Acoustic consequences of articulatory variability during productions of ∕t∕ and ∕k∕ and its implications for speech error research

Abstract

An increasing number of studies has linked certain types of articulatory or acoustic variability with speech errors, but no study has yet examined the relationship between such articulatory variability and acoustics. The present study aims to evaluate the acoustic properties of articulatorily errorful ∕k∕ and ∕t∕ stimuli to determine whether these errors are consistently reflected in the acoustics. The most frequent error observed in the articulatory data is the production of ∕k∕ and ∕t∕ with simultaneous tongue tip and tongue dorsum constrictions. Spectral analysis of these stimuli’s bursts shows that ∕k∕ and ∕t∕ are differently affected by such co-production errors: co-production of tongue tip and tongue dorsum during intended ∕k∕ results in typical ∕k∕ spectra (and hence in tokens robustly classified as ∕k∕), while co-productions during intended ∕t∕ result in spectra with roughly equal prominence at both the mid-frequency (∕k∕-like) and high-frequency (∕t∕-like) ranges (and hence in tokens ambiguous between ∕k∕ and ∕t∕). This outcome is not due to an articulatory timing difference, but to tongue dorsum constriction having an overall greater effect on the acoustic than a tongue tip constriction when the two are co-produced.

INTRODUCTION

The current study investigates the relationship between articulation and acoustics in utterances with alternating initial consonants in order to increase our understanding of how articulatory variability during production of coronal and dorsal stops, potentially resulting in speech errors, is reflected in the acoustic signal. Several studies have found that the alternating consonants in such utterances display an increased amount of articulatory and acoustic variability compared to environments in which these consonants do not alternate. Under certain circumstances, this variability may be perceived as errorful by listeners (Boucher, 1994; Goldstein et al., 2007; McMillan et al. 2009; Mowrey and MacKay, 1990; Pouplier, 2003, 2007, 2008; Pouplier and Goldstein, 2005). However, there has been no systematic study to examine the relationship between such articulatory variability and its acoustic consequences. That is, previous studies either examined articulatory variability without a systematic analysis of its impact on acoustics or they examined acoustic variability without the availability of information on the articulations that give rise to the acoustics. Due to the complex, nonlinear relationship between articulation and acoustics, it is, however, important to gain a principled understanding of how errorful articulatory and acoustic variability relate to each other. The present study aims to address this issue by evaluating the acoustic properties of ∕k∕ and ∕t∕ stimuli with known articulatory configurations in order to determine how the increased articulatory variability may be reflected acoustically and also to determine whether it may be reflected acoustically equally for both intended ∕k∕ and ∕t∕.

An examination of the acoustic properties of errors is especially opportune given the great importance of error data for models of speech production (Dell, 1986; Levelt, 1989; Levelt et al., 1999; Rapp and Goldrick, 2000) and in view of the divergent findings between studies that rely on auditory perception for error detection on the one hand, and studies that investigate errors articulatorily on the other. Thus based on the former, speech errors have traditionally been described in categorical terms as substitution of one symbolic phonological unit with another (Fromkin, 1971, 1973; Shattuck-Hufnagel, 1979, 1983). However, physiological studies have shown first that such perceived categorical substitutions may, in fact, involve the simultaneous production of two constrictions (one intended and one errorful), and second that these constrictions may be produced along a gradient continuum of magnitudes, exhibiting patterns intermediate between those typical for a given category (Boucher, 1994; Goldstein et al., 2007; McMillan et al., 2009; Mowrey and MacKay, 1990; Pouplier, 2003, 2007, 2008).

Different results have also emerged from auditory and articulatory analyses as far as the extent to which coronals and non-coronals are prone to errors. The auditory analysis of Stemberger (1991) showed that coronals are disproportionally susceptible to be replaced by non-coronals in errors. He interpreted these results as providing strong evidence for the phonological underspecification of coronals since an un(der)specified place of articulation can easily be “replaced” by any other, phonologically specified place of articulation. Articulatory studies on the other hand (Goldstein et al., 2007; Pouplier, 2003, 2008) did not observe this asymmetry in error-proneness between ∕k∕ and ∕t∕: the articulatory errors documented in these studies occurred with equal frequency during productions of both ∕k∕ and ∕t∕. We are left, then, with the following discrepancy: auditory analyses suggest a place asymmetry in speech errors, but physiological analyses have shown that there is none.

An explanation for the discrepancy between these results is that errors involving coronals may be auditorily more salient. That is, the articulatory deviation due to a production error may result in a greater acoustic deviation from the corresponding error-free production for coronals than for dorsals. Under this interpretation, the bias reported in auditorily-based analyses may come about not because coronals are inherently more error-prone, but instead because the hypothesized greater acoustic deviation makes the error much more noticeable than in the case of dorsals. It is precisely this issue that we test in the present study by examining the acoustic properties of speech errors with known articulatory configurations.

Our study is therefore concerned with how articulatory variability is reflected in the acoustic domain: we investigate “partial” errors that involve simultaneous production (henceforth co-production) of two constrictions—one intended, one un-intended (or intruding)—of the type reported by Pouplier (2003) (cf. also Goldstein et al., 2007). Specifically, that study used a repetition task to elicit productions of ∕k∕ and ∕t∕ in utterances with alternating initial consonants (e.g., cop top), and the most frequent error observed in their articulatory data was an intrusion of a second articulatory gesture (or constriction) without the intended gesture being reduced. This resulted in the simultaneous presence of both tongue tip (TT) and tongue dorsum (TD) constrictions during the production of errorful ∕k∕ or ∕t∕: while ∕k∕ is normally produced with only a tongue dorsum constriction, in an error, a tongue tip constriction is produced simultaneously with the dorsal constriction, without the intended dorsal constriction being reduced. The intruding tongue tip gesture can display a range of gestural magnitudes, ranging from minimal variability to an articulator position typical for the production of a coronal stop. Likewise during the production of an intended ∕t∕, they observed that the intended tongue tip constriction can, in errorful tokens, be co-produced with an intruding tongue dorsum constriction. In terms of their frequency of occurrence, these co-productions were the most frequent type of error observed; reductions in intended constrictions (e.g., a tongue tip constriction for intended ∕t∕ produced with a reduced constriction) and substitutions (e.g., only a ∕k∕-like tongue dorsum constriction during intended ∕t∕) were observed only rarely.

Furthermore, co-productions occurred with equal frequency during intended ∕k∕ and ∕t∕. However, although this type of error was as likely to occur during production of either ∕k∕ or ∕t∕, there has been a reported asymmetry in the perceptual consequences of co-productions during ∕k∕ vs ∕t∕. In their perception experiment, using a subset of the data collected by Pouplier (2003), Pouplier and Goldstein (2005) found that intruding tongue dorsum gestures during ∕t∕ had a systematic perceptual effect, resulting in significantly lower correct identification scores and longer reaction times than for error-free ∕t∕. However, intruding tongue tip gestures during intended ∕k∕ did not significantly affect identification or reaction times. It seems therefore that while ∕k∕ and ∕t∕ are equally prone to error at the articulatory level, the perceptual effects of co-productions are different depending on whether ∕k∕ or ∕t∕ is the intended consonant. Since the acoustic properties of co-productions have not been investigated so far, it is not known whether this difference is due to perceptual biases (cf. for instance, Hume et al., 1999; Smits et al., 1996; Winters, 2000 on the lower perceptual salience of singleton coronals compared to labials and velars) or whether the influence of the additional constriction exerted on the acoustics varies as a function of the constricting articulator∕place of articulation of the intruding gesture. By examining the acoustic properties of tokens produced with an intruding gesture, the current study can determine, as described below, whether the previously reported perceptual asymmetry between coronals and dorsals produced with an intruding gesture is due to a difference at the acoustic level or to a perceptual∕auditory bias.

It is well established that articulatory changes in the vocal tract will affect the acoustic output to different degrees, depending on the exact location and size of a given constriction formation (cf. Stevens, 1972, 1989). Since in co-productions the intended constriction is stronger both spatially and temporally compared to the intruding constriction (Pouplier, 2003; Pouplier and Waltl, 2008; Pouplier and Goldstein, in press), “adding” a coronal constriction to an intended dorsal constriction may affect the vocal tract area function differently compared to adding a dorsal constriction to an intended coronal constriction. Specifically, an intruding constriction formed behind the main constriction (as is the case for an intended ∕t∕ with an intruding dorsal constriction) could affect the pressure build-up and hence the acoustic properties of the consonant release more than an intruding constriction formed in front of the main constriction (as is the case for an intended ∕k∕ with an intruding coronal constriction). As a result, the acoustics of intended coronals could be affected more by an intruding tongue dorsum gesture than the acoustics of dorsals by a tongue tip intrusion. If an intruding constriction (or gesture) affects the acoustic properties of coronals but not the acoustic properties of dorsals, then the observed perceptual asymmetry could be based on differences at the acoustic level. Under this hypothesis, we predict that an intruding tongue dorsum gesture during ∕t∕ will result in tokens acoustically different from error-free ∕t∕, while an intruding tongue tip gesture during ∕k∕ will result in tokens acoustically similar to error-free ∕k∕.

On the other hand, Winitz et al. (1972) remarked that “it is difficult to smear a high-energy English ∕t∕ into a ∕p∕ or a ∕k∕, but not difficult to smear ∕p∕ into ∕k∕ or the reverse” (pp. 1972–1973), suggesting that acoustically, ∕t∕ bursts should be at least as robust as ∕k∕ bursts, and if anything dorsals should be acoustically more sensitive to articulatory variability compared to coronals. If so, the perceptual results reported by Pouplier and Goldstein (2005) could be due not to an asymmetry at the acoustic level but to a bias exclusively at the auditory∕perceptual level. It has been observed that perception of coronal stops produced by native speakers of several languages is generally worse than that of non-coronals either in singleton contexts (Hume et al., 1999; Smits et al., 1996; Winters, 2000)1 or in clusters (Kochetov and So, 2007; Surprenant and Goldstein, 1998), and also that their perception is degraded more readily than perception of non-coronals by articulatory variability. Byrd (1992) and Chen (2003) observed, using articulatory synthesized stimuli, that perception of coronal stops is more vulnerable to increased articulatory overlap than perception of labial stops. It is not implausible therefore to expect that an intruding gesture may affect the acoustic properties of both coronals and dorsals, but that perception is more sensitive to the changes in the acoustic patterns of coronals compared to dorsals (or in other words, that more acoustic variability is tolerated in dorsals than in coronals before their perception is degraded). Under this hypothesis, we predict that an intruding tongue dorsum gesture during either ∕t∕ or ∕k∕ will result in tokens acoustically different from error-free ∕t∕ and ∕k∕, and that the perceptual patterns reported by Pouplier and Goldstein (2005) may be due to a bias in how robustly these acoustic changes can be auditorily detected. To decide between these two possibilities, we analyzed the relationship between articulation and acoustics for ∕t∕ and ∕k∕ tokens that were produced with an intended as well as an intruding gesture, the latter covering a range of different gestural magnitudes.

A further question we address is whether the acoustic consequences of co-produced intended and intruding gestures are influenced by the timing relation between these two gestures. It is conceivable that different timing relations between the two gestures have different acoustic consequences, depending on which gesture is released last. Pouplier and Goldstein (2005) did not control for articulatory timing in their experiment. Thus, the perceptual pattern they reported may not be due to an asymmetry in how acoustics and∕or perception are affected by tongue dorsum vs tongue tip intrusion gestures but rather to different timing patterns between intended and intruding articulations. Pouplier and Goldstein (in press) performed a detailed articulatory timing analysis of the Pouplier (2003) data and found that generally the intended gesture was released last in the case of both intended ∕k∕ and ∕t∕, with relatively few tokens showing the reverse pattern. In conjunction with the results of the perception experiment, this suggests that timing patterns are not a strong predictor of the acoustic consequences: the perception experiment had reported an asymmetry between coronal and dorsal stimuli, yet the timing revealed that for both coronals and dorsals, it was usually the intended gesture that was released last. However, since timing was not explicitly controlled for in the perception experiment, it is possible that, by chance, the perceptual experiment included errorful ∕t∕ tokens with the intruding gesture released last, and no errorful ∕k∕ tokens with the intruding gesture released last, resulting in the systematic lower identification scores for errorful ∕t∕ than ∕k∕. We examined therefore the extent to which acoustics were determined not only by the presence∕absence of an intruding gesture but also by the intruding gesture’s relative timing to the intended gesture.

METHOD

Gestural classification

To determine the relationship between the acoustic and articulatory properties of speech errors, we used data for which both acoustic and articulatory information was available. The dataset consisted of simultaneously recorded articulatory and acoustic data collected by Pouplier (2003). Articulatory data were recorded using the Perkell-system articulograph at Haskins Laboratories (Perkell et al., 1992). For the recordings, four sensors were placed on the tongue: TT (attached about 1 cm behind the actual tongue tip), anterior tongue body, posterior tongue body, and TD. Additional sensors were placed one each on the upper and lower lips, the lower teeth to track jaw movement, and, to be able to correct for head movement, the nose ridge and the upper incisors. Standard calibration and postprocessing techniques were performed for each experiment. The articulatory data were sampled at 500 Hz and low-pass filtered at 15 Hz during postprocessing. For the simultaneous recording of acoustic data, a Sennheiser shotgun microphone was positioned about 1 m in front of the subject; acoustic data were sampled at 20 kHz and for one subject (JP) at 48 kHz.

Data from seven speakers of American English were recorded. Subjects were instructed to produce utterances with alternating onset consonants (cop top, top cop, kip tip, tip kip) in synchrony to a metronome beat. For the duration of each trial, the subjects saw the utterance they were instructed to pronounce on a computer screen in front of them, and stress placement was indicated in capital letters (e.g., COP top). Experimental variables included two stress conditions (iambic vs trochaic), two vowel contexts (top cop vstip kip), phrase position (top cop vs cop top), and three speaking rates (fast, at 120 beats per minute, medium at 104 beats per minute, and slow at 80 beats per minute, allowing for speaker-specific adjustments within a ±4 beats per minute range of the target rates). Productions of utterances with non-alternating initial consonants (cop cop, top top, kip kip, tip tip) were also included in the dataset and served as controls for the analysis of articulator kinematics, but only stops produced in alternating trials were included in the acoustic analyses. The experimental variables were fully crossed. The data recording and processing procedures are detailed in Pouplier (2003).

The movement time functions obtained through the electromagnetic midsagittal articulometer system were analyzed using software algorithms developed at Haskins Laboratories. For consonants ∕t∕ and ∕k∕, vertical position maxima of the tongue tip and tongue dorsum transducer coils were automatically determined on the basis of changes in their velocity profiles. As illustrated in Fig. 1, a vertical position maximum (MAX) was defined as the kinematic event where velocity was at its minimum between two velocity peaks corresponding to the articulator moving toward and away from the constriction. If the labeling algorithm did not find a maximum in one of the signals (e.g., in tongue dorsum during ∕t∕ and tongue tip during ∕k∕), its vertical amplitude value was measured at the time of a maximum in the other signal which the algorithm had identified. For instance, if there was no vertical position maximum for tongue dorsum during ∕t∕ (since the tongue dorsum is not expected to rise during ∕t∕), tongue dorsum was measured at the time of the tongue tip maximum [cf. Fig. 1b].

Figure 1.

Example articulatory measurements for ∕t∕ in “top,” illustrated on the basis of two “cop top” repetitions produced by subject JX at the fast speaking rate. The panels show vertical position (mm) and vertical velocity (cm∕s) profiles of the tongue tip and tongue dorsum sensors. Identified on the figures are maximum velocity points during movement toward the constriction (Peak 1) and away from the constriction (Peak 2) as well as the constriction maxima (MAX) and releases. (a) Production of “top” for which both tongue tip and tongue dorsum movement showed a constriction. Temporal lag between the release of the tongue tip and the release of the tongue dorsum constriction is indicated by the arrow. (b) Production of “top” showing a tongue tip constriction only. For such tokens, tongue dorsum height was extracted at the time of tongue tip maximum. No temporal lag between release of tongue tip and tongue dorsum could be calculated for such tokens.

The vertical position maxima in alternating utterances span a whole range of values, from minimally variable to values typical for a canonical controlled stop constriction. Production of ∕k∕ and ∕t∕ was determined as “errorful” or “error-free” on the basis of articulator height (cf. Pouplier, 2003). Typical vertical articulatory positions for TT and TD during production of ∕k∕ and ∕t∕ were determined on the basis of matching conditions from the non-alternating utterances (cf. Goldstein et al., 2007; Pouplier, 2003). Based on a working criterion, tokens were considered errorful if TT height during ∕k∕ and TD height during ∕t∕ were 2 standard deviations away from their mean in non-alternating productions. Errorful tokens were further classified into two constriction magnitude categories—“gradient” and “categorical:” if the maximal vertical position of TT∕TD was within 2 standard deviations of the other category mean, the error was considered categorical (C); otherwise it was considered gradient (G). In order to evaluate how the acoustics are affected by different vertical articulator positions (indicative of constriction degree, at least for stop consonants), we followed the classification of Pouplier (2003) procedure here. Several studies have shown that the increased variability in articulator height can, in the right circumstances, be perceived as a speech error (Goldrick and Blumstein, 2006; Pouplier and Goldstein, 2005; Wood, 1997). Under which conditions any given production can be deemed errorful has been subject to vigorous debate. The current paper focuses on the acoustic consequences of variability of articulator height which is observed in utterances that typically elicit speech errors; the question how to negotiate the relationship of “variability” and “error” for any given token is not the focus of the paper. The terms error-free and errorful are labels of convenience to denote ranges of expected values of articulator positions.

Co-production errors were defined as the simultaneous production of an un-intended (or intruding) TT or TD gesture with the intended one. An error-free ∕t∕ is produced with an active TT closure gesture and no actively controlled TD; a co-production error during intended ∕t∕ occurs when a TD gesture is produced along with TT. An error-free ∕k∕ is produced with an active TD closure gesture and no actively controlled TT; a co-production error during intended ∕k∕ occurs when TT is produced along with TD. To summarize, on the basis of the articulatory metric, the following error-free and errorful ∕k∕ and ∕t∕ categories were defined:

• K: error-free ∕k∕—produced with tongue dorsum and tongue tip heights typical for ∕k∕ as determined on the basis of the non-alternating utterances;

• T: error-free ∕t∕—produced with tongue dorsum and tongue tip heights determined typical on the basis of ∕t∕ production in non-alternating utterances;

• KC: ∕k∕ produced with a categorical error—tongue dorsum height is typical for ∕k∕ in non-alternating utterances, tongue tip height is within 2 standard deviations of the mean of non-alternating ∕t∕;

• KG: ∕k∕ produced with a gradient error—tongue dorsum height is typical for ∕k∕ in non-alternating utterances, tongue tip height is 2 standard deviations away from the mean of non-alternating ∕k∕, but not within 2 standard deviations of the mean of non-alternating ∕t∕;

• TC: ∕t∕ produced with a categorical error—tongue tip height is typical for ∕t∕ in non-alternating utterances, tongue dorsum height is within 2 standard deviations of a typical ∕k∕; and

• TG: ∕t∕ produced with a gradient error—tongue tip height is typical for ∕t∕ in non-alternating utterances, tongue dorsum height is 2 standard deviations away from a typical ∕t∕, but not within 2 standard deviations of a typical ∕k∕.

Figure 2a illustrates the error metric schematically; Fig. 2b gives the normalized distributions of tokens within the gradient and categorical error categories for speaker JX (the speaker whose data are used in the classification analysis below).2 The histograms in Fig. 2b show that categorically errorful ∕k∕ and ∕t∕ are similarly distributed within their respective category. For gradient errors, the TG distribution is skewed leftward, indicating that there are more tokens with tongue dorsum heights closer to the values for error-free ∕t∕ than for error-free ∕k∕.

Figure 2.

(a) Schematized cut-off points for gradient and categorical errors determined on the basis of the distributions of articulator height during ∕k∕ and ∕t∕ productions in control (non-alternating) utterances. The gradient error interval is defined by the cut-off points labeled with A and B; the categorical error interval is defined by the cut-off points labeled with B and C. (b) Histograms showing the distribution of normalized articulator heights for errorful tokens within the respective category ranges (between cut-off points A and B for gradient errors and between B and C for categorical errors). Plotted are tokens from speaker JX.

Our data, summarized in Table 1, consisted therefore of ∕k∕ and ∕t∕ produced in alternating utterances (cop top and similar) and defined articulatorily as errorful (KC, KG, TC, and TG) or error-free (K and T). Subsets of the data were used for various analyses, as will be detailed in Secs. 2B, 2E.

Table 1.

Number of tokens from alternating trials produced by seven subjects.

	Articulatory category						Total
	K	T	KC	KG	TC	TG
Number of tokens	873	733	125	186	105	282	2304

Acoustic analysis procedure

For each articulatorily classified initial consonant (K, T, KC, KG, TC, and TG), the acoustic signal was labeled in PRAAT 4.6.38 (Boersma and Weenink) from the release burst to the beginning of periodic vibration for the following vowel. There is evidence that the place of articulation in an oral stop can be related to the shape of the spectrum in the burst; dorsals are characterized by a mid-frequency spectral peak, resulting in a “compact” spectrum, while coronals are characterized by a high-frequency peak of greater energy than at lower frequencies, resulting in a rising spectrum (Blumstein and Stevens, 1979; Fant, 1960; Halle et al., 1957; Jakobson et al., 1963; Stevens and Blumstein, 1978; Stevens, 1989). It has also been established that temporal information in the spectra is important for the identification of place of articulation of stop consonants (Kewley-Port, 1983; Kewley-Port and Luce, 1984; Kewley-Port et al., 1983), and that it contains cues that are especially important for the identification of dorsals, that is, their compact spectrum persists as a function of time in the burst (Kewley-Port, 1983). Furthermore, previous studies (Forrest et al., 1988; Nossair and Zahorian, 1991) have shown that voiceless stops can be successfully classified on the basis of statistical properties such as mean, slope, and curvature of their burst over time. We therefore analyzed ∕k∕ and ∕t∕ on the basis of the time-varying spectral information available in their burst (from acoustic release to vowel onset) expressed in terms of the spectrum mean, slope, and curvature; the analysis was performed using the EMU speech data analysis system (Cassidy and Harrington, 2001). The spectral data were calculated with a 256 point discrete Fourier transform with a 40 Hz frequency resolution and a 5 ms Blackman window shifting in 5 ms increments over the entire length of the burst-to-vowel interval sampled at 20 kHz. The frequency axis was warped to the auditory bark scale in the frequency range 0–8500 Hz (0–21.26 bark), using the formula in Traunmüller (1990).

The parametrization of the spectral data to include time-varying information is illustrated with an example in Fig. 3. After converting the spectra between the burst onset and vowel onset to bark, each stop consists of a running spectral display, as shown in Fig. 1a, with bark spectra at intervals of 5 ms. The next step was to reduce each individual spectrum from such a running display to just three values and more specifically to the first three coefficients (C₀,C₁,C₂) that are obtained after applying the discrete cosine transformation (DCT). For an N-point bark spectrum, x(n), extending in frequency from n=0 to N−1 points, the mth DCT-coefficient C_m (m=0,1,2) was calculated with

$$C_m=\frac{2k_m}{N}\sum _{n=0}^{N-1}x\left(n\right)\cos \left(\frac{(2n+1)m\pi }{2N}\right),$$ (1)

$$k_m=\frac{1}{\sqrt{2}},m=0,k_m=1,m\ne 0.$$

These three coefficients, which are the amplitudes of the first three half-cycle cosine waves derived from the DCT, are proportional to the spectrum’s mean, slope, and curvature, respectively, and are also essentially equivalent to bark-scaled cepstral coefficients (see Harrington et al., 2008; Nossair and Zahorian, 1991; Watson and Harrington, 1999 for formulas and further details). Consequently, after applying Eq. 1, the stop burst [Fig. 3a] was reduced to a triplet of values (the first three DCT-coefficients), with one triplet every 5 ms: these triplets of DCT-coefficients as a function of time can be used to derive a (cepstrally) smoothed spectrum [Fig. 3b]. We denote the triplets of DCT-coefficients across time by C_0t, C_1t, and C_2t, as shown in Fig. 3c.

Figure 3.

Analysis of a ∕t∕ stop burst over time produced by subject JX in the phrase “cop TOP.” (a) Bark-scale spectra at 5 ms intervals of the burst between the stop’s release (burst onset) and vowel onset. (b) The same spectra as in (a) but smoothed using three DCT-coefficients (C₀, C₁, and C₂), capturing the individual spectra’s mean, slope, and curvature. (c) The values of the DCT-coefficients (C₀, C₁, and C₂) obtained for each spectral slice from burst onset to vowel onset in 5 ms increments; each temporal curve (C_0t, C_1t, and C_2t) is fitted using the first three DCT-coefficients capturing its mean, slope, and curvature, resulting in nine coefficients that encode the spectral time-varying properties of the burst.

We now needed to find a way to compress C_0t, C_1t, and C_2t prior to classification. The approach that we used was to apply Eq. 1 again separately to each of the time-varying C_0t, C_1t, and C_2t. This is exactly equivalent to the methodology used in Harrington et al. (2008) for compressing time-varying formant trajectories. Thus, whereas each time-varying formant of a vowel was reduced with the DCT to three values in Harrington et al. (2008), here we have reduced separately the stop burst’s time-varying spectral mean (C_0t), time-varying spectral slope (C_1t), and time-varying spectral curvature (C_2t) each to three values using Eq. 1, a procedure equivalent to a second order polynomial fitting. The end result, then, is that we have compressed the bark scaled spectral information of each stop burst between the release and vowel onset [Fig. 3a] to a single point in a nine-dimensional space and moreover in such a way that this compression encodes time-varying information.

Classification procedure

We classified the stops in the nine-dimensional space described in Sec. 2B using a support vector machine (SVM) algorithm (Baayen, 2008; Bennett and Campbell, 2000; Cortes and Vapnik, 1995; Duda et al., 2000). Non-technically, a SVM separates classes not on the basis of their center or mean but instead on the basis of their margins; to accomplish this, points are projected into a high dimensional space and a separating hyperplane is determined in this space. Among the advantages of this classification method is the fact that SVM makes no assumptions about normality of the data, and that it can handle cases where a class is broken into non-contiguous regions. This is especially important with speech data where phonetic classes can contain non-contiguous members due to context. This consideration is also important for our current dataset since we collapsed over several experimental variables (rate, vowel, stress, and phrase position).3 Previous work on phonetic classification of vowels and consonants in running sentences (Clarkson and Moreno, 2000) has shown that SVM performs at least as well as Gaussian classifiers. SVM was implemented using the “e1071” library for R (Mayer, 2001) using a Gaussian radial basis function kernel. For classification of speech classes (both vowels and consonants), the choice of kernel is reported not to have a major impact on accuracy (Clarkson and Moreno, 2000).

For classification, the data were split into separate training and testing parts. Our training data were correctly produced stops from six speakers, and our test data were stops produced by a new speaker (JX) not included in training (Table 2). Speaker JX was selected for testing as this was the speaker whose production was also used in the perceptual experiment reported by Pouplier and Goldstein (2005), and we reasoned that selecting data from the same speaker for the acoustic analysis would allow for an investigation of the relationship between articulation, acoustics, and perception. Furthermore, this speaker’s dataset was relatively balanced for number of error-free ∕t∕ and ∕k∕ tokens as well as for number of errorful tokens. Splitting this subject’s data by the conditions stress, rate, phrase position, and vowel context resulted in a low number of errorful tokens for some of the conditions (cf. Table 7 in the Appendix). For this reason, the acoustic analyses reported in the main body of the paper were carried out on data collapsed across the conditions stress, rate, phrase position, and vowel context. Analyses by conditions are, as far as they were feasible in terms of number of tokens, reported in the Appendix.

Table 2.

Number of tokens used for training and testing: Training data were produced by six subjects; test data were produced by a new subject (JX) not included in the training.

	Articulatory category						Total
	K	T	KC	KG	TC	TG
Training data	691	577					1268
Test data	182	156	52	44	29	86	549
Total	873	733	52	44	29	86	1817

Table 7.

Number of tokens for speaker JX split by conditions vowel context, rate, stress, and phrase position.

Condition	Level	Articulatory category						Total
		K	T	KC	KG	TC	TG
Vowel context	∕ɪ∕	57	46	23	27	12	41	206
	∕ɑ∕	125	110	29	17	17	45	343
Rate	Fast	43	48	36	15	21	27	190
	Medium	75	50	14	27	7	46	219
	Slow	64	58	2	2	1	13	140
Stress	Stressed	80	90	28	14	14	34	260
	Unstressed	102	66	24	30	15	52	289
Phrase position	Initial	90	68	30	20	15	43	266
	Final	92	88	22	24	14	43	283

Acoustic proximity calculations

We further quantified the acoustic properties of each token in the test data by calculating the Mahalanobis (M) distance of each token to the centroids of both error-free ∕k∕ (M_k) and ∕t∕ (M_t) in the nine-dimensional space to which each token’s burst properties were compressed. We used the Mahalanobis distance for its capability to factor in the categories’ distributions (in our case the distributional shapes of error-free ∕k∕ and ∕t∕). Relative proximity P of each token to either error-free ∕k∕ or ∕t∕ was calculated as the difference between the two Mahalanobis distances (on the logarithmic scale), using the formula in Eq. 2:

$$P=\log \left(M_{\mathrm{k}}\right)-\log \left(M_{\mathrm{t}}\right),$$ (2)

where M_k is the Mahalanobis distance of a token to the centroid of error-free ∕k∕ and M_t is the Mahalanobis distance of a token to the centroid of error-free ∕t∕.

When P is 0, the token is equidistant between ∕k∕ and ∕t∕; when it is positive, the token is closer to ∕t∕ than to ∕k∕; and when it is negative, the token is closer to ∕k∕ than to ∕t∕.

Measures used from previous studies: d^′ perceptual score and articulatory timing

To assess the relationship between acoustics and perception, we used the perceptual measure employed by Pouplier and Goldstein (2005) in their experiment. To examine the role of relative timing of the intended and intruding gestures in shaping the tokens’ acoustics, we use the timing measure employed by Pouplier and Goldstein (in press). In what follows we summarize these measures, and the data subsets for which these measures are available.

Pouplier and Goldstein (2005) used in their perceptual experiment a total of 60 tokens, selected from each articulatory classification category (no error, gradient error, and categorical error) and covering within their category a range of different articulator heights for the intruding gesture. Ten tokens were selected per category (except for KC that included 11 tokens and KG that included 9 tokens), all produced by the same speaker (JX). The perceptual responses were obtained for individual tokens from 11 native speakers of English in a go-no go perceptual identification task (for details, see Pouplier and Goldstein, 2005). For each token, we used the perceptual scores (d^′) (MacMillan and Creelman, 1991) obtained in their experiment.4 These d^′ perceptual scores represent the difference between correct and incorrect identifications and were calculated using Eq. 3.

$$d^{\prime }=z\left(H\right)-z\left(F\right),$$ (3)

where H is the proportion of correct identification responses relative to number of trials, F is the proportion of incorrect identification responses relative to number of trials, and z is the standardized score.

A d^′ score of 4.65 represents perfect accuracy (H=99%, F=1%; MacMillan and Creelman, 1991), while a negative score means that the proportion of incorrect responses is greater than that of correct ones. In this way, the consistent correct identification of any given token as either ∕k∕ or ∕t∕ has a maximum score of +4.65, while consistent incorrect identification has a negative score to a minimum of −4.65.

For relative timing between intended and intruding articulatory gestures, we used the timing measure employed by Pouplier and Goldstein (in press). For determining articulatory timing, the vertical movement time series of both the intended and intruding gestures were labeled at constriction release, as shown in Fig. 1a (cf. Pouplier and Goldstein, in press for details on the segmentation procedure employed).5 Relative timing at release was calculated as the lag between intended and intruding gestures by subtracting the release timestamp of tongue tip from the release timestamp of tongue dorsum (lag=release_TD−release_TT). A negative lag means that the tongue tip constriction was released last, and a positive lag means that the tongue dorsum was released last. For subject JX, the release lag measure was available for 54 KC tokens, 41 KG tokens, 28 TC tokens, and 43 TG tokens. Because for most error-free tokens the uncontrolled articulator could not be measured [cf. Fig. 1b], relative timing for these tokens could not be computed and hence they were not included in the analysis.

RESULTS

SVM classification

For the classification analysis, training was performed on correctly produced stops from six speakers and testing on stops produced by speaker JX (cf. Table 2). Results from both a closed test (training and testing on the training data) and a semi-open test (training and testing on the training data using a four-fold cross-validation) show that error-free ∕k∕ and ∕t∕ are correctly classified by the SVM for the vast majority of cases (Tables 3, 4). It must be noted that no speaker normalization was performed for the training data, and that the data were undifferentiated for stress conditions, phrase positions, speech rates, and vowel contexts (cf. Sec. 2A).

Table 3.

Classification (%) from a SVM closed test in which training and testing were carried out on error-free K and T produced by all six subjects. The main diagonal shows the hit-rate per category. All percentages have been rounded.

Closed test	Articulatory category
	K	T
Classified as ∕k∕	95	5
Classified as ∕t∕	11	89

Table 4.

Classification (%) in a semi-open SVM test using four-fold cross-validation. The training data were randomly split into four subsets, and each time three subsets were used for training and the fourth was used for testing. All percentages have been rounded.

Semi-open test (four-fold cross-validation)
Total accuracy	89
Single accuracies	91	84	91	91

The test data from subject JX were classified on the basis of the training results obtained from error-free data from six subjects. The confusion matrix (Table 5) for the test data shows that error-free ∕k∕ and ∕t∕ were accurately classified at 90% and 85%, respectively. While productions of ∕k∕ with intruding tongue tip gestures were predominantly classified as ∕k∕ (83% for categorical intrusions and 89% for gradient intrusions), there was greater ambiguity in whether errorful ∕t∕ was classified as ∕k∕ or ∕t∕. Thus, about half of ∕t∕ tokens produced with an intruding tongue dorsum of categorical magnitude (TC) were classified as ∕k∕ and about half as ∕t∕. The overall classification pattern, with ambiguity in the classification of TC, remained the same when the data were split for conditions stress, rate, phrase position, and vowel context (Table 8 in the Appendix). TC tokens were ambiguously classified as ∕k∕ or ∕t∕ regardless of stress, rate, phrase position, or vowel context, while no such ambiguity was observed for errorful ∕k∕ tokens.

Table 5.

Classification (%) in an open SVM test. The training data included the error-free T and K bursts from six subjects, and testing was carried out on all of subject JX’s stops. All percentages have been rounded.

	Articulatory category
	K	T	KC	KG	TC	TG
Classified as ∕k∕	90	15	83	89	52	27
Classified as ∕t∕	10	85	17	11	48	73

Table 8.

Classification scores (%) for speaker JX, split by conditions vowel context, rate, stress, and phrase position. The numbers represent rounded percentages of tokens classified as ∕k∕. Because for the slow rate there were very few tokens for some of the errorful categories, the classification pattern for the slow rate was not included.

Condition	Level	Articulatory category
		K	T	KC	KG	TC	TG
Vowel context	∕ɪ∕	86	13	87	89	58	15
	∕ɑ∕	91	15	79	88	47	38
Rate	Fast	93	15	83	93	57	41
	Medium	89	18	79	89	43	22
Stress	Stressed	86	11	89	93	57	41
	Unstressed	92	20	75	87	47	17
Phrase position	Initial	89	21	90	95	47	26
	Final	89	10	77	83	57	28

The distribution of posterior probabilities (Fig. 4) shows that most TC tokens occupied a space between unambiguous ∕k∕ and ∕t∕ (rather than being evenly assigned to the center of the ∕k∕ and ∕t∕ spaces). Thus, while ∕k∕ tokens (errorful or not) and error-free ∕t∕ tokens show a skewed distribution, with half of the tokens having a probability of 90% or more of being correctly classified, errorful ∕t∕ tokens show a much flatter distribution along the probability continuum: for TC, only $\frac{1}{4}$ of the tokens have a probability over 90% of being classified as ∕t∕, another $\frac{1}{4}$ have a probability under 20% of being correctly classified, with half of the tokens falling in the middle of the continuum. This asymmetry cannot be explained by the distributions of articulator heights between errorful ∕k∕ and ∕t∕. Articulator height histograms [Fig. 2b] showed that on the basis of vertical position of the intruding articulator, KC and TC were similarly distributed within their defined intervals. For the gradient categories, there were more TG tokens close to the boundary between error-free and errorful ∕t∕ than were KG tokens to the boundary between error-free and errorful ∕k∕ [boundary A in Fig. 2a]. Nevertheless, there were more ambiguous TG tokens than KG tokens, although articulator height distributions alone would have predicted the opposite pattern.

Figure 4.

Histograms of posterior probabilities from a SVM classification showing the probability of being classified as ∕k∕ for categories K, KC, and KG and of being classified as ∕t∕ for categories T, TC, and TG. Reference marks (dotted lines) are placed at the 25th, 50th, and 75th percentiles, respectively, ordered from left to right.

Proximity measure P

To quantify the acoustic similarity of errorful ∕k∕ and ∕t∕ to either typical velars or alveolars, we measured each token’s proximity to the centroids of error-free ∕k∕ and ∕t∕. For this measure, described in Sec. 2D, we expected that error-free ∕k∕ and ∕t∕ should each be close to their own centroids, resulting in negative P values for ∕k∕ and positive values for ∕t∕, which is indeed the pattern observed (Fig. 5). In terms of acoustic proximity P of the error tokens to either error-free ∕k∕ or ∕t∕, we observe similar median values for all three ∕k∕ categories (error-free, categorical, and gradient error), but more divergent median values for the ∕t∕ categories, with (some) error ∕t∕ tokens having intermediate values between ∕k∕ and ∕t∕. A Welch’s variance-weighted ANOVA (to correct for unequal variances) with dependent variable relative proximity index P and factor category (K, KC, KG, T, TC, and TG) was significant [F(5,145.765)=267.183, p<0.001]. A follow-up posthoc test (Games-Howell, appropriate for unequal variances and group sizes, cf. Toothaker, 1993) showed that none of the ∕k∕ groups differed significantly from each other (p>0.05), while TC and TG differed from T (p<0.001), but not from each other (p>0.05); all ∕t∕ groups also differed from the ∕k∕ groups (p<0.001). These results show that while errorful ∕k∕ tokens are acoustically close to error-free ∕k∕, errorful ∕t∕ tokens as a group are acoustically close to neither error-free ∕t∕ nor ∕k∕, a result that corroborates the distribution of probabilities from the classification analysis. This shows that an intruding tongue tip during ∕k∕ results in tokens acoustically similar to error-free ∕k∕, while an intruding tongue dorsum during ∕t∕ results in tokens acoustically different from error-free ∕t∕. Relative proximity patterns for the data split according to stress, rate, phrase position, and vowel context remained similar to the overall pattern with no diverging pattern in any of the conditions (Fig. 11 in the Appendix).

Figure 5.

Boxplots showing the median (thick horizontal bar), interquartile range (boxes), error bars (vertical lines), and outliers (circles) for the acoustic measure P, the token proximity to ∕k∕ (negative values), or ∕t∕ (positive values). All ∕k∕ categories were significantly different from all ∕t∕ categories. Significant differences within ∕k∕ or ∕t∕ are indicated by ^*.

Figure 11.

Boxplots showing the median (thick horizontal bar), interquartile range (boxes), error bars (vertical lines), and outliers (circles) for the acoustic measure P, the token proximity to ∕k∕ (negative values), or ∕t∕ (positive values), split by conditions vowel context (a), rate (b), stress (c), and phrase position (d). Because for the slow rate there were very few tokens for some of the errorful categories, the slow rate was not included in this by-rate analysis.

Relationship between acoustics and perception

Looking exclusively at the data subset used by Pouplier and Goldstein (2005) in their perceptual experiment (cf. Sec. 2E), we found that errorful TC tokens differed from error-free ∕t∕ tokens both in terms of their acoustics and in terms of how they were perceived, while errorful ∕k∕ tokens did not differ either acoustically or perceptually from error-free ∕k∕ (Fig. 6). For acoustics, the proximity P measure was used, which quantifies relative proximity of a given token to either ∕k∕ or ∕t∕ (described in Sec. 2D). For perception, the d^′ score from Pouplier and Goldstein (2005) was used (described in Sec. 2E). Independent sample t-tests showed that errorful TC tokens were significantly different from error-free ∕t∕ tokens on both the d^′ score measure [Welch’s t(9.363)=3.145, p=0.011] and on the acoustic measure [t(18)=4.053, p=0.001]. (TG tokens were not significantly different from error-free ∕t∕, neither on the perceptual measure [t(18)=1.42, p=0.173] nor on the acoustic measure, at alpha level 0.012 corrected for multiple comparisons [t(18)=2.284, p=0.035].6 Thus, the acoustic results match the previously reported perceptual results when performed on the same dataset (note that the same acoustic pattern is observed for the larger dataset as well). The asymmetry observed in perception is matched by an acoustic asymmetry, suggesting that the basis for the asymmetry observed in perception was not due to a bias at perceptual level (a bias of the perceptual system) but rather that the bias originated in the acoustic signal and hence the underlying articulatory pattern.

Figure 6.

Boxplots showing the median (horizontal bar), interquartile range (boxes), error bars (vertical lines), and outliers (circles) for perceptual d^′ score (a) and acoustic measure P (b). Significant differences are indicated by ^*. Total number of tokens across categories for the data subset is N=60. Perceptual d^′ scores range from +4.65 representing maximum consistent correct identification to −4.65 representing consistent incorrect identification. Acoustic proximity indices range from close to ∕t∕ (positive values) to close to ∕k∕ (negative values).

Spectral characteristics of errorful ∕k∕ and ∕t∕

The results so far show that while co-production of an intruding tongue tip had a negligible acoustic and perceptual influence on ∕k∕, co-production of an intruding tongue dorsum with an intended tongue tip for ∕t∕ made these tokens more ambiguous acoustically and perceptually. The question that arises in light of these results is how the characteristics of ∕k∕ and ∕t∕ spectra are affected by a second intruding constriction so that errorful intended ∕t∕ tokens become acoustically ambiguous, while intended ∕k∕ tokens remain acoustically unaffected. To address this question, we looked at the acoustics of error-free and errorful ∕k∕ and ∕t∕ between the burst onset and vowel onset in cepstrally smoothed running spectra (Fig. 7) derived from the same triplets of DCT-coefficients that were used to compress the burst to a point in a nine-dimensional space which had formed part of the acoustic classification and distance analyses discussed above.

Figure 7.

Ensemble-averaged, linearly time-normalized spectra of error-free and errorful ∕k∕ and ∕t∕. Time points are proportional, proceeding in 25% increments from burst onset (release) to vowel onset. The spectra were smoothed using the first three DCT-coefficients. The figures show information equivalent to the coefficients used for classification and acoustic distance calculation.

The main acoustic characteristic of a typical ∕k∕ is a spectral peak at mid-frequency (maintained over time) due to the long front cavity in front of the dorsal constriction, while a typical ∕t∕ is mainly characterized by high spectral energy at high-frequency due to the short cavity in front of the constriction (cf. Blumstein and Stevens, 1979; Stevens, 1989; Stevens and Blumstein, 1978). Figure 7 shows that while the mid-frequency energy for ∕k∕ is not altered by an intruding coronal constriction (that is, errorful ∕k∕ spectra do not differ from error-free ∕k∕), the high-frequency energy characteristic for ∕t∕ is affected by an intruding dorsal constriction. More specifically, TC (and to a lesser extent TG) spectra have less energy at high-frequencies than error-free ∕t∕.

However, since TC spectra have greater high-frequency energy than ∕k∕ spectra, they are spectrally neither quite like a ∕k∕ nor a ∕t∕: that is, they are acoustically ambiguous between the error-free ∕k∕ and ∕t∕ stops. For a more detailed observation, we examined ensemble-averaged spectra at the burst onset (Fig. 8), i.e., the spectra at proportional time point zero in the running spectral displays in Fig. 7. The spectral shape at the burst onset was the same for both errorful and error-free ∕k∕ tokens, with a spectral energy peak at mid-frequency typical for ∕k∕. On the other hand, the spectral shape at the burst onset for errorful TC tokens differed from a typical ∕t∕ spectrum.7 The spectrum for TC (the continuous line in the left panel in Fig. 8) showed energy peaks both at mid-frequency (∕k∕-like) and at high-frequency (∕t∕-like), albeit both peaks were reduced in absolute amplitude compared to either typical ∕k∕ or ∕t∕. Crucially, the energy of the high-frequency peak was considerably lowered so that the mid- and high-frequency peaks were of roughly similar magnitudes, in contrast to the spectral shape for a typical ∕t∕ which has an energy peak at high frequencies, resulting in ∕t∕’s characteristic rising spectrum.

Figure 8.

Ensemble-averaged spectra of error-free and errorful ∕k∕ and ∕t∕ at burst onset smoothed using three DCT-coefficients. Arrows indicate spectral energy peaks for spectra of error-free ∕t∕ and ∕k∕ and for ∕t∕ produced with an intruding tongue dorsum of categorical magnitude (TC).

Qualitatively, the same general pattern was observed if the spectral shapes were analyzed taking into account vowel context (Figure 12 in the Appendix). Error-free ∕k∕ and ∕t∕ were, not unexpectedly, different as a function of vowel context: when followed by vowel ∕ɪ∕, the amplitude at mid-frequency for ∕k∕ and at high-frequency for ∕t∕ was higher than in the ∕ɑ∕-vowel context. However, the spectral shape for the errorful tokens was qualitatively similar to the overall observed pattern: errorful ∕k∕ tokens were not different from error-free ∕k∕ in either vowel context, while errorful ∕t∕ tokens (TC, in particular) differed from error-free ∕k∕ and ∕t∕ tokens in both vowel contexts. In both ∕ɪ∕- and ∕ɑ∕-vowel contexts, TC tokens showed energy peaks of comparable amplitudes at both mid- and high-frequencies, with high-frequency amplitudes lower than those of error-free ∕t∕ tokens.

Figure 12.

Ensemble-averaged spectra of error-free and errorful ∕k∕ and ∕t∕ by vowel context, smoothed using three DCT-coefficients. The figures show spectral shape at burst onset. Pictured in (a) are spectra of tokens produced in the ∕ɪ∕-vowel context and in (b) are spectra of tokens produced in the ∕ɑ∕-vowel context. At all time-points, TC spectral shape is different from T spectral shape, except at vowel onset, where ∕t∕ and ∕k∕ spectra are similar in shape, reflecting the properties of the vowel.

Previous research (Blumstein and Stevens, 1980; Ohde and Stevens, 1983) has shown that lowering the spectral energy at high-frequency results in tokens less likely to be identified as ∕t∕. It is therefore plausible to suggest that the lower energy at high-frequency observed for our TC tokens, combined with an almost equal energy peak at mid-frequency, is the factor responsible for these tokens’ acoustic ambiguity both in our classification data and in Pouplier and Goldstein’s (2005) perceptual results. The spectral shape for TG was closer to that of T than was TC (Fig. 8): TG’s closer proximity to T also matched the classification and perceptual analyses.

Therefore, intrusion of a second constriction affects the spectral properties of the burst asymmetrically: whereas a tongue tip intrusion during the production of an intended ∕k∕ has a marginal effect on the spectrum, a tongue dorsum intrusion during an intended ∕t∕ is accompanied by a change in spectral shape. Recall that the intruding constrictions are weaker than the intended ones both spatially and temporally (cf. Pouplier, 2003; Pouplier and Goldstein, in press), so although both errorful ∕t∕ and ∕k∕ involve the same articulatory gestures, they differ in terms of which gesture is stronger. As shown in Figs. 78, the weaker coronal constriction during intended ∕k∕ does not affect the spectral shape of the burst. The weaker dorsal constriction during intended ∕t∕ on the other hand affects the spectrum by lowering the spectral energy at high-frequency enough to result in a qualitative change in spectral shape (from a rising spectrum typical for ∕t∕ to a flatter one, with comparable mid- and high-frequency peaks), thereby making TC spectra ambiguous between a ∕k∕ and a ∕t∕. In this sense, it can be stated that the intruding tongue dorsum during an intended ∕t∕ has a qualitative effect on the spectrum, whereas the effect of the intruding tongue tip is marginal.

Relationship between acoustics and articulatory timing

Recall that the articulatory measure used for classifying tokens into errorful or error-free was maximal vertical position of the intended and intruding gestures (cf. Sec. 2A). This measure provides no insight into how the two gestures are timed relative to each other. Thus, while both error ∕k∕ and ∕t∕ were produced with an intended and intruding gesture, these co-produced gestures might have been timed differently for ∕t∕ and ∕k∕ tokens, and this timing difference may be the cause of the observed acoustic asymmetry between error ∕k∕ and ∕t∕. If, for instance, TD were always released last whether intended or intruding, this would lead to an asymmetry in acoustics between ∕t∕ and ∕k∕, assuming that the gesture released last contributes relatively more to the overall acoustic shape of the burst. For the timing measure, release lag from Pouplier and Goldstein’s (in press) analysis was used, as described in Sec. 2E. For the classification pattern, we used the results from the general classification analysis, as described in Sec. 3A, pertaining to the tokens for which the timing measure was available (50 KC, 41 KG, 28 TC, and 34 TG).

Lag values between intended and intruding gestures at release are shown in Fig. 9. In general, median values indicate that most ∕k∕-tokens had positive release lags, and most ∕t∕-tokens negative lags. This means that for both intended ∕k∕ and ∕t∕, constriction of the intended gesture (TD and TT, respectively) was released last. However, the interquartile range for TC spans from negative to positive values, indicating a range from tokens with intended (TT) gesture released last to tokens with intruding (TD) gesture released last. Given this distribution, one may suspect that the asymmetry observed acoustically does not arise from the mere presence of an intruding gesture during ∕t∕ but rather from how these intruding gestures are timed, in a way that is similar to the timing pattern observed for the opposite category. If many of the errorful ∕t∕ tokens show a timing pattern specific to ∕k∕ (i.e., TD released last, possibly as a result of TD being a slower articulator compared to TT), and these are specifically the tokens classified as ∕k∕, then the relative timing between intruding and intended gestures may have been responsible for the acoustic asymmetry between intruded ∕k∕ and ∕t∕. To address this question, we look at the tokens’ distribution as a function of both classification and timing pattern (Table 6).

Figure 9.

Boxplots showing the median (horizontal bar), interquartile range (boxes), error bars (vertical lines), and outliers (circles) for release lag, measuring relative timing between intended and intruding gestures during errorful ∕k∕ and ∕t∕. Positive values indicate that TD is released later than TT.

Table 6.

Distribution of token types as a function of classification results and relative timing patterns. Percentages in parentheses have been rounded.

Articulatory category	Articulatory timing pattern
	TT released last		TD released last
	Classified as ∕k∕	Classified as ∕t∕	Classified as ∕k∕	Classified as ∕t∕
KC	0	1 (2%)	41 (82%)	8 (16%)
KG	0	0	37 (90%)	4 (10%)
TC	9 (32%)	9 (32%)	5 (18%)	5 (18%)
TG	11 (32%)	17 (50%)	2 (6%)	4 (12%)

Overall, as shown in Table 6, intended ∕k∕ and ∕t∕ exhibit distinct timing patterns, with the intended gesture (TD and TT, respectively) being released last in a majority of the tokens, confirming the result of Pouplier and Goldstein (in press) for our subset of the data. For errorful ∕k∕, there were only a couple of tokens for which the intruding gesture was released last, amounting to 2% of the data. Taking the classification pattern into account, with the exception of one token, ∕k∕ tokens classified acoustically as ∕t∕ exhibited the same timing pattern as the majority of ∕k∕ tokens, that is, a timing pattern with TD constriction released last. For ∕t∕ tokens, the majority of both TC (64%) and TG (82%) show a pattern with TT released last, and not the timing pattern common for ∕k∕ tokens (with TD released last). The classification pattern further shows that more errorful ∕t∕ tokens were classified as ∕k∕ with a ∕t∕-like timing pattern (TT released last) than with a ∕k∕-like timing pattern (TD released last), indicating that the classification of ∕t∕ tokens as ∕k∕ is not due to a ∕k∕-like timing pattern. Furthermore, in the case of TC, for tokens with the same timing pattern (either TT or TD released last), half were classified as ∕k∕ and half as ∕t∕, indicating that the timing pattern is not a good predictor of the classification pattern.

Additionally, if timing were responsible for the observed acoustic asymmetry between the effect of an intruding gesture during ∕t∕ vs during ∕k∕, we would expect different timing patterns to result in different spectral shapes for the ambiguous category TC. Specifically, we have shown that the spectral shapes of ∕t∕ tokens with categorical intrusion error exhibit spectral properties of both ∕t∕ and ∕k∕, while errorful ∕k∕ spectra are entirely ∕k∕-like in shape (cf. Fig. 8). We have also seen that of all errorful categories, TC has the most tokens in which intruding gesture is released last (36%). If the gesture released last shapes the overall acoustic pattern, it may be that the shape observed for TC is an average between very ∕k∕-like tokens, that is, tokens where TD is released last (hence the mid-frequency peak energy), and very ∕t∕-like tokens, that is, tokens with TT released last (hence the high-frequency peak energy). If this is the case, we expect the spectral shape for TC tokens with TD released last to look ∕k∕-like, and the spectral shape for TC tokens with TT released last to look ∕t∕-like. Figure 10 shows the spectra of TC tokens with either release pattern. While the timing pattern shows some effect on the spectral shape of the TC tokens, overall the spectral shape for TC tokens is ambiguous between ∕t∕ and ∕k∕ for either timing pattern. The spectra for tokens with TT released last differ from both ∕k∕ and ∕t∕ spectral shapes by having both a mid-frequency and a high-frequency energy peak. The spectra of tokens with TD released last look a bit more ∕k∕-like in that the mid-frequency peak is more prominent; however, unlike ∕k∕, this spectrum still includes an energy peak at high-frequency (roughly equal to the mid-frequency peak), absent from ∕k∕ tokens. For both timing patterns, the energy peak at high-frequency is lower for TC tokens than for error-free ∕t∕, and higher than for error-free ∕k∕ tokens. The overall characteristic spectral shape of TC tokens can therefore not be (exclusively) due to the relative timing between the two gestures, but is instead due to the overall effect that a tongue dorsum constriction has on the energy of the spectrum at both mid- and high-frequencies.

Figure 10.

Ensemble-averaged spectra at burst onset smoothed using three DCT-coefficients of TC tokens with TD released last (N=10), TC tokens with TT released last (N=18), error-free ∕k∕, and error-free ∕t∕.

DISCUSSION AND CONCLUSION

Overall, the classification analysis has shown that an intruding tongue dorsum constriction with a ∕k∕-like amplitude (i.e., TC tokens) results in ∕k∕-like acoustics in about half of the intended ∕t∕ tokens. On the other hand, intruding tongue tip constrictions during ∕k∕, even when in the range of intended ∕t∕ in terms of articulator height (KC tokens), result in ∕t∕-like acoustics in only about 11% of the tokens. It has also been shown that the relative timing between intended and intruding gestures cannot explain this asymmetry: instead, the difference is due to different acoustic consequences of an intruding TT vs TD constriction. Overall, the presence of a TD constriction, whether intended or intruding, is likely to result in a ∕k∕ classification for any given token due to the mid-frequency spectral energy peak and the lower high-frequency energies caused by a dorsal constriction. This implies that TD will affect the acoustics even when it is co-produced with a TT constriction with amplitudes in the range for an intended ∕t∕, as is the case for KC and TC tokens. While KC was predominantly classified as ∕k∕ by the SVM algorithm, the TC tokens were classified at chance level as either ∕t∕ or ∕k∕. The probability distribution of the classification algorithm (cf. Fig. 6) revealed that many of the TC tokens were ambiguous between ∕k∕ and ∕t∕. In line with these results, the spectral analysis suggested that the ambiguity in the case of TC tokens was due to the characteristic shape of these tokens, showing both a mid-frequency energy peak (∕k∕-like) and a high-energy peak (∕t∕-like), although both these peaks were notably lower than those of error-free ∕k∕ and ∕t∕. For an intruding TT constriction, a different result became apparent: very few tokens with an intruding TT constriction were ambiguous between ∕t∕ and ∕k∕ in terms of their classification probabilities. The spectral shape of these tokens was indistinguishable from that of tokens produced without a tongue tip intrusion.

The acoustic cues for ∕k∕ and ∕t∕ are differently affected by the type of articulatory variability analyzed here. On the one hand, we observed relatively robust mid-frequency spectral energy in dorsal stops, demonstrated by the lack of difference in spectral shape between errorful and error-free ∕k∕ tokens. By contrast the high-frequency spectral energy that is a major cue for coronal stops was much more variable, as shown by the quantitative and qualitative differences in the spectrum of errorful vs error-free ∕t∕ tokens. Our finding shows, contra the prediction by Winitz et al. (1972), that articulatory variability of the type discussed here “smears” particularly the high-frequency energy of ∕t∕ bursts, while it leaves mid-frequency energy, and hence ∕k∕ bursts, unaffected. However, the effect is not uniform across our data: recall that the asymmetry between ∕t∕ and ∕k∕ only became evident for the categorical errors, not for the gradient ones. This means that articulator height is one of the main factors conditioning the results: this is because the intruding gesture had to be of a certain magnitude in order to affect sufficiently the acoustic classification results. However, for categorical errors, the asymmetric acoustic pattern for ∕t∕ and ∕k∕ showed that articulator height alone is insufficient to predict the results: unlike for the gradient errors, the location of the constriction becomes relevant. That is, if two categorical constrictions (one intended and one errorful) are present in the vocal tract during the same time interval, it is the constriction more posterior in the vocal tract that will dominate the acoustics. Surprisingly, this effect is observed irrespective of the timing of the release of the constrictions and irrespective of which one of the two constrictions was intended or intruding.

Our results suggest that the perceptual asymmetry observed by Pouplier and Goldstein (2005) is matched by an acoustic asymmetry between the robustness of dorsal stops but vulnerability of coronal stops to articulatory variability. This finding also suggests that coronals’ perceptual vulnerability in the context of articulatory variability observed elsewhere (in consonant clusters, for example, cf. Byrd, 1992; Chen, 2003; Kochetov and So, 2007) is likely the result of their acoustic sensitivity to articulatory variability, rather than the result of a bias exclusively at the perceptual∕auditory level. The results make predictions about when articulatory variability of the type described here is more likely to be perceived, possibly as a speech error. If, as suggested by the analyses reported in this paper, co-productions of an intruding TD constriction on an intended TT constriction for ∕t∕ have more robust acoustic consequences than co-productions of intruding TT with an intended TD for ∕k∕, then the expectation is that on the basis of acoustic information alone more variability, and hence more potential errors, during ∕t∕ can be detected than errors during ∕k∕. This may explain why, for instance, ∕t∕ substitution by ∕k∕ is reported more frequently than ∕k∕ substitution by ∕t∕ in studies that rely on auditory perception for error detection (Stemberger, 1991) [note that at least some of these transcribed “substitutions” may actually be co-production errors, cf. Boucher (1994) and Wood (1997)]. Our acoustic results suggest that rather than reflecting an error distribution pattern, the observed asymmetries between ∕t∕ and ∕k∕ in transcribed speech corpora (Stemberger, 1991) and in error perception (Pouplier and Goldstein, 2005) have their basis at the acoustic level. Both errorful ∕t∕ and ∕k∕ are equally distributed at the articulatory level—intruding gestures are as likely during intended ∕t∕ and ∕k∕. However, since errors during intended ∕t∕ are more reliably cued acoustically, they are bound to be more readily detected auditorily. On the other hand, if errors during intended ∕k∕ are not reflected in the tokens’ acoustics, errorful ∕k∕ productions are much more likely to be missed and therefore to be underrepresented in transcriptions. The theoretical implication is that if the transcription asymmetry does not reflect a production asymmetry, but is instead explained by asymmetric acoustic consequences of intruding gestures at different constriction locations, then no theoretical apparatus (such as coronal underspecification, cf. Stemberger, 1991) is needed to account for the ∕k∕-∕t∕ asymmetry in speech errors.

To summarize, the results presented in this paper showed that not all intruding gestures have detectable acoustic consequences. Thus, while an intruding tongue dorsum during ∕t∕ results in tokens acoustically different from error-free ∕t∕, an intruding tongue tip during ∕k∕ often has no acoustic consequences, that is, these tokens overall remain similar to error-free ∕k∕. The observed acoustic pattern is also similar to results from a previous perceptual experiment, and it explains those results as being grounded in acoustics. While ∕k∕ tokens are more robust acoustically to co-production of both intended and intruding gestures, ∕t∕ tokens are sensitive acoustically and perceptually to the presence of a TD intruding gesture. The examination of the timing pattern of the intruding gesture relative to the intended gesture showed that the timing pattern could not explain on its own the acoustic properties of the tokens. Rather the amplitude of the intruding gesture seems to determine the acoustic pattern, and specifically, the amplitude of TD seems to have an influence on acoustics regardless of whether it is an intended or intruding gesture.

The study also contributes to the general knowledge on the acoustics of ∕k∕ and ∕t∕. There is ample evidence that ∕k∕ and ∕t∕ are robustly discriminable on the basis of their acoustic properties (Blumstein and Stevens, 1979; Fant, 1960; Halle et al., 1957; Jakobson et al., 1963; Kewley-Port, 1983; Stevens, 1989; Stevens and Blumstein, 1978), and also that the acoustic properties of ∕k∕ and ∕t∕ show different degrees of sensitivity to vowel context: ∕t∕ is more robust than ∕k∕ to vowel coarticulation, as shown by the well-known context-dependent variation in velars (cf. Halle et al., 1957) and by the greater convergence of alveolars to a common locus frequency, even when the following vowel context varies (cf. for example, Kewley-Port, 1982; Lehiste and Peterson, 1961; Lindblom, 1963; Sussman et al., 1991). The results presented here likewise suggest that the acoustic properties of ∕k∕ and ∕t∕ are differently affected by the type of articulatory variation documented here, namely, co-production of an intruding constriction along with the intended one (in a very general sense, this co-production could be viewed as coarticulation with another consonant). However, in contrast to vowel coarticulation, in the case of co-productions the acoustics of ∕k∕ are more robust to this type of articulatory variation compared to the acoustics of ∕t∕. These two patterns of results may seem surprising at first sight but are actually quite consistent with each other when considering that vowel coarticulation influences low-frequency energy, leaving the salient high-frequency energy for ∕t∕ unaffected, but shifting the mid-frequency peak for ∕k∕. In the case of co-productions, an intruding tongue dorsum constriction has a noticeable impact on the high-frequency energy for ∕t∕, while an intruding tongue tip leaves the mid-frequency peak for ∕k∕ unaffected. The results of our study have more general implications for the reliability of acoustic information in detecting articulatory variations during production of ∕k∕ and ∕t∕ and contribute to our knowledge about the relationship between different types of articulatory variability and acoustics.

APPENDIX

A description of the data for speaker JX split by conditions vowel context, rate, stress, and phrase position is shown in Table 7, and classification scores (%) for speaker JX, split by the same conditions are shown in Table 8. Relative proximity patterns for the data split according to vowel context, rate, stress, and phrase position are illustrated in Fig. 11. Ensemble-averaged spectra of error-free and errorful ∕k∕ and ∕t∕ by vowel context are shown in Fig. 12. The results in the analyses by condition do not diverge qualitatively from the general pattern of results discussed in the main text.