Retroflex or rhotic vowels are found in fewer than 1% of the world’s languages (Maddieson, 1984; Moran, McCloy, & Wright, 2014). While vowel rhoticity may be considered marginal from a broad crosslinguistic perspective, it is a basic vowel feature in Kalasha. To help contextualize the interaction of rhoticity and vowel quality in Kalasha, we begin by surveying various phonetic vowel distinctions and their interaction with the lingual articulation of vowel quality. Table 1 shows the proportion of languages (defined as distinct ISO 693-3 codes) in the PHOIBLE database (Moran et al., 2014) that employ various phonetic distinctions in their vowel systems, as well as vowel quality dimensions that they are particularly likely to interact with.1 We did not require these distinctions to be minimal, only to be present (i.e., /i/ vs. /u/ counts as both backness and rounding).

While lip rounding is utilized in nearly all vowel systems, it is worth considering how it interacts with tongue posture. Although the lips and tongue are articulatorily independent, they may interact through the trading relations involving their effects on formant frequencies. Vowel pairs such as /i y/ that ostensibly differ only in lip rounding often differ in tongue position as well (Jackson & McGowan, 2012). Length and nasalization are the most frequent additional features that are at least partially independent of vowel quality, followed by various forms of laryngealization (creakiness/glottalization/ejective), breathiness, pharyngealization, and rhoticity. Each of these semi-independent vowel features has opportunities to interact with vowel quality.

A prototypical example of length-quality interaction is the development of Persian vowels: Classical Persian has been analyzed as having a three-way quality contrast combined with a two-way length contrast /a aː i iː u uː/ (Krámskỳ, 1939), but in Modern Persian this is a six-way quality contrast /a ɑ e i o u/ (Nye, 1955) or /a ɑː e iː o uː/ (Toosarvandani, 2004). In this case, the Classical Persian long vowels have developed higher and/or more peripheral qualities in Modern Persian than the corresponding short vowels. This is consistent with the idea that short vowels are more vulnerable to undershoot (Lindblom, 1963), which can be reinterpreted as a basic property of a vowel. The quality differences among the non-low vowels are also consistent with the idea that higher vowels sound longer than lower vowels and speakers may use lowering to signal short duration and raising to signal long duration (Gussenhoven, 2007).

Vowel nasalization is achieved by velum lowering, which is also independent of tongue position but has overlapping acoustic consequences that may lead to lingual differences among ostensibly similar oral-nasal pairs. Nasalization leads to F1 raising in high vowels and F1 lowering in low vowels due to an additional vocal tract resonance in the vicinity of an F1 frequency that is typical for a low-mid vowel (Diehl, Kluender, Walsh, & Parker, 1991; Feng & Castelli, 1996; Fujimura & Lindqvist, 1971; Serrurier & Badin, 2008). This acoustic effect of nasalization may lead to enhancement or compensation (Beddor, 1982; Krakow, Beddor, Goldstein, & Fowler, 1988). The acoustic effects of nasalization are enhanced with a more neutral tongue height in Northern Metropolitan French (Carignan, 2014) and Brazilian Portuguese (Barlaz et al., 2015), and also in Kalasha (Hussain & Mielke, 2021).

Creaky voice quality and glottalization are associated with larynx raising, which shortens the vocal tract and raises F1 and other formants (Laver, 1980), making vowels sound lower, whereas breathy vowels are often produced with a lowered larynx, which has the opposite effect (Esposito, Sleeper, & Schäfer, 2021), making vowels sound higher. Indeed, listeners perceive creaky vowels as sounding lower (Brunner & Zygis, 2011) and breathy vowels as sounding higher (Lotto, Holt, & Kluender, 1997). It is reasonable to expect phonation differences to be enhanced by vowel height, much like length and nasalization differences (see Esposito et al., 2021 for more discussion of the interaction of voice quality and vowel quality).

Pharyngealized vowels are typically produced with centralization of F1 and F2, and they may or may not show signs of rhoticity such as low F3 (Catford, 1983). Pharyngealization makes the back cavity smaller and limits the tongue’s freedom of movement to produce extreme vowel postures. Hussain and Mielke (2021) concluded that there is probably considerable overlap between vowels described as pharyngealized and vowels described as rhotic, but that these terms are not equivalent.

Most of the vowel types described so far have acoustic or perceptual effects that may lead to changes in vowel quality. By contrast, rhotic vowels directly interact with the tongue movements used to produce vowels, and accordingly rhoticity is expected to be particularly aggressive at rearranging vowel systems it is introduced to. Rhotic vowels such as /ɚ/ and rhotic approximants such as retroflex (tip-up) [ɻ] and bunched (tip-down) [ɹ] are produced with a wide range of tongue shapes often grouped into retroflex and bunched categories (Delattre & Freeman, 1968; Hussain & Mielke, 2021; Mielke, 2015; Zhou et al., 2008). Retroflexion is achieved by raising and retracting the tongue tip (possibly involving subapical or sublaminal contact with the alveolar ridge). Bunching can be achieved by lowering and retracting the tongue tip while depressing the medial portion of the tongue dorsum, resulting in a concavity that is prominent in the mid-sagittal plane (Hussain & Mielke, 2021; Moisik, 2013; Stavness, Gick, Derrick, & Fels, 2012). Tongue dorsum concavity is a key characteristic of bunched [ɹ] and has also been observed in retroflex tongue shapes in English and Canadian French (Mielke, 2015; Zhou et al., 2008). Retroflexion, in addition to raising of the tongue tip towards hard palate, may also include a dip in between the tongue tip and dorsum (Hamann, 2003).

Low F3 is a hallmark of bunching and retroflexion (Lehiste, 1962). Tongue tip raising and tongue bunching both give rise to a large sublingual cavity, which results in lowering of F3 (Zhou et al., 2008). Delattre and Freeman (1968) reported a wide range of articulatory to acoustic correlations for the American English [ɹ]. (1) A narrow palato-velar constriction lowers the F3 or brings F2 and F3 close to each other. (2) A dip in the tongue dorsum lowers F3. (3) A wider pharyngeal constriction increases the distance between F2 and F3 but a narrow pharyngeal constriction brings the two formants closer. (4) Lip rounding lowers all the formants.

Table 2 organizes the vowel distinctions that are at least as frequent as rhoticity in descending order of their expected effect on the lingual articulation of vowels. Rhoticity directly affects most aspects of tongue posture, and pharyngeal constriction and tongue root movements affect the posterior tongue. The others have effects that are mediated primarily by acoustics, by affecting the end of the vocal tract as in lip rounding and laryngeal gestures, or the effect of velopharyngeal coupling on F1, or primarily by perception, as in the case of length.

The question of how rhotic vowels emerged in Kalasha is a major issue in the current Dardic literature (Cooper, 2005; Di Carlo, 2016; Heegård & Mørch, 2004; Hussain & Mielke, 2022; Kochetov et al., 2021). There are reasons to attribute the development of rhotic vowels to internal sound change as well as to external factors. The internal source of rhoticity is the occurrence of retroflex consonants in the environment of a vowel that developed rhoticity. The oral plain vowels of Northern (Birir, Bumburet, and Rumbur) and Southern (Urtsun and Jinjiret) dialects of Kalasha underwent rhoticization due to the presence of liquids and retroflex consonants in a word. For instance, the rhotic-nasal vowels of modern Kalasha can be reconstructed from the Old Indo-Aryan (Sanskrit) retroflex nasal /ɳ/ (Sanskrit /paɳi/ ‘hand’ → Kalasha /pẽ˞/ ‘palm of the hand’: Heegård & Mørch, 2004).

Some evidence about earlier stages of Kalasha comes from fieldwork by Leitner in 1866–72 (Leitner, 1880) and Morgenstierne in the late 1920s (Morgenstierne, 1973). In Leitner and Morgenstierne’s wordlists, Kalasha rhotic vowels were transcribed as sequences of plain vowels+palatal fricative /ř/ or rhotics /r ṛ/ (an underdot is generally used to denote retroflexion in Indo-Aryan and Nuristani literature). For example, the word for ‘heart’ was transcribed as /héra/ by Leitner and /hïːřa/ by Morgenstierne; in modern Bumburet Kalasha, the same word is produced as /hi˞a/, with a rhotic vowel. Morgenstierne (1973) originally used the term palatal fricative to refer to a class of r-colored speech sounds in Dardic and Nuristani languages, which may affect the quality of the neighboring vowels. This resembles modern descriptions of Dameli and Nuristani languages (Eastern Kataviri and Kamviri), which have non-phonemic and r-colored vowels in the vicinity of /ɻ/ (Perder, 2013; Strand, 2011).

We infer from these descriptions that the development of rhotic vowels in Kalasha is the result of vowels coalescing with following liquids and retroflex consonants and that researchers 95–160 years ago heard the consonantal portions as palatal fricative /ř/ or rhotics /r ṛ/. During the time period that Kalasha has been developing rhoticity in vowels that are followed by retroflex consonants, it has been in contact with Nuristani languages that have abundant phonetic vowel rhoticity. This vowel rhoticity takes the form of a contrastive retroflex approximant /ɻ/ and non-phonemic retroflex vowels (Heegård & Mørch, 2004; Morgenstierne, 1954), as well as r-coloring of vowels in the vicinity of the retroflex flap /ɽ/ (Strand, 2011).

In summary, Kalasha rhotic vowels are believed to have emerged via loss of retroflex consonants (e.g., /ɽ ɻ ɳ/). The development of phonemic rhotic vowels may have also been encouraged by intensive contact with the Nuristani languages with a contrastive retroflex approximant /ɻ/ (Di Carlo, 2016; Heegård & Mørch, 2004; Hussain & Mielke, 2021, 2022).

A handful of studies have investigated the phonetic correlates of rhotic vowels in Kalasha (Hussain & Mielke, 2021, 2022; Kochetov et al., 2021). Figure 2 shows mean formant frequencies for the ten plain and rhotic oral vowels of four male speakers reported by Hussain and Mielke (2021) for the tokens included in this study. It can be observed that the rhotic vowels are generally more centralized in F2 relative to their non-rhotic counterparts, their F1 is centralized or raised, and they have much lower F3 (as also shown by Kochetov et al., 2021).2 The rhotic vowels are close to steady-state (i.e., they are not generally more rhotic at the end than at the beginning; Hussain & Mielke, 2021).

Figure 3 shows Smoothing-Spline ANOVA (SSANOVA) comparisons of tongue shapes used to produce these ten vowels. The five non-rhotic vowels are articulated as expected (e.g., on the basis of Wood (1979): /i/ and /e/ have constrictions made toward the hard palate, /u/ has tongue raising toward the velum, and /o/ and /a/ have constrictions in the upper and lower pharynx, respectively). The five rhotic vowels are produced with tongue bunching (rather than retroflexion) by all speakers investigated by Hussain and Mielke (2021). In addition, all five rhotic vowels, including /a˞ o˞ u˞/, are produced with relatively front tongue body position.

While the rhotic vowel tongue shapes are quite different from the tongue shapes used to produce the corresponding plain vowels, Hussain and Mielke (2021) found no significant differences between the lip postures for rhotic vowels and the corresponding non-rhotic vowels. /u/, /u˞/, /o/, and /o˞/ and their nasal counterparts are all rounded and all the other vowels are not. /u/ and /u˞/ are produced with a slightly smaller lip opening than /o/ and /o˞/.

In this paper we model the coarticulation between non-rhotic vowels and rhotic consonants. The tongue shapes involved in coarticulated vowel+rhotic sequences are determined by the combination of muscle activations involved in vowels and rhotic consonants. We begin by reviewing the muscle activations involved in producing vowels and rhotic approximants. The human tongue is controlled by intrinsic and extrinsic sets of muscles (see Sanders & Mu, 2013; chapters 8–9 of Gick, Wilson, & Derrick, 2013; and Figures 1, 2, 3, 4 in Jang, 2022 and references therein for more details). Minor contractions in intrinsic muscles change the shape of the tongue from the inside. The intrinsic tongue muscles consist of inferior longitudinal, which lowers and retracts the tongue tip; superior longitudinal, which raises and retracts the tongue tip; verticalis, which flattens the tongue body; and transversus, which narrows the tongue laterally and causes a sagittal expansion, enlarging the tongue along both anteroposterior and inferosuperior axes due to the muscular hydrostatic nature of the tongue (Smith & Kier, 1989).

The extrinsic tongue muscles connect the tongue to other parts of the body (see Honda, 1996; Takano & Honda, 2007). The genioglossus courses from the superior mental spines inside the mandible to the full length of the tongue. Contracting the anterior fibers of the genioglossus lowers the front of the tongue and contracting middle fibers lowers the tongue dorsum. Contracting posterior fibers of the genioglossus moves the whole tongue forward and raises it toward the palate, as in the production of high and front vowels. The hyoglossus courses from the hyoid bone at the root of the tongue up to the sides of the tongue and pulls the tongue down and back when contracted (as in low and back vowels). The palatoglossus courses from the soft palate to the sides of the tongue and pulls the soft palate down or the tongue up depending on the state of other muscles attached to these structures. The styloglossus courses from the styloid processes in the skull below the ears forward to the sides of the tongue, and has the potential to retract and stabilize the tongue in back vowels. In addition to these intrinsic and extrinsic tongue muscles, the geniohyoid and mylohyoid are muscles that do not directly insert into the tongue but form the floor of the mouth and accordingly support the base of the tongue and facilitate tongue raising.

Stavness, Gick, et al. (2012) modeled the articulation of retroflex and bunched English /r/ variants using the ArtiSynth biomechanical modeling toolkit (www.artisynth.org; Lloyd, Stavness, & Fels, 2012). Their bunched /r/ involved the contraction of the superior longitudinal, inferior longitudinal, and anterior genioglossus (to retract the tongue tip without raising it), middle genioglossus (to lower the tongue dorsum medially), along with some retraction of the transversus and verticalis to bunch the tongue body. Their tip-up (retroflex) /r/ involved greater contraction of the superior longitudinal without contraction of the inferior longitudinal (to retract and raise the tongue tip), plus some contraction of the middle genioglossus (but less than in the bunched variant), and optionally contraction of the hyoglossus to do some of the work of retracting the tongue without depressing the tip. Stavness, Gick, et al. (2012) showed that their bunched /r/ is very compatible with their simulation of [i], which differs from it by principally having contraction of the posterior genioglossus to front and raise the tongue and less contraction of the middle genioglossus. Their retroflex /r/ is compatible with their simulation of [a], which similarly involves middle genioglossus and hyoglossus to lower the tongue body, and differs from retroflex /r/ in having contraction of the verticalis to further depress the tongue body and lacking contraction of the superior longitudinal (for no retroflexion). These results helped account for the observation that English /r/ is typically bunched in the context of /i/ and that retroflex /r/ is particularly frequent in the environment of /a/ (Mielke, Baker, & Archangeli, 2016; Ong & Stone, 1998).

The aim of the current study is to investigate the similarity between Kalasha rhotic vowels and the superposition of plain vowels and rhotic approximants (i.e., additive combination of the articulatory gestures of plain vowels and retroflex /ɻ/ and bunched /ɹ/ approximants). We use the phonetic data presented in Hussain and Mielke (2021, 2022) as the basis for the current investigation of the biomechanics involved in the production of Kalasha rhotic vowels and combine Kalasha plain vowels with Kamviri-style rhotic approximants /ɻ ɹ/. Moreover, we also examine the role of different tongue muscles in the production of plain and rhotic vowels of Kalasha and compare them with the retroflex and bunched approximants of Kamviri.

Acoustic and articulatory data used as the basis for simulations were described in more detail in Hussain and Mielke (2021, 2022). Recordings were made of four Kalasha (Bumburet dialect) and two Kamviri speakers (all males in their 20s or 30s). All six speakers were from Bumburet valley, Chitral, northern Pakistan. In addition to their native languages, all the speakers could speak Khowar, Pashto, Urdu, and/or English.

The modeling described in this paper is based on the rhotic vowels in the Kalasha words /pi˞ː/ ‘press’, /he˞/ ‘theft’, /ba˞/ ‘lazy’, /tʃo˞i/ ‘parasite’, and /k^hu˞/ ‘hat’, the non-rhotic vowels in the Kalasha words /pi/ ‘drink (verb); from’, /pe/ ‘if’, /paː/ ‘go’, /po/ ‘footprint’, and /tu/ ‘you’, and the word-final rhotic approximant /ɻ/ (retroflex) or /ɹ/ (bunched) in the Kamviri word /parmaɻ/ ‘child.’

The participants were invited into a quiet room at a hotel in Bumburet valley, Chitral, Pakistan. A Terason t3000 ultrasound machine with Ultraspeech 1.3 software (Hueber, Chollet, Denby, & Stone, 2008) was used for recording the ultrasound data. The tongue ultrasound and lip video recordings were made in direct-to-disk mode, generating 640 × 480 pixel bitmap images at 60 frames per second. A Terason 8MC3 3–8 MHz ultrasound transducer was positioned underneath each participant’s chin, stabilized with an Articulate Instruments aluminum Probe Stabilisation Headset (Scobbie, Wrench, & van der Linden, 2008). A frontal view of the lips was captured using a board camera (The Imaging Source DFM 22BUC03-ML with a 12 × 0.5 mm lens) mounted on the headset about five centimeters in front of each participant’s lips using two clip-on LED book lights, which also illuminated the participants’ lips.

Simultaneous audio recordings were made with a Shure Beta 53 head-mounted omnidirectional condenser microphone (44.1 kHz, 16-bit). Before the recordings, all the participants were familiarized with the task and went through the wordlists. After audio and ultrasound recording commenced, the participants were asked to hold a mouthful of water to generate ultrasound images of the palate (not used in this analysis) and then held a tongue depressor between their teeth and pressed their tongue against it in order to generate ultrasound images of the occlusal plane. The target wordlists were presented to the participants on a computer screen or they were described to them in Urdu, which is a lingua franca of Pakistan. All the words were elicited in citation form. Each target word was repeated five times.

The ultrasound frames were selected from the midpoints of the Kalasha vowel intervals and the Kamviri rhotic approximant intervals. The tongue contours and the lip opening were manually traced in Palatoglossatron (Baker, 2005). The lip data used to inform the modeling were two points placed mid-sagittally on the edge of the upper and lower lips. The frequencies of the first three formants were extracted at the same time points using Praat (Boersma & Weenink, 2007).

Our goal was to test whether Kalasha rhotic vowels are similar articulatorily and acoustically to the superposition of plain vowels and rhotic approximant articulations. Thus, we have taken plain vowels coarticulated with a following rhotic approximant to be the initial state for Kalasha rhotic vowels. To model this coarticulation, we used the ArtiSynth biomechanical modeling toolkit (www.artisynth.org; Lloyd et al., 2012). ArtiSynth is a free, open-source computational platform for simulating multibody systems comprising rigid and deformable bodies (the latter implemented as finite-element models or FEMs). These bodies can be made to interact via unilateral (e.g., contact/collision) and bilateral (e.g., joint) constraints and manipulated with force effectors of various kinds, such as musculature based on realistic mathematical muscle models. We performed two types of simulations: (i) Inverse simulations of the Kalasha vowel shapes, both plain and rhotic, and Kamviri rhotic approximants (both retroflex /ɻ/ and bunched /ɹ/ variants); and (ii) forward simulations, which combine the excitations computed during the inverse simulations of the Kalasha plain vowels with excitations of either of the two types of Kamviri rhotic approximant. Along with the biomechanical simulation, we also simulated 1-dimensional acoustics of these vowels, employing frequency-domain acoustic simulation (Birkholz, 2005; Birkholz & Jackel, 2004) and making use of the airway skin mesh (Anderson et al., 2017) to allow for estimation of the vocal tract area function. More details about the biomechanical modeling are included in the Supplementary Materials.

Biomechanical modeling approaches are generally characterized as either forward or inverse. Forward modeling (aka forward-dynamics simulation), is a process of controlling a biomechanical model with given muscle activation signals. Inverse modeling (aka inverse-dynamics simulation), in contrast, is a process which estimates the underlying muscle activations from previously obtained kinematic measurements by using a biomechanical model (Eskes et al., 2017). The ArtiSynth forward models (retroflex and bunched versions) represent the predicted vocal tract shapes due to superposing a bunched or retroflex approximant on plain vowels. The ArtiSynth inverse model of Kalasha vowels is meant to be a close approximation to the actual observed Kalasha vocal tract shapes. When the inverse simulation tongue shapes are quite different from the forward simulation tongue shapes, it suggests that Kalasha speakers are doing something different (such as a more optimal articulatory strategy to achieve a particular perceptual target). If the acoustic output is also different, this suggests that Kalasha has phonologized new perceptual targets for rhotic vowels (i.e., the goal for the phonological category does not even sound like the vowel+rhotic superposition that it is thought to have originated from).

We next describe the inverse simulations, which form the basis of the forward simulations. Inverse models in ArtiSynth take time-varying target points — or trajectories — as input, and they output a set of muscle activations that minimize trajectory-tracking errors while being subject to additional terms for resolving muscle redundancy (Anderson et al., 2017; Stavness, Lloyd, & Fels, 2012) and ensuring smooth activations (as rapid changes can lead to model instability). In our simulations, we used the empirical data from the lips and the tongue to define the trajectories. The final set of inverse target points were two targets for the face FEM (on the midline of the upper and lower lips) and eleven target points along the contour of the tongue, running from the tongue tip to the tongue root. We also developed target points for the mandible (one on the central incisors and one on the pogonion) and hyoid bone (one point on the anterosuperior most point of the body) giving optional parameters to use in cases where model stability was an issue. In all cases, the inverse trajectories started at 0.0 s from their initial configuration and ended at their target location at 0.2 s.

We used MATLAB (MATLAB, 2019) to register the participants’ data (lip points and tongue contours) against corresponding details of the ArtiSynth model (Figure 4). While it was straightforward to identify points on the lips that match the flesh points tracked on the participants’ lips, it was less clear how to map the ultrasound tongue contour data into the ArtiSynth model. This is because we have no information in the ultrasound image as to what part of the tongue exactly is being imaged, and the imaged portion of the tongue also changes from frame to frame. Thus, homology cannot be guaranteed in the registration, and it was therefore necessary to make assumptions about what the typical visible portion of the tongue was and select reference points on the ArtiSynth tongue model (from tongue tip to root) that matched this. With this in mind, we extracted the location of the lower lip, upper lip, mouth corners, and midsagittal contour of the tongue from tip to root from the ArtiSynth model in its neutral configuration and imported these landmarks into MATLAB for further processing alongside the empirical articulatory data. For each participant, the lip and tongue data were independently registered (using Procrustes superimposition) against the ArtiSynth landmarks. In the case of the tongue, we registered the (participant-wise) mean observed tongue contour against the ArtiSynth tongue contour, using resampling to ensure all contours had the same number of sample points. The registered empirical data were then brought into ArtiSynth and visually examined for how well they fit within the ArtiSynth vocal tract, with the possibility of making slight adjustments to the overall scaling and translation of the registered data once it was in the ArtiSynth environment. The entire process was iterated upon using (most notably) slightly different selections for tongue tip and root positions on the ArtiSynth model to try to best fit the tongue contours while also being articulatorily reasonable. The task proved difficult. Ideally, if more participant data were available for other vocal tract structures, the fit could be improved; it would even be possible to register the ArtiSynth model itself to the participant (if, for example, structural MRI data were available for the participant). In practice, the inverse simulation does not always manage to match the target points exactly and thus no severe acoustic issues arose from the articulation occasionally treading slightly outside of the airway skin.3 The appearance of the tongue contour data within the ArtiSynth vocal tract setting is illustrated in Figure 4.

While alternative reference points on the ArtiSynth tongue model could have been explored systematically, small differences in reference points would not result in large differences with the current findings (see, e.g., Howson, Moisik, & Żygis, 2022). This is in part because there is always some amount of error that the inverse simulation makes in hitting the targets (particularly when there are many of them for a given contour and many contours are being used across a large set of simulations). Systematic exploration of this choice is infeasible, especially given the many other assumptions we have made alongside this that could also arguably be deserving of similar attention (such as the number of inverse targets to employ). The best we can do then is to present our findings in the light of the model design choices that we have made with the knowledge that small deviations (such as shifting the reference nodes by one node forward or backward or by using more or less inverse target nodes) would lead to similarly small changes to the results.

For the inverse simulation, we simulated selected productions from four Kalasha participants. We ran simulations covering five basic vowel qualities /i e a o u/ within two vowel types (plain and rhotic), each with approximately five tokens, as shown in Table 3, giving us 208 simulations. We also simulated five tokens each of the Kamviri rhotic approximant variants (retroflex and bunched), using data from two different participants who produced the sound differently. The process of bringing these data into ArtiSynth followed the same procedure as that used for the Kalasha simulations outlined above. Figure 5 illustrates inverse simulations of /o/ and /o˞/.

Once the inverse simulations were complete, we proceeded with the second type of modeling by creating forward simulations of the Kalasha rhotic vowels using the muscle activations estimated in the inverse simulations. Specifically, for both the retroflex and bunched versions of the Kamviri rhotic approximants, we combined the token-wise means of the muscle activations of these sounds with the token-wise means of the activations that were estimated for the Kalasha plain vowels. This resulted in a further 10 sets of simulations of “pseudo” Kalasha rhotic vowels – five with a retroflex basis and five with a bunched basis – that were intended to serve as a point of comparison against the inverse simulations of the Kalasha rhotic vowels. To accomplish the superposition of the muscle activations, we used a simple additive combination rule, adding activations from each component articulation (plain vowel and rhotic approximant variant) for each muscle exciter. To model a range of possible coarticulatory blends of plain vowels and rhotic approximants, each rhotic vowel was simulated using 11 different mixtures of plain vowel and rhotic approximant activations, essentially a “crossfade” from 100% plain vowel to 100% rhotic approximant at 10% increments. This resulted in 11 steps of rhotic mix proportion for each of the five forward simulation rhotic vowels that could be compared with the inverse simulation of the same rhotic vowel.

We applied several measures to the simulated tongue postures in order to compare them, as illustrated in Figure 6. Each tongue shape is represented by a polygon with 50 vertices. The centroid of the polygon is indicated by a dot in the middle of the polygon. Its x and y coordinates represent the overall advancement and height of the tongue body, respectively. The most posterior point on each polygon (at a point indicated by another dot) represents tongue root advancement. The tongue tip is defined as the most anterior point on the tongue polygon (indicated by a third dot). The x value of this point represents tongue tip advancement. The angle above the horizontal from the tongue centroid to the tongue tip (represented by a line segment) is an indicator of retroflexion. The tongue blade is taken to be the portion of the tongue that is 2–5 points (out of the 50 points) posterior to the tip. The angle between the two points defining the tongue blade (represented by a thick line between these two points) is another indicator of retroflexion.

Here we reprise the research questions introduced at the end of §1 in terms of the inverse and forward simulations:

(a) Do the rhotic vowels retain the lingual articulation of the corresponding non-rhotic vowels? This is a tongue shape comparison between the inverse simulation rhotic vowels (representing modern Kalasha rhotic vowels) and the retroflex and bunched forward simulations (representing an earlier coarticulatory stage). Articulatory properties of the inverse simulation rhotic vowels that are not found in the forward simulations suggest an articulatory reorganization of the Kalasha vowel system.

(b) Do the rhotic vowels retain any signs of retroflexion of the historically present retroflex consonants? This is also a tongue shape comparison between the inverse simulation rhotic vowels and the retroflex and bunched forward simulations. Articulatory properties of the inverse simulation rhotic vowels that resemble the retroflex forward simulations in particular suggest that the modern bunched rhotic vowels retain articulatory signs of their retroflex origins.

(c) Do the formant frequencies of rhotic vowels differ from what would be expected from adding retroflexion or bunching to their non-rhotic counterparts? This is a formant comparison (based on the acoustic synthesis derived from the biomechanical models), comparing the inverse simulation rhotic vowels with the retroflex and bunched forward simulations, particularly looking for acoustic similarities between the inverse simulations and retroflex forward similations (suggesting that the modern Kalasha vowels are preserving acoustic details attributable to the original coarticulatory basis) and looking for signs that the inverse simulation vowels are acoustically more distinct than would be expected from the forward simulation vowels (suggesting compensation for the centralizing effects of rhoticity).

To address these questions, we have compared a set of inverse simulations based on actual productions by four Kalasha speakers (representing our best biomechanical models of actual Kalasha vowels) to 22 different forward simulations for each rhotic vowel, representing 11 different degrees of overlap between averaged inverse simulation Kalasha plain vowels and averaged inverse simulation Kamviri retroflex and bunched approximants (the rhotic mix proportion). Any point along the continuum from 100% plain vowel to 100% rhotic could have formed the basis for modern Kalasha rhotic vowels, so we consider these possibilities as a group, asking, for example, does the inverse simulation /o˞/ resemble any of the mixtures of /o/ and /ɻ/ or /ɹ/ among the forward simulations?

Do the rhotic vowels retain the lingual articulation of the corresponding non-rhotic vowels? The Kalasha plain vowels /i e a o u/ differ from each other in tongue height and advancement in the expected ways, as seen above in Figure 16: /i e/ have a relatively advanced tongue body, /u o a/ have a relatively retracted tongue body, and within those front and back groups the vowels are distinguished by tongue body height. /i/ has the most advanced tongue root, followed by /e u/ and then /a o/. For most of these vowels, adding either bunching or retroflexion is expected to increase tongue body height and neutralize advancement while also increasing tongue root retraction.

The inverse simulation rhotic vowels /i˞ e˞ o˞ u˞/ all have similar tongue body height, and /a˞/ is lower. The retroflex and bunched forward simulations all generally capture these tongue height effects, indicating that tongue height in most rhotic vowels is attributable to the results of coarticulation. The exception is retroflex /o˞/, which shows none of the tongue body raising observed in /o˞/.

Turning to tongue body advancement, the inverse simulation /e˞ o˞ u˞/ have advancement similar to each other and similar to plain /u/. /i˞/ is more advanced and /a˞/ is less advanced. The retroflex forward simulations capture the tongue body advancement of /i˞ e˞ a˞/ well, and the bunched forward simulations have steps that match the degree of tongue body advancement seen in the inverse simulation, but the step that is most similar acoustically has too much tongue body advancement for these three vowels. For /o˞ u˞/, the bunched forward simulations are closer. Retroflex inverse simulation /o˞/ has insufficient advancement and retroflex inverse simulation /u˞/ introduces unnecessary retraction. As with tongue body height, introducing retroflexion to plain /o/ does not yield appropriate tongue body advancement for /o˞/.

Turning to tongue root advancement, the inverse simulation /i˞ o˞ u˞/ have similar tongue root position, while /e˞ a˞/ show tongue root retraction similar to plain /a o/. The bunched and retroflex forward simulations of /i˞ e˞ u˞/ all include steps with tongue root retraction similar to the inverse simulation rhotic vowels, although the retroflex /u˞/’s tongue root retraction match occurs at a step that is not similar acoustically to inverse simulation /u˞/. None of the forward simulations of /a˞ o˞/ approach the tongue root advancement that is seen in these vowels, which is particularly large for /o˞/.

In summary, the advancement and raising of /o˞/ is not accounted for by coarticulation to any type of rhotic. It is similar in tongue posture to /e˞/, from which it is distinguished by lip rounding. Hussain and Mielke (2021) concluded that /o˞/ might better be classified as a front vowel, and we have shown that this fronting is not accounted for by coarticulation to a rhotic consonant. Beyond this fact about /o˞/, bunching does the best job of accounting for the tongue position of back rhotic vowels and retroflexion does the best job of accounting for the tongue position of front rhotic vowels.6

The addition of rhoticity to plain vowels does a good job of capturing the tongue body and tongue root position found in the front rhotic vowels /i˞ e˞/, and the retroflex version is more accurate, particularly for tongue body advancement. On the other hand, adding bunching to the back vowels yields a closer match to the rhotic vowels than adding retroflexion. Retroflexion misses the tongue body and tongue root advancement of /o˞ u˞/ and the tongue body raising of /o˞/. Bunching provides a much closer approximation of /o˞ u˞/ but misses the tongue root advancement of /o˞/ and underestimates its tongue body advancement. The bunched and retroflex forward simulations of /a˞/ are similar, and the main miss is the slight tongue root advancement.

A possible interpretation of these facts is that the front vowels straightforwardly reflect the effects of coarticulation to retroflex consonants, and the tongue body fronting observed in back vowels may have been introduced at a stage when the dominant articulatory strategy for rhotic vowels shifted from retroflexion to bunching. This shift seems likely to have occurred once the vowel+retroflex consonant sequences were reinterpreted as vowels. Rhotic vowels have been found to be predominantly bunched (more so than rhotic approximants) in languages where they have been studied articulatorily (Jiang, Chang, & Hsieh, 2019; Mielke, 2015; Mielke et al., 2016).

Do Kalasha rhotic vowels retain any signs of retroflexion of the historically present retroflex consonants? Although the direct source of Kalasha rhotic vowels is believed to be coarticulation to a following retroflex (not bunched) consonant, Hussain and Mielke (2022) found only bunched variants of Kalasha rhotic vowels, for all vowel qualities. Here we simulated coarticulation to both retroflex and bunched rhotic approximants. As seen above in Figure 17, the inverse simulation rhotic vowels all have higher tongue blade angle and a higher angle to the tongue tip than their non-rhotic counterparts, and all but /o˞/ have a more retracted tongue tip. The bunched forward simulation rhotic vowels achieve a much better match to the inverse simulation rhotic vowels in terms of tongue blade angle, and they are comparable in terms of tongue tip advancement and the angle to the tongue tip. Coarticulation to the Kamviri bunched approximant provides a clearly better match to Kalasha rhotic vowels than coarticulation to the Kamviri retroflex approximant does, and this difference is most apparent in tongue blade angle. Kalasha /o˞/ has a more advanced tongue tip than would be expected for a retroflex version of /o/ because it is a more advanced vowel than /o/, but the bunched simulation nevertheless does a good job of approximating the observed tongue tip advancement.

Do the formant frequencies of rhotic vowels differ from what would be expected from adding retroflexion or bunching to their non-rhotic counterparts? Nearly all of the ways that the observed Kalasha rhotic vowels differ from their plain counterparts are replicated in the inverse simulation vowels, although the magnitudes of the differences vary a lot. This is shown above in Figure 10. The rhotic vowels all have lower F3 than their plain counterparts. F2 is lower in front rhotic vowels /i˞ e˞/ and higher in back rhotic vowels /a˞ o˞ u˞/ relative to their plain counterparts. F1 is higher in /i˞ u˞ e˞/ and lower in /a˞/, and it is similar between /o˞/ and its non-rhotic counterpart. This differs somewhat from the wholesale F1 increase shown in Figure 2, and we have suggested that the F1 increase in Kalasha rhotic vowels could be due to larynx raising, which is not included in any of the simulations.

The bunched and retroflex forward simulations both do a good job of capturing the F1 increase and F2 and F3 reduction observed in /i˞ e˞/. Both forward simulations of /a˞/ have F1 and F2 that are too low. The bunched and retroflex forward simulations differ the most for the two back rounded rhotic vowels /o˞ u˞/, with higher F3 for bunched /o˞/ and higher F2 for bunched /u˞/, relative to the retroflex versions of these vowels. The bunched models are somewhat better at capturing the F3 values (the retroflex models yield too much F3 decrease), but all of the models of these vowels are too low in F2. They do not account for the acoustic centralization or fronting of these vowels. In summary, there does not seem to be any evidence that any acoustic details of the Kalasha rhotic vowels are attributable specifically to the retroflexion in their history rather than rhoticity in general.

An important possibility to consider is that Kalasha rhotic vowels are somehow optimized to maintain perceptual distinctiveness within the entire vowel system. This is explored in the next subsection.

Kalasha appears to have once had a system of five oral vowels distinguished primarily by F1 and F2, and now it has a system of ten oral vowels distinguished by F1, F2, and F3.7 Figure 18 shows how adding rhoticity affects the dispersion of vowels in F1–F2–F3 space. The top panel shows that at a rhotic proportion of zero, all rhotic vowels are identical to their non-rhotic counterparts, and at a rhotic proportion of one, all rhotic vowels are identical to each other. As the rhotic proportion is increased from zero to one, the difference within rhotic-non-rhotic pairs generally increases, and the difference between rhotic vowels generally decreased. The curves for rhotic vowels and rhotic-non-rhotic pairs cross at a rhotic proportion between 0.7 and 0.8, where the average distances between vowels are closely matched by the average distances between inverse simulation vowels. This is also a rhotic mix proportion that results in vowels that most closely match the inverse simulation acoustically. At low rhotic mix proportions, bunched rhotic vowels are somewhat less distinct from each other than similar retroflex rhotic vowels, but these differences disappear before the rhotic mix proportion reaches 0.7. We note that for /i˞ e˞/, the two vowels with a good acoustic match between inverse and forward simulations, the best match was found at a rhotic mix proportion of 0.5–0.7 (a mixture of 50–70% bunched or retroflex approximant and 30–50% plain vowel). For the vowels with a relatively poor acoustic match, the closest step tended to be closer to the 1.0 rhotic approximant end of the scale. Thus, maximizing the acoustic dispersion of the forward simulation vowels and maximizing their acoustic similarity to inverse simulation vowels both point to 70% rhotic approximant and 30% plain vowel as a reasonable mixture, at least for rhotic front vowels, or at least for vowels that resemble rhotic versions of plain vowels.

The middle and bottom panels show all rhotic-non-rhotic pairs, and all pairs of rhotic vowels, respectively. Liu and Kewley-Port (2004) identify 0.37 barks as a threshold for listeners to distinguish vowels.8 All pairs of vowels at rhotic mix proportions from 0.2 to 0.9 exceed this threshold. The most indistinct rhotic-non-rhotic pair is /o o˞/. The most indistinct pairs of rhotic vowels are bunched /a˞ o˞/, retroflex /e˞ i˞/, and bunched /e˞ i˞/. Pairs of vowels differing in both quality and rhoticity are not depicted here, but for all rhotic mix proportions from 0.2 to 0.7, and for both retroflex and bunched simulations, the most indistinct among these pairs is /e i˞/.

If Kalasha vowels are more dispersed than would be expected based on coarticulation, we expect the inverse simulation vowels to be more dispersed than the forward simulation vowels. Looking at the whole system, the inverse simulation vowels are no more dispersed than any step of rhotic proportion, and bunching does not make for a more dispersed vowel system than retroflexion. The mean dispersion within the most vulnerable vowels (the rhotic-non-rhotic pairs and the pairs of rhotic vowels) is very similar between the inverse simulation vowels and the forward simulation vowels at a rhotic mix proportion of 0.7, which is also the point where the forward simulation rhotic tended to match the inverse simulation vowels most closely. There does appear to be some exaggeration of the differences in particular vulnerable pairs of vowels. /o o˞/ is the least distinct pair of vowels in the forward simulations, but it is the most distinct pair of vowels in the inverse simulations, and in the observed Kalasha tongue shapes. As previously discussed, /o˞/ is considerably different from /o/ in articulation, and probably better described as a front vowel with a tongue shape similar to /e˞/ combined with lip rounding similar to /o/.

Some Kalasha vowels are more dispersed acoustically than they would be if they were simply plain vowels combined with either type of a rhotic approximant. This is consistent with adaptive dispersion (de Boer, 2000; Flemming, 2002; Lindblom, 1986, 1990; Padgett & Tabain, 2005) manifesting early in the development of a new vowel sub-system. The observed acoustic dispersion involves articulatory gestures not explained by the rhotic approximants or the plain vowels believed to form the basis for the new rhotic vowels. However, we do not observe dispersion generally across the Kalasha vowel system. If it is an active force here, it appears to be limited to the most vulnerable pairs of vowels that are created by adding rhoticity to the system.

The most likely sequence of events in the development of Kalasha vowels seems to be that coarticulatory retroflexion was exaggerated and extended to more of the vowel interval, introducing new vowel qualities that were achieved through tongue bunching by later generations. When the vowels coalesced with rhoticity, they retained their characteristic lip postures. In the course of developing new vowel categories, the back rhotic vowels, and /o˞/ in particular, were established as front rounded vowels. The development of rhotic vowels in Canadian French (e.g., [pnø] ∼ [pnɚ] ‘tire’) has shown a similar reorganization from a different starting point: rhotic vowels developed from front rounded vowels, which were undergoing backing over time (Mielke, 2013). The modern rhotic vowels are produced as retroflex by some speakers (Mielke, 2015). The Kalasha /o˞/ is phonetically similar to the Canadian French rhotic /ø/, both produced with lip rounding and a bunched tongue in the front of the oral cavity, despite one originating from a back vowel and retroflexion and the other originating from a front vowel and no articulatory source of retroflexion. See Hussain and Mielke (2022) for further discussion of these two cases.

The reorganization of the rhotic vowel subsystem recalls the reorganization that is seen in nasalized vowel subsystems. Vowel nasalization changes the acoustic output of the vocal tract in ways that interact with the perception of vowel quality, such as by making high vowels sound lower and low vowels sound higher (Diehl et al., 1991; Feng & Castelli, 1996; Fujimura & Lindqvist, 1971; Serrurier & Badin, 2008). As such, nasalization is articulatorily independent but acoustically integrated with vowel quality. The acoustic effects of vowel nasalization may be enhanced or compensated for through direct changes to tongue or pharynx posture (Barlaz et al., 2015; Beddor, 1982; Carignan, 2014, 2018; Carignan, Shosted, Fu, Liang, & Sutton, 2015; Krakow et al., 1988). Articulatory enhancement of vowel nasalization is also seen in Kalasha /ã õ ũ/ and /ã˞/, which appears to be merged with /ẽ˞/ in some speakers (Hussain and Mielke, 2021).

Since rhoticity is achieved largely with the tongue, it is less independent of vowel quality than nasalization is. The articulatory gestures that help achieve acoustic characteristics of rhoticity such as low F3 also directly affect the quality of vowels as realized through F1 and F2 by changing the shape of the oral cavity and pharynx. We have seen that the present-day Kalasha rhotic vowel subsystem has apparently compensated for some of these effects through enhancement of F1 and F2 differences among the rhotic vowels. It would not have been possible to observe this as enhancement without the reference point provided by the biomechanical and acoustic modeling.

It seems very likely that Kalasha went through a stage with distinct pre-rhotic vowel allophones prior to developing monophthongal rhotic vowels from coarticulated vowel-rhotic sequences. North American English has a bunched/retroflex rhotic approximant that affects the quality of vowels around it. We can examine the pre-rhotic vowel system of North American English for possible clues about the earlier development of Kalasha rhotic vowels before they became established as monophthongs.

North American English is typically described as having one rhotic vowel quality /ɚ/ (which may be transcribed /ɜ˞/ or /ɹ̩/), but it has many distinct pre-rhotic vowel variants. Thomas (2001, p. 44) summarizes the effects of following /ɹ/ on English vowels as follows:

Kalasha vowels are generally monophthongal (Hussain & Mielke, 2021), so they are less susceptible to changes in gliding, and Kalasha has fewer non-rhotic oral vowel qualities than English, so mergers may be less likely. The syllabic R of North American English is the result of a merger of Middle English /ɛɹ ɪɹ ʊɹ ɜɹ əɹ/ (Wells, 1982). None of these vowel qualities are found in Kalasha. The remaining English pre-rhotic vowels are more similar to the Kalasha vowels that merged with rhotics.

Thomas (2001, pp. 44–48) describes North American English monophthongs before /ɹ/ as follows. /iɹ/ has retracted and sporadically merged with /eɹ/. /eɹ/ lacks the upgliding found in non-pre-rhotic contexts and it is lowered and retracted (and sporadically merged with /iɹ/). /ɑɹ/ varies considerably in the front-back dimension ([ɑɹ] to [æɹ]) and also may be rounded. /oɹ/ has mostly merged with /ɔɹ/ and is pronounced as [oɹ] (without the upgliding found in non-pre-rhotic contexts). In words which historically had /uɹ/, this sequence has merged with /ɜ˞/ or /oɹ/, or it has been reinterpreted as bisyllabic /uɚ/. These patterns in English are largely consistent with Kalasha rhotic vowels. We have seen that rhoticity causes F2 decrease in Kalasha front vowels, and /e˞ i˞/ are very close together in the simulations. Kalasha /a˞/ is acoustically fronted, much like English /ɑɹ/. Kalasha /o˞/ is quite different from English /oɹ/, and much more like English /ɜ˞/. Kalasha /u˞/ is acoustically lowered, which could have caused it to merge with /o˞/ if /o˞/ had not moved toward the front of the vowel space. Indeed, /u˞/ and /o˞/ are very close in the forward simulations, which do not take into account the fronting of Kalasha /o˞/. The fronting of /oɹ/ to avoid a merger with /uɹ/ would have been more problematic in North American English, with /ɚ/ sitting in front of /oɹ/ in the vowel space.

Thomas (2001, p. 44) notes that the distinct pre-rhotic variants of English vowels are difficult for speakers to connect to vowel categories occurring in non-pre-rhotic contexts. While the conventional IPA transcription /i˞ e˞ a˞ o˞ u˞/ suggests a close relationship between rhotic vowels and their non-rhotic counterparts, we have seen that some pairs, most notably /o o˞/, bear very little resemblance to each other in the way of lingual articulation. The rhotic vowels are spelled <a’ e’ i’ o’ u’>, transparently relating them their non-rhotic counterparts <a e i o u> in Cooper’s (2005) orthography. This may encourage association between historically related vowel pairs among speakers who read and write using this orthography. We have not collected metalinguistic judgments about associations between rhotic and non-rhotic vowels, and we are not aware of any phonological patterns supporting phonological relationships between particular vowels (see Kochetov et al. 2021), but we note one similarity (lip rounding) which may support the continued connection between rhotic vowels and their historically related non-rhotic vowels. Rhotic vowels are produced with virtually identical lip postures to their non-rhotic counterparts (Hussain & Mielke, 2021). Even though lip rounding would be an excellent way to help achieve the low F3 targets for these vowels, speakers maintain lip postures that match the vowels’ historical non-rhotic counterparts.

Walker and Proctor (2019) show that American English /ɑɹ/ and /oɹ/ involve little movement of the posterior tongue compared to /iɹ/ and /eɹ/, in which the tongue retracts considerably going from the vowel to the rhotic. They interpret this as a reason why /ɑɹ/ and /oɹ/ appear to only have a single mora each and may be followed by coda consonants as in dark and fork, whereas other vowel+/ɹ/ sequences appear to be bimoraic and cannot be followed by coda consonants. Walker and Proctor (2019) suggest that /ɑɹ/ and /oɹ/ might be particularly well-suited to being monophthongal rhotic vowels resembling coarticulated sequences of plain vowels and rhotic approximants. However, we have seen that the anterior tongue position is quite different between rhotic and non-rhotic /a/ and /o/ in Kalasha, and the rhotic vowels are rather different from what is predicted based on coarticulation. In summary, what makes /ɑɹ/ and /oɹ/ particularly good sequences in English does not extend well to monophthongal rhotic vowels with a single tongue-front posture throughout the vowel.