Relative resistance determines the distribution of duration across the syllable

Modeling voiceless obstruents as high elasticity, and voiced obstruents, as low elasticity, we will show that the Expandibility Hypothesis parsimoniously accounts for the production data on the voicing effect, and is also, crucially, consistent with the existing perception data.

2.6 Perception

It turns out that vowel duration is not the only cue, and may not even be the main cue, to the voicing distinction in final obstruents. Wardrip-Fruin (1982) demonstrates that when preceding vowel duration conflicts with either formant transition cues, or actual vocal fold vibration, the latter dominates. Hogan and Rozsypal (1980) also report that, for certain voiceless-final words, lengthening the vowel does not change the percept to voiced, but produces no effect, or results in stimuli that sound unnatural. Revoile et al. (1982), using naturally produced stimuli, find that the identification of voiced stops is most strongly disrupted by removing vowel offset cues (see also Nittrouer, 2004; O’Kane, 1978), while the identification of voiceless stops is most strongly disrupted by removing the release burst. Similarly, Repp and Williams (1985) find that the addition of a release burst to otherwise ambiguous stimuli reduces voiced responses. Changes to vowel duration, on the contrary, have little effect on voicing perception in their study.

It is our hypothesis that the perception results are based primarily on obstruent duration. It was established quite early on that the perceptual boundary between the fricatives /s/ and /z/ in final position is dependent on both consonant and vowel duration (Denes, 1955); see also Raphael (1981) and Repp and Williams (1985). In fact, the literature on voicing in word-medial position standardly describes the perceptual boundary in terms of the ratio of closure duration to preceding vowel duration (e.g., Lisker, 1957; Port, 1979, 1981; Port & Dalby, 1982). The C/V ratio effectively normalizes stop duration relative to estimated speaking rate. This is exactly what we believe occurs in final position, with final lengthening accounting for the magnitude of the effect.

3.1 The data

The Buckeye Corpus consists of segmented and transcribed sound files. These are taken from interviews, each lasting about an hour, with 40 different speakers, all middle-class and Caucasian, who are also natives of central Ohio. Intertranscriber reliability of the phonetic symbols for stops and fricatives was reported for a sample of the Buckeye Corpus at 91.2% and 92.9%, respectively. For the unanimously transcribed subset of this sample, segmentation boundaries differed by an average of 16 ms. (Pitt et al., 2005). However, Raymond et al. (2002) report a difference in segmentation agreement for shorter versus longer phones: 73% of phones that were longer than average agreed within 20% of the average length of the two phones on either side of the segment boundary, whereas only 50% of phones that were shorter than average agreed within 20%. Shorter phones were thus proportionally less consistently transcribed than longer phones. In the absence of a consistent bias in the placement of the boundary, such errors could wash out a small voicing effect. Given that the voicing effect is expected to be larger for longer durations, however, this is unlikely to affect the outcome significantly. The segmentation of the vowel and final consonant are inherently negatively correlated; an error in which the vowel duration is longer will also produce an error in which the final obstruent is shorter. However, such ambiguity is more likely to arise with voiced than with voiceless stops. Thus, we would expect such errors to inflate any voicing effect.

From the Buckeye Corpus we extracted all monosyllabic words of the form (C)onsonant-(V)owel-(C)onsonant ending with one of the following obstruents: voiced (d,b,g,z,ʒ,v) or voiceless (t,p,k,s,ʃ,f). Consonant–vowel–consonant (CVC) words were selected because they were expected to show the largest voicing effect. Complex onsets were excluded to eliminate potential variability. No nasalized or rhotacized vowels were included, to be sure that each word had exactly three underlying segments. Only tokens that were both phonemically and phonetically CVCs were included. For example, tokens of “past” realized as [pæs], and tokens of “allowed” realized as [lâʊd] were both excluded. Because the transcription of the corpus is quasi-phonetic, we constructed a dictionary of citation forms to ensure that the phonological voicing category was correctly assigned to each word. Because there were no words ending in voiced dental fricatives, those ending in voiceless dental fricatives were also removed. The vowel /oȏɪ/ was also excluded for reasons of data sparsity. In all, 20.3% of the stops in the remaining data were transcribed as glottalized (tq), which could represent a glottal stop or unreleased stop with glottalization on the vowel, but less than 1% of those were underlyingly voiced, so all such tokens were removed from analysis. Affricates were excluded due to the possibility that they might straddle a word boundary.

In Figure 1, raw vowel durations for the set of CVC word tokens used in the following analyses are plotted as a function of the voicing feature of the final obstruent. If a voicing effect does exist in these data, it is masked by factors that affect vowel duration more strongly. The density plot on the right suggests that there is a very small effect of voicing at the longest durations. However, the actual counts given in the left panel show that there are never more voiced than voiceless tokens at any duration. This is due to the fact that there are considerably more word tokens with (phonemically) voiceless coda obstruents (over twice as many as voiced tokens, although there are more voiced than voiceless fricative tokens; see Appendix A). Vowels preceding voiceless obstruents have a slightly longer mode than those preceding voiced obstruents, and at the longer durations (above 175 ms.), the relative proportion of the voiced-preceding distribution is larger than the voiceless-preceding. For the most part, however, the two distributions are completely overlapped, showing no transparent voicing effect.

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Figure 1.

All CVC vowel durations: a) histogram b) density plot c) log duration density plot.

3.2 Model factors

The following factors, each of which is known to affect segment duration, are included in the statistical model of vowel duration. Because the analysis was limited to CVC words, stress and word length are not included:

3.3 Method

All statistics were performed using the lme4 package in R. Linear mixed effects models were run using the function lmer, fit by REML. The lmerTest function was used to obtain estimated p-values. All continuous numerical variables were log-transformed and mean-centered to approximate a normal distribution with a mean of zero. Following Tanner et al. (2019), we normalize by dividing by two standard deviations. Random intercepts for word and speaker were included in all models. Place of articulation of the final obstruent, although known to affect consonant duration, was too small of an effect to significantly improve model fit, and was therefore left out of the final model. Due to the asymmetric distribution of the data, it was not possible to used paired data in analyzing the voicing effect. All factors were sum-coded so that each individual factor was assessed at the mean value of all other factors. Three-way interactions were avoided for reasons of interpretability as well as model convergence.

3.4 Results

For each variable, the average value of its levels (if a factor), or of its range of values (if a continuous numerical variable) was the baseline for analysis. This allows us to conceptualize the results in a way that is similar to analysis of variance (ANOVA), where each effect is an adjustment to the average value for the model. For example, the effect of Vowel Class is determined by whether the average duration of the class of tense vowels is significantly different from the global vowel duration average, calculated over both tense and lax vowels.

We begin the analysis with a simple model of vowel duration, containing no interactions, but using random intercepts for word, speaker, and vowel quality (models with random slopes did not converge); see Table 1.

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Table 1.

Results of the Following Linear Regression Model: Vowel Duration as a Function of Vowel Height (Non-High = 1), Vowel Length (Tense = 1), Speaking Rate, Voicing (Voiced = 1), Obstruent (Stop = 1), Phrase Postion (Final = 1), and Frequency (No Interactions Included).

	Estimate	Std. error	df	t value	Pr(>|t|)
(intercept)	4.48	0.05	18.2	83.4	<2e-1 6
Vowel type	0.08	0.04	10.7	1.99	.07
Vowel height	1.56	0.05	10.3	3.36	.007
Speaking rate	−0.17	6.0e-3	1.9e4	−27.6	<2e-16
Voicing	0.07	0.01	341	4.85	1.85e-6
Obstruent type	−0.04	0.01	1.2e3	−3.29	.001
Phrase position	0.41	7.9e-3	1.9e4	52.2	<2e-16
Frequency	−.20	0.02	347	−9.43	<2e-16

As expected, there was a significant main effect of speaking rate. Longer vowel durations were found at slower than average speaking rates. Word frequency also had the expected negative effect on vowel duration, such that words with higher than average frequency had shorter vowel durations. As predicted, high vowels were shorter than the average of high and low vowels. However, tense vowels were not significantly longer than the average of tense and lax vowels. Pre-pausal tokens were longer than phrase-medial. Voicing was also significant: vowels preceding voiced obstruents were longer than vowels preceding voiceless obstruents.

Our second model included interactions between voicing and speaking rate, voicing and frequency, voicing and vowel height, voicing and vowel length, and voicing and phrase-position. Frequency, speaking rate, and phrase-position remained significant, but voicing did not. See Table 2. The result was the same for a model including only pre-pausal tokens.

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Table 2.

Results of the Following Linear Regression Model: Vowel Duration as a Function of Vowel Height (Non-High = 1), Vowel Length (Tense = 1), Speaking Rate, Voicing (Voiced = 1), Obstruent (Stop = 1), Phrase Postion (Final = 1), and Frequency, and the Interaction Between Voicing and Speaking Rate, Voicing and Frequency, Voicing and Vowel Height, Voicing and Vowel Class, and Voicing and Phrase-Position.

	Estimate	Std. error	df	t values	Pr(|t|)
(Intercept)	4.48	0.05	18.6	83.1	<2e-16
Vowel height	0.15	0.05	10.4	3.30	0.008
Vowel length	0.09	0.04	10.9	2.09	0.06
Voicing	0.02	0.02	220	0.99	0.32
Speaking rate	−0.2	6.1e-3	1.9e4	−27.5	<2e16
Obstruent type	−0.04	0.01	1.2e3	−3.23	0.001
Frequency	−0.98	0.02	3449	−9.24	<2e16
Phrase-position	0.42	8.1e-3	1.9e4	51.5	<2e16
Voicing: speaking rate	−2.4e-3	5.9e-3	1.9e4	−0.40	0.69
Voicing: frequency	−0.04	0.02	351	−1.86	0.06
Voicing: phrase-position	0.03	8.1e-3	1.9e4	3.27	0.001
Voicing:vowel height	0.01	0.02	307	0.75	0.45
Voicing: vowel length	0.02	0.01	325	1.31	0.19

This is somewhat surprising, given that Tanner et al. (2019) report a voicing effect for phrase-final tokens in the Buckeye Corpus. However, they use a model that includes interactions between voicing and frequency, voicing and vowel type, voicing and obstruent type, and voicing and word class. They included random intercepts for speaker, word, and vowel quality, as well as random slopes for speaker by frequency, vowel type, obstruent type, word class, and by the interaction of voicing and obstruent type. Random slopes were also included for word by both speaking rate measures that they used. This model overfits our data and does not converge. We did find a significant interaction between voicing and phrase position, and a marginal interaction between voicing and frequency. Both factors increase the voicing effect, and both factors also increase the duration of the word. This suggests that the significant voicing effect in the simple model was driven by longer words. We posit that this effect, in turn, is driven by the difference in obstruent duration, which increases with increasing word duration.

A regression model with obstruent duration as the dependent variable shows that voicing is significantly negatively correlated (see Table 3). Interactions between voicing, and rate, frequency, and phrase-position are all significant, indicating that the (negative) effect of voicing is reduced for fast rates, high frequency words, and non-pre-pausal position, as predicted. Although these results, in and of themselves, cannot prove the hypothesis that vowel duration differences arise from consonant duration differences, they are consistent with that hypothesis.

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Table 3.

Linear Regression Model of: Consonant Duration as a Function of Voicing, Rate, Stop Type, Frequency, Phrase Position, and Interactions Between Voicing and Rate, Frequency and Phrase-Position.

	Estimate	Std. error	df	t value	Pr(>|t|)
(intercept)	−0.07	0.02	170	−3.25	0.001
Voicing	−0.06	0.02	172	−3.30	0.001
Speaking rate	−0.17	6.1e-3	1.9e4	−30.0	<2e-16
Obstruent type	−0.14	9.8e-3	69.8	−14.7	<2e-16
Frequency	−0.13	0.02	313	−7.32	2.0e-12
Phrase position	−0.47	8.2e-3	1.9e4	57.3	<2e-16
Voicing: Rate	0.03	5.9e-3	1.9e4	4.30	1.7e-5
Voicing: Frequency	0.05	0.02	313	2.81	0.005
Voicing: Phrase	0.10	8.1e4	1.9e4	11.8	<2e-16

3.5 Summary and discussion of corpus results

The corpus results show that voicing is a significant predictor in the simple model, but not in the model containing interactions, failing to replicate the finding of Tanner et al. (2019). We also see a dependence of the voicing factor on absolute durations in interaction terms with phrase-position and frequency. Consonant duration is also strongly (negatively) correlated with voicing and shows the same interactions for phrase-position and frequency, respectively. This is expected if the voicing effect is actually an effect of consonant duration, where the difference in obstruent duration between voiced and voiceless obstruents increases with increasing duration.

On the contrary, laboratory production studies find that there is a large and consistent voicing effect; vowels preceding voiced obstruents can be up to twice as long as vowels preceding voiceless obstruents (Chen, 1970; House, 1961; Luce & Charles-Luce, 1985; Mack, 1982; Peterson & Lehiste, 1960; Umeda, 1975). Similarly, voiceless stop closure durations can be from 25% to 50% longer than voiced stop closures (Chen, 1970; Luce, 1986). These discrepancies can be explained by the large difference in absolute durations between the corpus and the laboratory. Vowel durations in these studies are reported in the range of 175–300 ms (House, 1961; Luce & Charles-Luce, 1985; Mack, 1982; Peterson & Lehiste, 1960; Umeda, 1975), with voiceless stop closures ranging from 95 to 140 ms (Chen, 1970; Luce & Charles-Luce, 1985). For the vowel tokens in the Buckeye Corpus, on the contrary, durations this long are rare. Among the set of CVC words ending in voiced obstruents, less than 7% reach durations of 200 ms or above. Even restricting the sample to just characteristically longer vowels, only 13% of such tokens fall in this range. Median vowel duration over the complete set of CVC words used in this study is only 83 ms. Median vowel duration for just the voiced tokens is actually lower than that, at 75 ms. Similarly, only 9% of CVC-final voiceless stops reach durations of 100 ms or above in the Buckeye Corpus, while the median closure duration is 46 ms.

4.1 Methodology

4.2 Data selection and annotation

Each participant produced approximately 8 tokens of each word at each rate. To avoid edge effects, and fluctuations in rate, a single representative token from the center of the group was selected and measured. Because each token was surrounded by other tokens at the same repetition rate, it was possible to segment both the closure and the release interval for each stop. Occasionally, at the fastest rates, final stops did not have a clear release. In those cases, the end of the stop was set to the end of the voicing bar (for voiced stops), or the point at which the amplitude returned to background levels (for the voiceless stop). Background level was estimated by the amount of noise visible during the gaps between successive words.

The most ambiguous cases involved the segmentation of the sonorant /l/ from the following /o/ vowel, given a large degree of coarticulation. At faster rates, the point at which the release of the final /d/ became the initial fricative of the following token of “feed” could also be hard to determine. This was also true of the final /v/ and the initial /θ/ in “thieve” sequences. Measurement variability is likely to be highest in those contexts. Note, however, that any measurement errors for these kinds of tokens will only introduce error for one of the measured variables. For “lo,” the vowel duration will be affected by where the segment boundary is placed, but not the final p/b. For “feedfeed” and “thievethieve” the coda duration will be affected by where the segment boundary is placed, but not the vowel duration. Furthermore, any possible annotator bias in segmenting the sequence “lo,” for example, would have a minimal impact on the results, first because each participant was assigned to a single annotator, meaning that any effect could be absorbed into a random effect by speaker, and second, because both the voiced and voiceless minimal pairs would be segmented in the same way, such that the voicing effect (the difference in vowel durations) would not be affected by any bias. There is a possibility of resyllabification for the fastest word repetition rates, but this is only likely for p#l and b#l sequences in the lope/lobe pair. If such resyllabification occurred, we might expect the stop to be shorter, with reduced aspiration. In fact, this might explain the abrupt drop in VOT between rates 4 and 5 for this word pair (see Figure 2).

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Figure 2.

Closure duration, VOT, and Total duration (TDur) for final stops as a function of repetition rate (decreasing from left to right). Means and standard error bars.

The data for the first two word pairs (feet/feed, thief/thieve) were randomly assigned to three undergraduate research assistants for annotation. One of the authors and two of the RAs then re-measured a subset of the data produced by the other two annotators. Discrepancies between any two raters were discussed as a group to establish shared criteria for ambiguous tokens. The two RAs then individually reviewed their previous measurements and made adjustments where their original segmentation did not meet the discussed criteria. The same two RAs each also re-measured half the data of the third RA who had left the lab at that point. The second set of words (lobe/lope, doze/dose) were measured later, by an additional two RAs. Measurement verification was conducted in the same way. It was stressed that the most important criterion was consistency. As a final check, 2% of all tokens from each annotator were re-measured by the first author, selected in pairs in order to assess the discrepancy in the measured voicing effect. In terms of absolute durations, vowel measurements differed by an average of 12 ms, and total consonant durations differed by an average of 21 ms. The difference in vowel duration between voiced and voiceless minimal pairs differed by 13 ms, and the difference in total consonant duration by 30 ms. However, because the durations were sometimes longer than the first author’s measurements, and sometimes shorter, the actual effect of discrepancies in this sample of data were much smaller: 6 ms shorter for vowel duration; 12 ms shorter for total consonant duration, a vowel duration difference that was 3.6 ms smaller, and a consonant duration difference that was 15 ms larger.

Occasionally the voiced stops and fricatives at the slower repetition rates were produced with a final epenthetic schwa. There were 29 such tokens. Any words with final schwa were removed from the analysis. Praat (Boersma & Weenink, 2009) was used for segmentation and annotation.

4.3 Results

In Figure 2, final consonant durations for the stop-final words are plotted as a function of repetition rate (shown as a number between 1 and 5, where 5 is the fastest rate, and 1 the slowest). Voiced and voiceless tokens are plotted separately, and three different duration measures are given: closure (black), VOT (light gray), and the sum of the two (TDur: dark gray). Closure duration for final voiced stops varied relatively little across repetition rates. However, most stops were also produced with a period of aspiration (VOT). Voiced stops show a clear increase in total duration as rate decreases, but one that appears to plateau at the slowest rates. For voiceless stops, closure duration increases steadily, patterning very closely with VOT. Because both duration measures show a dependence on rate, total duration was used as the dependent variable for testing the Expandability Hypothesis.

Figure 3 provides duration data for the full set of words, both vowel duration (triangles), and total obstruent duration (filled circles). Visual inspection shows that larger vowel durations were reached by the voiced member of each minimal pair, while larger obstruent durations were reached by the voiceless member. There is also a larger difference between consonant and vowel durations for voiced-final tokens across all repetition rates, and that difference increases with decreasing repetition rate.

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Figure 3.

Total consonant duration and preceding vowel duration, as a function of repetition rate. Means and standard error bars.

A linear mixed-effects model was fit to the vowel duration data as a function of repetition rate and consonant duration. Consonant duration was treated as a continuous variable, and repetition rate, as an ordinal variable. Random intercepts for participant and word were included. Random slopes were not used as they caused the model to fail to converge, or led to singularity. As expected, a significant (linear and quadratic) effect of speaking rate was found (vowels were longer at slower speaking rates). There was also a main effect of consonant duration; vowels were longer when the coda consonant was shorter. The interaction between rate and consonant duration also reached significance; the negative effect of consonant duration was strongest at the slowest rates (see Table 4).

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Table 4.

Mixed-Effects Linear Regression Model of Vowel Duration as a Function of Speaking Rate and Consonant Duration and Their Interaction.

	Estimate	Std. error	Estimated df	t value	p value
(Intercept)	355	25.1	27.3	14.2	4.1e-14
rate.L	324	15.0	970	21.6	<2e-16
rate.Q	42.5	15.2	969	2.8	.005
rate.C	4.17	15.6	968	0.27	.79
rate 4	−12.6	15.7	967	−0.80	.42
Consonant Duration	−0.17	0.06	978	−2.88	.004
rate.L: C Duration	−0.64	0.11	969	−5.66	2.0e-8
rate.Q: C Duration	−0.08	0.11	969	−0.77	.44
rate.C: C Duration	−0.06	0.11	968	−0.59	.55
rate 4: C Duration	0.10	0.10	967	0.98	.33

A separate model of vowel duration as a function of rate and voicing behaves very similarly. As before, random intercepts were used for participant and word, but random slopes were not used as they caused the model to fail to converge, or led to singularity. Main effects of (linear) rate and voicing are found (reference level is Voiceless), as well as an interaction between voicing and rate such that the positive effect of voicing is strongest at slower rates.

The model of consonant duration as a function of voicing confirms the interpretation that the “voicing” effect is driven by consonant duration (see Table 5). Random intercepts for participant and word were included. Random slopes were not used as they caused the model to fail to converge, or led to singularity. A fully crossed rate, voicing, and manner model produced significant main effects of speaking rate (linear), voicing, and manner. Fricatives were significantly longer than stops (reference level is Stops). A significant interaction between rate (linear) and voicing was also found, indicating, as expected, that differences in duration between voiced and voiceless consonants increased with decreasing repetition rate. An interaction between manner and rate (linear) also reached significance: the difference in duration between fricatives and stops was even larger at slower rates.

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Table 5.

Mixed-Effects Linear Regression Model of Consonant Duration as a Function of Speaking Rate, Voicing, and Manner, With Full Interactions (Three-Way Interactions Are Not Included).

	Estimate	Std. error	Estimated df	t value	p value
(Intercept)	160.1	7.253	7.175	22.07	7.37e-8
rate.L	87.84	6.835	960.2	12.85	<2e-16
rate.Q	−3.07	6.85	960	−0.45	.65
rate.C	−2.38	6.86	960	−0.35	.73
rate^4	−1.26.	6.88	960	−0.18	.86
voicing	−54.96	8.804	3.987	−6.243	.003
manner	28.83	8.812	4.001	3.272	.031
rate.L:voicing	−46.76	9.702	960.2	−4.819	1.67e-6
rate.Q:voicing	−9.77	9.70	960	−1.01	.31
rate.C:voicing	4.61	9.69	960	0.48	.63
rate^4:voicing	−1.13	9.69	960	−0.12	.91
rate.L:manner	19.59	9.715	960.2	2.016	.044
rate.Q:manner	−18.7	9.71	960	−1.93	.05
rate.C:manner	4.60	9.75	960	0.47	.64
rate^4: manner	3.88	9.73	960	0.40	.69
voicing: manner	−14.2	12.5	4.00	−1.14	.32

A final analysis of the paired duration differences confirms the negative correlation between the difference in duration of voiceless and voiced consonants, and the difference in duration of their preceding vowels. Random intercepts for participant and word were included. Random slopes were excluded as they caused the model to fail to converge, or led to singularity. Adding manner to the model also resulted in singularity. The final model of ∆ V  =  ( V V L − V V D ) included rate and consonant duration difference, Δ C = ( C V L − C V D ) , and their interactions. A significant main effect of rate (quadratic) and ∆ C were found, and significant interactions between ∆ C and rate, for both the linear and the quadratic terms. Thus the voicing effect (∆ V ) is shown to be larger for larger negative values of ∆ C , which are enhanced at the slowest speeds (see Table 6). Only significant factors are shown.

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Table 6.

Mixed-Effects Linear Regression Model of Vowel Duration Difference as a Function of Consonant Duration Difference, Manner and Rate, With Full Interactions.

	Estimate	Std. error	Estimated df	t value	p value
(Intercept)	−57.37	12.34	6.891	−4.649	.002
Δ C	−0.217	0.064	475.8	−3.390	.001
rate.L	−14.7	11.1	455	−1.33	.19
rate.Q	30.11	10.94	451.8	2.751	.006
rate.C	8.26	11.1	448	0.75	.46
rate^4	−4.53	10.8	448	−0.42	.68
rate.L: ∆C	−0.376	0.139	460.4	−2.701	.007
rate.Q: Δ C	−0.277	0.133	455.8	−2.081	.038
rate.C: ∆C	−0.06	0.13	451	−0.48	.63
rate^4: ∆C	−0.006	0.13	451	−0.05	.96

4.4 Discussion

These results strongly support the Expandability Hypothesis. First, we confirm the predicted difference in lengthening between voiced and voiceless consonants in coda position, paralleling what has been repeatedly found in initial and medial position (Miller & Baer, 1983; Miller & Volaitis, 1989; Port, 1976, 1981; Volaitis & Miller, 1992). There is a difference in consonant durations at all rates, ¹⁵ and there is also a large difference in the slopes of the duration curves. The difference in consonant duration increases with decreasing rate, as does the vowel duration difference. Pairing consonant duration differences with vowel duration differences at each speaking rate shows that the strength of the voicing effect is significantly correlated with the size of the consonant duration difference, something that cannot be captured with a binary voicing feature. The significant interaction between rate and consonant duration (vowels), and between rate and voicing (consonants), is precisely what is predicted if vowel duration differences derive from consonant duration differences. In fact, absolute vowel duration differences and consonant duration differences are very close. Rhyme (VC) durations were significantly different between voiceless and voiced, but not large, at 26 ms. For stops, the rhyme duration difference was only 2.8 ms. These results probably overestimate the degree to which vowel and consonant duration are traded off, given that the experimental task is highly unnatural, and likely to bias more toward uniform syllable duration than natural speech contexts.

5.1 A competing constraints model of the voicing effect

In this section we model the voicing effect as the outcome of a competition between duration targets at the segment level which conflict with final-targeted lengthening. Each segment possesses an inherent elasticity which is implemented as the weighting factor on a constraint that acts to keep the segment at its preferred duration. Constraints are implemented as Normal probability distributions. Each distribution assigns the highest probability to its preferred duration (the mean of the distribution), and smoothly decreasing probabilities for durations both longer and shorter than that mean. The variance of the distribution controls how quickly the probability decreases. ¹⁶ The smaller the variance, the more rapid the decrease, and the greater the resistance to deviations from the mean. Its variance thus acts effectively as a weighting factor for each constraint. This means that, all else being equal, a segment with a broader probability distribution will be lengthened or shortened more than a segment with a narrower probability distribution. Variance thus also maps to segment elasticity. Constraint “competition” in this model is realized through maximization of the joint probability function over all constraints. This function exhibits the desired behavior: one constraint may be “violated” to a greater degree (a decrease in probability) if this allows another, more highly weighted constraint to be less “violated” (a greater increase in probability).

The results reported here are for VC syllables. The three segment-level constraints for the voicing effect model are shown graphically in Figure 4. Voiced and voiceless obstruent constraints are given the same mean value in these simulations, differing only in their variance. In the absence of a lengthening force it is assumed that segments default to their preferred durations.

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Figure 4.

Probability densities for: voiced obstruent (solid); voiceless obstruent (thick solid); and vowel (dashed).

A nonzero lengthening force generates target durations for consonant and vowel. To model final lengthening, this force is not distributed equally, but is biased toward the segment closest to the prosodic boundary (the consonant in this case). Furthermore, lengthening under applied force is calculated proportionally. In other words, the same force applied to consonant and vowel will lengthen each the same relative amount, but not by the same amount in absolute terms. The variable α controls the distribution of the lengthening force. Constraints associated with target durations impose a penalty for deviating from that target, expressed as a function of the normalized difference between target ( S t ) and actual segment ( S a ) duration: S t − S a S t .

For a given force value, the model conducts a brute force search for the durations of the coda consonant (D or T), vowel (V), and alpha value ( α ) that result in the highest joint probability over the entire set of constraints. ¹⁷ Although the model simply tries all possible combinations of values, the search space is restricted with each variable constrained to fall within a fixed maximum and minimum. A fixed step size of 10 ms for both consonant and vowel is used to search this space. To simplify, each variable is assumed to be independent, therefore the joint probability is given as the product of the individual probabilities (see Appendix B for further details of the model).

Figure 5 shows the result of running the model for a set of force values ranging between 0 and 10 (x-axis). On the y-axis, vowel duration, consonant duration, and syllable duration (V + C) are plotted for both voiced (black) and voiceless (gray) syllables. Each point on the graph corresponds to a VC word (V₀ = µ_V; C₀ = µ_C), after the given lengthening has been applied to the segments. For example, for a lengthening force of 3, and a voiced-final syllable, the optimal vowel duration is 420 ms, and the optimal voiced obstruent duration is 90 ms, for a total syllable duration of 510 ms. For a voiceless-final syllable, on the contrary, the optimal vowel duration is 350 ms, and the optimal voiceless obstruent duration is 125 ms (for a syllable duration of 475 ms). Both sets of points are shown as filled circles in Figure 4. The vowel, like each obstruent type, prefers the mean duration of its probability distribution (150 ms in this case). It is forced to lengthen due to the pressures of the other constraints. Because the voiced obstruent constraint is more highly weighted than the voiceless obstruent constraint (smaller variance), it does not shift as far from its preferred duration (at 50 ms). Therefore, the vowel is forced to lengthen more when it co-occurs with a voiced obstruent than with a voiceless obstruent.

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Figure 5.

Behavior of the competing constraints model of segment duration as a function of lengthening force.

At shorter target syllable durations, voiced and voiceless obstruents (black and gray solid lines, respectively) are more or less identical in duration; preceding vowel durations (black and gray dashed lines) are also identical within the same range. As target syllable duration continues to increase, the consonant durations start to diverge. Because of its much smaller variance, the voiced obstruent not only resists lengthening more strongly than the voiceless, but that resistance also grows faster, leading to smaller and smaller increases in duration. As a result, either the vowel must lengthen more, or the divergence from the target vowel duration must increase, or both. Here the vowel duration difference continues to increase with increasing duration, meaning that the magnitude of the voicing effect increases as well. This is true up to the point at which the vowel duration of the voiced stop hits an effective maximum value.

Syllables closed by voiced obstruents also appear to be longer than those closed by voiceless obstruents (cf. Luce & Charles-Luce, 1985). There are two model features that produce this result. First, more of the force, on average, is distributed to the coda than the nucleus. Second, the translation from force to length is given as a proportion of preferred segment duration. In other words, instead of distributing syllable length over the vowel and consonant, the same amount of force is assumed to affect lengthening in the two segments relative to their default durations (see Campbell, 1992 for a similar approach). Greater lengthening applied to the coda consonant will be diverted in larger amounts to the vowel in the voiced case, due to the high weight of the voiced consonant constraint, whereas more of that lengthening will stay with the voiceless coda, due to the lower weight of its associated constraint. This interaction is what allows the vowel preceding the voiced coda to lengthen additionally relative to the vowel preceding the voiceless coda.

For comparison we created a baseline model that determines the length of the vowel preceding the voiced obstruent as a fixed percentage (30%) of the length of the vowel preceding the voiceless obstruent. Both segments also lengthen as the lengthening force increases, by a fixed percentage of their current durations at each step (10%). The resulting vowel duration functions look somewhat similar to the vowel duration functions in the competing constraints model, at least at the low end (see Figure 6). This simple model, however, does not allow interactions between vowel duration and consonant duration. Therefore, an apparent connection between the two would have to be due to chance.

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Figure 6.

Baseline percentage increase model.

As a proof of concept, the competition model does quite well at capturing the critical behaviors that motivated our re-analysis of the voicing effect in English, and without a directly compensatory mechanism. The model can also capture the interaction between the voicing effect and vowel length, using a lower elasticity parameter for inherently shorter vowels. ¹⁸ Reducing the variance of the vowel probability distribution, but keeping all other parameters the same, results in a smaller duration difference between the paired preceding-voiced/preceding-voiceless vowels, and much less of a difference in syllable duration between the two. Both obstruents are also longer in the short vowel model. Nevertheless, the difference in duration between the obstruents is comparable for both types of syllable (see Appendix B). Qualitatively, this behavior is consistent with the finding that the voicing effect is significantly reduced in preceding vowels that are inherently short (Crystal & House, 1982; de Jong, 2004; Umeda, 1975). Because very few studies on the voicing effect report final obstruent durations, it remains to be seen whether this prediction is borne out. Note that the baseline model cannot capture the difference between long and short vowels. Starting the model with a lower vowel duration leads to less lengthening before voiced stops, but also to less lengthening, as a function of force, before voiceless stops. Therefore, the size of the voicing effect is almost identical for the two types of syllable.

The lengthening force in our model is treated as an independent variable derived from various sources, such as speaking rate, and final lengthening. For the largest durations/strongest forces, a robust voicing effect is found both in laboratory speech, (e.g., House, 1961; Luce & Charles-Luce, 1985; Mack, 1982; Peterson & Lehiste, 1960; Umeda, 1975), and in phrase-final position. A particularly large final lengthening effect in English (e.g., Delattre, 1966), we conjecture, may be largely responsible for the particularly large voicing effect in this language.

6.1 Perception of voicing in final position

A review of the perception literature in Section 2.6 has shown that other cues to the voicing contrast are likely to be stronger than preceding vowel duration, and categorical perception results may only be possible with highly impoverished stimuli. Meanwhile, categorical perception results have been obtained by varying obstruent duration alone (e.g., Denes, 1955). Based on these results, we hypothesize that listeners are using stop duration itself as the cue to voicing when final stops are both voiceless and unaspirated. Vowel duration factors into the classification decision insofar as it provides information about stop duration indirectly, as a measure of speaking rate. ¹⁹ In essence, the listener’s task is to decide whether what they are hearing is a voiced stop spoken slowly or a voiceless stop spoken quickly. Shorter vowel durations, which comprise the majority of the corpus data, correspond to speaking rates at which voiced and voiceless stop durations are not significantly different from one another. In this range, vowel duration is ineffective as a cue to voicing. Only as speaking rate slows to the point where the voiced and voiceless expansion trajectories begin to diverge, does vowel duration become predictive.

The competition model of Section 4 is used to illustrate this hypothesis (see Figure 7). The duration of the voiceless stop (gray solid line) gradually diverges from the duration of its voiced counterpart (black solid line), as the lengthening force increases. This divergence is mirrored in the preceding vowel duration (gray dashed line—preceding voiceless stop; black dashed line—preceding voiced stop). If the listener is exposed to a relatively short vowel (Figure 7(a): horizontal gray line), their expectation for the duration of the upcoming stop will be roughly the same whether it is voiced or voiceless (vertical difference between the lower open circles). An observed stop duration (lower dotted line) that falls close enough to both expected values is assumed to be acceptable for either member of the pair, and will not be sufficient to distinguish between the two in the absence of other cues.

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Figure 7.

Competition simulation: Observed vowel duration is marked by the horizontal gray line in both figures. Vertical solid lines intersect expected lengthening force, and expected stop duration. Left line: voiced stop coda; Right line: voiceless stop coda. The lower dotted line indicates the actual duration of the following stop. (a) Short vowel token. (b) Long vowel token.

For a longer vowel, on the contrary, there is a larger difference in the expected durations of the voiced and voiceless stops. See Figure 7(b). The same observed stop duration (lower dotted line) now falls significantly below both expected values. In a two-alternative forced choice task we predict that this stimulus should sound more like a voiced than a voiceless stop. In general, an ambiguous final stop of fixed duration should sound more and more like a voiced stop as vowel duration increases. We assume that the category cross-over point from voiceless to voiced falls where the stimulus is significantly shorter than expected for a voiceless stop at that rate. After that, the likelihood of a voiced stop continues to increase (cf. Massaro & Cohen, 1983).

The foregoing can thus explain the increase in voiced responses with increasing vowel duration. However, given that we hypothesize that shorter vowels should not provide any cues to the voicing contrast, we would expect, all else being equal, that listeners would be at chance in identifying tokens in the short half of the continuum. Here it is the nature of the actual experimental stimuli that may bias perception strongly toward the voiceless stop. In the first place, ambiguous tokens are, by definition, phonetically voiceless. Depending on how exactly such stimuli were created, they may retain other cues to the original speech token from which they were generated, such as an F1 offset that is more consistent with a voiceless, than a voiced, stop. The synthetic stimuli used in Denes (1955), for example, were based on originally voiceless tokens. Whereas Repp and Williams (1985), using naturally produced stimuli, found a large perceptual difference between continua generated from an originally voiced stop (lab), versus an originally voiceless stop (lap). Voiced responses were about 40% higher for the former across all but the two longest vowel durations.

We therefore posit that the categorical perception results are due, first, to a default voiceless percept, based on residual cues that are more consistent with the voiceless member of the contrast, and second, to unusually long vowel durations. At the longest vowel durations (vanishingly rare in the speech corpus), we posit that the expected duration of a voiceless stop is so long that its likelihood approaches zero. For such extreme tokens, selection/perception of the voiced alternative may occur prior to actually hearing the final segment. However, it appears that the addition of a period of strong aspiration at the end of the stop is sufficient to switch the percept to voiceless. ²⁰ Listeners may also be able to reliably select the voiced member of a minimal pair when final stops are entirely removed. We suspect that this is only possible in an explicit comparison task where listeners must label one token as voiced, and one as voiceless. In such a a task it is likely that listeners assume a uniform speech rate, leading them to attribute a somewhat longer vowel duration to the effect of a following voiced stop.

Additional support for this account of voicing perception comes from studies of the voicing contrast in initial position. It has been consistently found that the perceptual VOT boundary is longer than the boundary estimated from production data (e.g., Miller et al., 1986; Miller & Volaitis, 1989; Volaitis & Miller, 1992). However, the two boundaries coincide when naturally produced, unedited stimuli are used in the perception task. Nagao and de Jong (2007) suggest that the mismatch may arise from the fact that the stimuli typically used in perception experiments are artificially impoverished. In other words, the edited tokens are so ambiguous that they can only be confidently classified at very long VOT, or very slow speaking rates. The consistency in the reported perceptual cross-over point across experiments on word-final stops may be explained by the same artificiality. For voiceless closures with no audible release, the duration of the coda stop is indeterminate. Listeners may therefore assume a duration that is plausible given their language experience and consistent with experimental variables such as the inter-stimulus interval. It is therefore likely to be relatively stable across experiments involving native speakers of English.

6.2 Predictions

Our explanation of the perception results generates a number of testable hypotheses. For one, we predict that a change in the perception of voicing should lead to a change in the perception of speaking rate (greater force = slower speaking rate). During the course of vowel production, it is assumed that a hypothesis about both speaking rate and following segment duration is generated by the listener. In the absence of any information about the duration of the following stop (silent and unreleased), we posit that listeners will infer a duration that is consistent with those hypotheses. For a particularly long vowel, an expectation for a following phonologically voiced stop should lead listeners to infer the expected duration for a voiced obstruent, and the lengthening force associated with that duration (as depicted in Figure 7(a) and 7(b): the intercepts of the leftmost vertical line with the voiced obstruent duration curve and the x-axis, respectively). In the case where that lengthening force comes from differences in speaking rate, they are predicting the associated rate for each token. However, if listeners subsequently experience unambiguous release or aspiration cues, then we hypothesize that there should be a noticeable correction to both the perceived stop class and the perceived speaking rate. The voiceless stop should indicate that the speaking rate is actually slower than previously supposed (represented by the x-intercept of the rightmost vertical line in Figure 7(b)). ²¹ Sanker (2019) has shown that the judgment of whether a vowel is “long” or “short” depends not only on the duration of the vowel, but on whether it is followed by a voiced or a voiceless obstruent. For vowels preceding voiced obstruents, longer durations are required to elicit a “long” response. Although she did not report obstruent duration, we interpret her results as deriving from the expectation for a specific vowel duration given the unambiguous obstruent duration and its voicing. Vowels shorter than this expected value would be perceived as “short,” and vowels longer than this value would be perceived as “long.”

The Expandability Hypothesis also predicts that it should be possible to find apparent compensation with segments other than immediately preceding or following vowels, as long as they are more expandable than voiced obstruents. This is corroborated to a certain extent. A difference in nasal duration preceding voiced versus voiceless stops has been found both for monosyllabic words of the form “dens/dense” (Beddor, 2009; Port & Cummins, 1992; Raphael et al., 1975), and polysyllabic words of the form “cantor/candor” (Vatikiotis-Bateson, 1984). Furthermore, Raphael et al. (1975) find that both vowel and nasal duration affect perception of voicing on final stops. In an eye-tracking study by Beddor et al. (2013), participants heard CVND words (such as “bend”), CVNT words (such as “bent”), and C V ~ C words ([b ε ~ d] vs. [b ε ~ t]), in which the nasal was missing but the vowel was nasalized. They found that, for C V ~ C tokens, participants were overall more likely to fixate on the image corresponding to the CVNT word than the CVND word. They interpret this result as deriving from listener expectation that the nasal gesture will be coordinated differently in the two contexts: initiating earlier before a voiceless stop, and later before a voiced stop. However, no explanation is offered as to why the phasing relationship should be different in the two contexts. This difference, however, can be accounted for under the Expandability Hypothesis if the competition at the word (or syllable) level affects both the duration of individual gestures, as well as their phasing, as occurs under changes in speaking rate (e.g., Hardcastle, 1985; Stetson, 1928), and other types of prosodic lengthening (e.g., Byrd et al., 2000; Byrd & Saltzman, 1998). A shorter voiced stop would thus correlate with both longer tautosyllabic segments, as well as a preceding VN sequence that is less coarticulated. Less coarticulation, in turn, would result in less vowel nasalization. Thus, a highly nasalized vowel is more likely to occur preceding a [t] than a [d].

An additional corollary of our account of the voicing effect is that actual voicing, or any feature other than length, is not required for a “voicing” effect to arise. In fact, active phonetic voicing cannot be a requirement when the strongest effect is seen in English pre-pausally, where final voiced obstruents are likely to undergo devoicing. Given our hypothesis, however, it should be possible to find a “voicing” effect involving segments that have low elasticity for a reason not related to historic voicing. Some evidence for this comes from Beguš (2017), who finds that stop duration correlates negatively with preceding vowel duration not just for voiced and voiceless stops in Georgian, but for ejectives as well, with ejectives intermediate between voiced and voiceless stops in terms of both consonant duration and preceding vowel duration.

In principle, any apparent temporal compensation phenomenon could be modeled using the competing constraints framework (see Section 4.1). All else being equal, we might also predict that an appreciable difference in consonant duration should lead to a complementary difference in preceding vowel duration in monosyllabic words. However, it may prove difficult to isolate elasticity-based effects from other factors that affect syllable duration. For example, vowels in monosyllables closed by nasals have been found to be as long, or longer, than vowels in monosyllables closed by voiced obstruents in English (e.g., Crystal & House, 1988; House & Fairbanks, 1953; Peterson & Lehiste, 1960; Umeda, 1975), which is the opposite of what one would expect for a sonorous segment like a nasal. However, both Crystal and House (1988) and Klatt (1975) report nasal durations that are comparable to those for voiced stops. Thus, it may be the case that nasals (and possibly other sonorants) are not as elastic as might have been expected. Another possibility is that the phasing relationship between vowel and coda may be different in the case where the two gestures can overlap significantly without masking. Thus vowels may be measured as longer, and nasals, as shorter, if there is significantly more coarticulation than occurs with other consonants. If this is correct, then the vowel should be acoustically highly nasalized when the nasal is short, reflecting the true length of the nasal. Note that this would be consistent with the results for C V ~ C words in Beddor et al. (2013).

There is also evidence that may argue against the Expandability Hypothesis. It has been found that vowels preceding voiced fricatives are longer than vowels preceding voiced stops, while vowels preceding voiceless fricatives are somewhat longer than those preceding voiceless stops (Peterson & Lehiste, 1960; Umeda, 1975). ²² Furthermore, the voicing effect has been reported to be larger for fricatives than for stops (e.g., House, 1961; House & Fairbanks, 1953). Although our production experiment was not designed to explicitly test fricatives against stops, our results are in line with these findings. In our data, vowel durations were longest before voiced fricatives, and a larger voicing effect was found for fricatives than stops (91 ms, vs. 56 ms ∆ V ); see Figure 8. However, the Expandability Hypothesis predicts that preceding vowel durations should be similar for voiced stops and fricatives, given that voiced fricatives were only 15 ms longer than voiced stops on average. It also predicts that vowels should be shorter before voiceless fricatives than voiceless stops, given that voiceless fricatives were about 29 ms longer than voiceless stops. A possible explanation could be that different consonants have different biasing functions (the model variable α ), thus exhibiting different distributions of lengthening. This could also interact with a higher elasticity among fricatives. Allowing α to vary by phoneme is undesirable from the perspective of theoretical economy. However, this hypothesis is testable, as are other aspects of the Expandability Hypothesis.

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Figure 8.

Production differences by voicing for each minimal pair.

The Expandability Hypothesis as developed here was designed for consistency with an already very large experimental literature, thus many of its predictions are actually postdictions. Nevertheless, we have offered a number of speculations that can, in principle, be tested. Among these are the hypothesis that longer vowels in CVN words are highly nasalized, and that less nasalization in VNC sequences is correlated with longer VN durations. The competing constraints model also offers the hypothesis that significant differences in obstruent duration can occur without apparent compensation on vowels that are inherently short (see Appendix B). Additional predictions about differences in effect size across final, medial, and initial position cannot be entirely determined by comparing across heterogeneous studies, but require carefully controlled experimentation to assess. More detailed information about gestural coordination between vowels and specific following consonants is also needed to fine-tune model predictions.

7.1 Contrast and allophony

Throughout this paper the relevant obstruent contrast in American English has been referred to as one of voicing. This is in spite of the fact that it is precisely because phonetic voicing is often absent from “voiced” stops that preceding vowel duration can be discussed as a possible cue to contrast. Clearly, the presence or absence of vocal fold vibration is not always necessary, or even sufficient, for phoneme identification. In order for the contrast to be described as one of voicing, it is necessary to treat the phonological voicing feature as distinct from the phonetic feature of the same name. The first is transformed to the second via a series of allophonic rules. For example, in absolute initial position the /-voice/ stop becomes [+spread glottis], while the /+voice/ stop may become [-voice]. In final position, a /-long/ vowel preceding a /+voice/ stop becomes [+long].

However, we have seen that apparent vowel lengthening varies considerably as a function of speaking rate, sentence and word position, stress, and other factors (e.g., Crystal & House, 1988; Umeda, 1975). Most importantly, longer vowels correlate with shorter consonants, and voiced obstruents tend, cross-linguistically, to be shorter than their voiceless counterparts. The apparent physiological difficulty of maintaining the necessary conditions for voicing over extended closure periods has been proposed as an explanation for this tendency (e.g., Ohala, 1983, 2011). Nevertheless, it is possible, by virtue of greater articulatory effort, to maintain voicing if desirable, at least up to a point. Partial, or total, devoicing is also a possible outcome. Therefore, we expect the duration differences between voiced and voiceless obstruents to be language specific. The fact that “voiced” stops in English are now frequently devoiced means that the observed duration differences are no longer the direct result of physiological constraints, but of what has become an underlyingly specified property of the segment. The fact that the difference in behavior between voiced and voiceless obstruents is only observable at long durations means that the specification is not for absolute duration, but for something that quantifies resistance to lengthening. The large voicing effect in English, we argue, is due to the voiced segment being pushed well beyond its preferred duration. Our claim is that vowel duration differences emerge directly from these elasticity differences. Therefore, we also conclude that vowel duration is not a feature that is specified in English, either at the phonological or phonetic level.

Although categorical perception effects have been demonstrated for the vowel duration cue, this is not particularly noteworthy, given that the number of acoustic cues to the contrast that listeners are able to exploit has been shown to be quite large. Duration and intensity of voicing, aspiration, and F0 contour, length of vowel formant transitions with respect to steady state duration (Fitch, 1981), F1 offset frequency (Crowther & Mann, 1992), speed of jaw lowering, and jaw offset position (Van Summers, 1987) all differ consistently between the two stop types in final position. In medial post-stress position, consistent differences have also been found in the timing of vocalic voice offset, and the signal decay time (Lisker, 1986), which should apply to final position as well. Furthermore, it is well known that cues can be “traded off” with one another. That is, while a long enough closure duration can cue a “voiceless” stop on its own, a shorter closure in tandem with a shortened vowel can also do so (e.g., Bailey & Summerfield, 1980; Fitch, 1981; Klatt, 1976; Kohler, 1979, 1984; Lisker, 1986; Malécot, 1968; Van Summers, 1987). Yet absolute vowel duration, and not closure duration or formant transition information, is frequently characterized as a phonological “voicing” feature, even though the latter two cues have been shown to influence perception to the same, or an even greater, degree. This may be due, in large part, to the privileging of “prominent” contexts in phonological theory.

7.2 Prominence

While the phonetic realization of underlyingly contrastive features is assumed to vary by context, the most prominent environment, usually initial pre-stress position, is assumed to most faithfully reflect those features. Not only that, but features are said to be enhanced, or more strongly signaled, in such contexts (e.g., Kingston & Diehl, 1994). Conversely, observed enhancement is taken to indicate features that are “controlled,” or underlyingly specified, as opposed to being supplied by context-sensitive rules (e.g., Ohala, 1981). Enhancement can be realized as an increase in acoustic amplitude, an increase in size of articulatory gestures, and/or an increase in gestural, and thus, segmental, duration (e.g., Beckman et al., 2013). In addition to making individual features more salient, enhancement is also assumed to be a mechanism for increasing discriminability between the members of a phonemic contrast (e.g., Cho, 2016; Cho & Jun, 2000; de Jong, 1995). For the above reasons, slower than normal speaking rate is considered to be an enhancement mechanism that should lead to lengthening, but only of contrastively specified features (e.g., Solé, 2007).

Underspecification theory applied to laryngeal contrasts typically makes use of the following privative features: [spread glottis], [voice], and [constricted glottis] (e.g., Iverson & Salmons, 1995; C.-W. Kim, 1970). This system yields three possible two-way contrast systems, one for each of the features, with the second member always unspecified. The phonetically voiceless stops in French and Thai fail to lengthen significantly with decreased speaking rate, and are therefore taken to be unspecified for laryngeal features, while the phonetically short lag/voiced stops in English are the unspecified member of the contrast ²⁴ (Beckman et al., 2013; Kessinger & Blumstein, 1997).

In the same vein, an observed interaction between a given phonetic cue, and any variable that affects duration, is taken to indicate that the cue is an inherent part of the contrast. It has been argued that vowel duration is purposefully manipulated by speakers to enhance the laryngeal contrast of the following obstruent, based on the following set of results: that the effect of stress is smaller for voiceless-preceding vowels than for voiced-preceding vowels in English (de Jong, 2004); that /-long/ voiced-preceding vowels lengthen less than they would otherwise, in order to avoid overlapping with /+long/ voiceless-preceding vowels, and preserve an existing long versus short vowel distinction in German (Braunschweiler, 1997); that vowel duration differences preceding voiced versus voiceless segments are greater for long vowels than for short vowels in English (Peterson & Lehiste, 1960); that the difference in duration between the stressed vowel in a monosyllabic word and the same vowel in a bisyllabic word is larger (by percentage) for syllables closed by voiced stops than those closed by voiceless stops (Crowther & Mann, 1992; de Jong, 1991; Klatt, 1973; Raphael, 1975; Smith, 2002; Van Summers, 1987); that the vowel shortening effect of affixation is greater (both absolutely, and proportionally) for a voiced-final stem than for a voiceless final (Lehiste, 1972).

In this paper, however, we have conceptualized stress, prosodic boundary marking, and speaking rate simply as external forces which, among others, can act to lengthen segments. Under our account, all segments are subject to such lengthening and shortening pressures. How much lengthening or shortening actually occurs, however, is governed by the interactions of all such constraints, some of which are more highly weighted than others. The apparently asymmetric effects on voiced versus voiceless syllables do not need to be explained as the result of speaker effort to avoid phonetic ambiguity, or to maintain a specific range of phonetic values. They follow directly from these two premises: that the voicing effect derives from differences in segment elasticity; and that the resulting differences in duration increase with increasing duration. Characterizing the voicing effect as a consequence of on-line timing adjustments (to which multiple factors can contribute) is therefore more parsimonious, and more explanatorily adequate, than the hypothesis that there is both a grammatical rule of vowel lengthening, and a set of deliberate adjustments made to preserve the output of that rule. Note that this analysis requires elasticity to be underlyingly specified. This is not the same, however, as an underlying specification for an abstract voice feature. In the first place, all segments are assumed to have their own characteristic elasticity. Furthermore, a specification of this kind is necessary for independent reasons: to account for the differing degrees to which segments respond to changes in speaking rate. Finally, relative duration values within a word cannot be derived from a /voice/ feature, or even a long/short duration feature, as they depend on potentially complex interactions between all the segments within a word.

If “prominent” contexts (such as slow speaking rate) do not actually enhance contrastive features, then the realization of the features in such contexts should not necessarily be taken as underlying. Doing so, in fact, requires potentially extensive transformations to arrive at the more frequent, non-prominent contexts of normal speech. If we reverse this relation, then very slow hyper-articulated speech is the exception, rather than the rule, and intense aspiration and especially long durations are derived from features that are more typical of the contrast in general. Large differences in preceding vowel duration are, almost exclusively, the product of atypical speech and therefore, in our view, should be considered the least central to the “voicing” contrast, not the most. This flipped view of contrast offers an intriguing avenue for future research.