Twenty-eight right-handed adult native speakers of American English (20 women, 8 men, age M = 22.93 years, SD = 3.93years, range = 18–31) with no self-reported history of speech, hearing or neurological disorders participated after providing written informed consent (all procedures were approved by the Institutional Review Board at the University of Washington). Based on a pure tone hearing screening, all participants had monaural thresholds at or below 20 dB HL at all octave frequencies from 250 Hz to 4 kHz in both ears.

The experiment was conducted in a sound-attenuated booth. First, participants completed a practice session with unaltered auditory feedback to familiarize themselves with the instrumentation set-up by producing 7 blocks of three target words. Each block consisted of the monosyllabic words “talk,” “tech,” and “tuck” in randomized order. These words were presented individually on a monitor in front of the participant, each word remaining visible for 3 s. To help participants maintain a consistent speaking style, visual feedback about speech intensity and duration was presented on the monitor after each production. The target intensity was between 72 and 80 dB SPL, and the target vowel duration was 100–400 ms.

The actual experiment then included a Pre-test and two versions of a Variability task that were each immediately followed by an Adaptation task (Figure 1A). The Pre-test served to determine each participant’s median frequencies for the first and second formant (F1, F2) for the three target words (details below). During productions of the same words in the Variability tasks, inter-trial formant variability in the auditory feedback was either manipulated (magnified for one group of 4 men and 10 women, attenuated for the other group of 4 men and 10 women) or left unaltered (a control condition completed by both groups). Each Variability task was followed by an Adaptation task during which participants again produced the same target words but this time while hearing auditory feedback with a consistent upward perturbation of F1 and F2 (details below). The order of completing the manipulated and control versions of the Variability task (each immediately followed by an identical Adaptation task) was counterbalanced across participants.

In all of the above tasks, each participant’s speech output was captured with a microphone (SM 58, Shure) positioned 15 cm from the mouth and connected to an audio interface (Babyface Pro, RME, Haimhausen, Germany) and computer located outside the soundbooth (Figure 1B). The computer used MATLAB (The MathWorks, Natick, MA, United States) to present the visual stimuli, manipulate real-time auditory feedback when necessary, and record the participant’s speech. Auditory feedback manipulations were implemented with the publicly available MATLAB software ‘‘Audapter’’¹ (Cai et al., 2008; Tourville et al., 2013). The output of the audio interface was amplified (HeadAmp6 Pro, ART ProAudio, Niagara Falls, NY, United States), and played back to the participant via insert earphones (ER-3A, Etymotic Research Inc., Grove Village, IL, United States). Before each participant’s experiment, the feedback system was calibrated such that speech input with an intensity of 75 dB SPL at the microphone resulted in 72 dB SPL output in the earphones (Cornelisse et al., 1991). For this calibration procedure, the intensity of the auditory feedback in the earphones was measured using a 2 cc coupler (Type 4946, Bruel & Kjaer Inc., Norcross, GA, United States) connected to a sound level meter (Type 2250A Hand Held Analyzer with Type 4947 ½″ Pressure Field Microphone, Bruel & Kjaer Inc., Norcross, GA, United States).

The speech signal from all tasks (Pre-test task, Variability tasks, and Adaptation tasks) was digitized by Audapter. Using a custom-written MATLAB script, we examined the production data from all tasks offline to exclude productions containing production errors (e.g., mispronunciations or yawning; 0.45% of productions were rejected for this reason), manually marked the onset and offset of the vowel in each production based on visual inspection of its waveform and spectrogram, and extracted the first two formant frequencies (F1 and F2) as tracked by the linear predictive coding algorithm implemented in Praat (Boersma, 2001). To disentangle feedforward adaptive learning vs. online feedback-driven corrections within trials, F1 and F2 formant values for each trial were extracted both across an initial portion of the vowel (5–30% into its total duration) and a middle portion of the vowel (40–60% into total duration). Additionally, to verify accuracy of the auditory feedback manipulation in the experimental conditions of the Variability task (Magnified and Attenuated variability), we extracted F1 and F2 also across the same middle portion of the vowel in the recorded feedback signal.

Statistical analyses for the Variability task and the Adaptation task made use of paired two-sample t-tests or, in a few cases, one-sample t-tests, with the significance level set at 0.05. When multiple statistical comparisons were carried out as one family of tests, p-values were adjusted with the Holm–Bonferroni method (Holm, 1979). Cohen’s d was used for effect size calculations (Cohen, 1988). All statistical tests were conducted in the R software (R Core Team, 2019).

Figure 8 shows group mean formant frequencies produced throughout the Adaptation tasks that followed immediately after different conditions of the Variability task (data are in cents relative to the end of the preceding Variability task, measured at the initial portion of the vowel, and averaged across F1 and F2 and across the 3 trials per block). Recall that separate groups of participants completed the Magnified and Attenuated experimental conditions of the Variability task, and that, therefore, each group completed their own Control condition of the Variability task with no feedback perturbation. The Control versus experimental condition within-group comparisons in Figure 8 suggest that adaptation was not affected by the prior formant feedback variability manipulations. Statistical testing confirmed the absence of any significant differences between Control and Magnified or between Control and Attenuated for early adaptation extent (average formant frequency of the first 15 adaptation trials; Figure 9A), learning rate during early adaptation (slope of a linear regression line over the formant frequencies of the first 15 adaptation trials; Figure 8B), or final adaptation extent (average formant frequency of the last 15 perturbation trials; Figure 8C). The p values for all statistical comparisons are included with the data visualizations in Figure 9.

After the Pre-test with unaltered auditory feedback, participants completed two conditions of a Variability task (each followed by an Adaptation task): one was a Control condition with unaltered formant feedback, and the other condition had either Magnified or Attenuated formant variability in the auditory feedback, depending on the participant’s group assignment. Signal processing algorithms generating the feedback signal in these experimental conditions increased or decreased the distance between the formants produced in a given trial and the participants’ median formants for the same word in the Pre-test. We therefore quantified participants’ productions with a DI that expressed produced formant frequencies also in terms of their distance to the pre-test median.

Compared with each group’s own Control condition, the condition with Magnified feedback variability did not result in an adjustment in distance, but the condition with Attenuated feedback variability led to a gradual increase in distance between produced trials and the pre-test median (thus opposing the feedback manipulation). This increasing distance between produced formants and pre-test median formants was detected in both the initial portion of the vowel (5–30% into the total vowel duration; results in Figure 4) and the middle portion of the vowel (40–60% into the total vowel duration; results in Figure 5) portions of the vowel, and, thus, reflects gradual changes in movement planning rather than online within-vowel corrections. In fact, neither of the experimental conditions affected the extent of within-vowel corrections as compared with the same participants’ Control condition. As it is theoretically possible for DI to increase even in the absence of an increase in variability (e.g., if a participant moved their formants further from the pre-test median but always to the same location in acoustic F1F2 space), we followed up by determining the size of the area in acoustic space covered by each participants’ productions. This analysis confirmed that during the early stages of exposure to Attenuated variability feedback, most—but not all—participants did actually increase the overall spread of their productions in the two-dimensional acoustic space (i.e., increased formant production variability; results in Figure 6).

It is not straightforward to compare this finding of active variability regulation with those from prior limb motor control studies that magnified and/or attenuated the dispersion of feedback across trials as a by-product of manipulating the magnitude of target error in each trial. The study by Wong et al. (2009) only increased the size of perceived target errors (and thus feedback dispersion), and, consequently, one cannot necessarily attribute the resulting decrease in motor variability to the magnified feedback variability as opposed to a control strategy that seeks to avoid large errors on each trial individually. The study by van Beers (2009) did implement both magnified and attenuated target errors, but focused on the temporal structure of movement endpoint adjustments across trials (see below Section “Temporal Structure”). Nevertheless, for reaching movements with unperturbed visual feedback, van Beers (2009) reported that trial-to-trial adjustments are made in such a way that movement variability is minimized.

Our data from speech articulation are not consistent with the idea that the central nervous system generally aims to minimize variability. In fact, these data suggest a strikingly different situation: when the feedback perturbation magnified inter-trial formant variability, this extended variability was tolerated and not opposed, but when the perturbation attenuated inter-trial formant variability, articulation was gradually adjusted such that the acoustic output counteracted the perturbation. Thus, overall, the present data are consistent with the interpretation that a sufficiently large level of feedback variability is desirable, and that this level of variability is actively regulated through adjustments in motor planning.

In light of this overall support for the hypothesis that variability is actively regulated, it is reasonable to wonder why the increase in production variability in the Attenuated condition was not statistically significant in some of the later stages of the task. As shown in Figure 4, the increase in DI_initial relative to stage 1 was significant in stages 2 and 3 but not in stages 4 and 5 (in both cases p = 0.076 with medium effect sizes). Closer inspection reveals that, at Stage 4, the mean DI_initial value had further increased, but the standard error of the mean was also larger at this stage. At Stage 5, the mean DI_initial value did decrease, but it never returned to its original value from stage 1. As shown in Figure 5, the increase in DI_mid relative to stage 1 was still statistically significant in the last stage of the task, only not in the preceding Stage 4 (p = 0.078, medium effect size). Thus, there was a trend for the increased production variability to be not sustained at its maximum level in the later stages of the task, but any attempts at interpreting the specific results for Stage 4 would be purely speculative.

It should also be acknowledged that an alternative explanation might be offered for the absence of formant variability regulation in the Magnified condition of our Variability task. Specifically, one could argue that the highly practiced speech movements may have been performed with minimized variability from the very beginning of the task, and that, therefore, a floor effect prevented further reduction of this variability in the Magnified condition. This would be a reasonable argument as the lower bound of variability seems to be physiologically constrained by the stochastic nature of events in the peripheral motor system such as synaptic transmission (Calvin and Stevens, 1968) and muscle contraction (Clamann, 1969; Hamilton et al., 2004), which together are referred to as execution or performance noise in theoretical models of motor control (Van Beers et al., 2004; Cheng and Sabes, 2006; van Beers, 2009; Dhawale et al., 2017; van der Vliet et al., 2018). Only a separate component of motor variability, namely, planning or state noise (Cheng and Sabes, 2006; van Beers, 2009), may be subject to regulation by the central nervous system (Wu et al., 2014; Dhawale et al., 2017, 2019). Total system noise always comprises both execution and planning noise, and, thus, cannot be regulated to a level lower than that of the execution noise itself. In fact, work on limb motor control has estimated the planning noise to be substantially smaller than the execution noise, the former accounting for only about 20∼30% of total motor variability (Cheng and Sabes, 2007; van Beers, 2009; van der Vliet et al., 2018).

However, the argument that the central nervous system does control speech movements in such a way that total system noise is minimized is not compatible with our results from the Attenuated condition. There would be no reason to implement adjustments in the direction of more variability in this condition if the controller seeks to minimize total system noise (given that the Attenuated feedback signal indicates a variability level that is minimized even below the presumed lower bound in typical speech). Consequently, our results from the two conditions taken together support the aforementioned interpretation that, at least for speech articulation, a certain non-minimal level of feedback variability is desirable and actively maintained, possibly in function of providing sensorimotor exploration (Wu et al., 2014; Dhawale et al., 2017, 2019). Moreover, this conclusion implies that the speech motor control system not only calculates and keeps track of distribution features for key aspects of the auditory feedback signal (e.g., dispersion measures such as variance of the formant frequencies), but also compares these features with the expected distributions and then updates future movement planning accordingly (Parrell and Houde, 2019). If our findings are replicated in future studies, computational and conceptual models of speech motor control will need to start incorporating such more complex feedback mechanisms, analogous to suggestions that have been made in the non-speech motor control literature (e.g., Herzfeld et al., 2014; Dhawale et al., 2019).

If articulatory adjustments in the Attenuated condition of the Variability task relied on error-based learning mechanisms similar to those driving auditory-motor adaptation with predictable formant perturbations (Houde and Jordan, 1998; Daliri and Dittman, 2019), then the temporal structure of adjustments across trials—such as indexed by the lag 1 autocorrelation [ACF(1)] of the overall sequence of productions—would be expected to vary depending on the feedback manipulation (van Beers, 2009). It should be noted at this time that the authors of one previous publication on variability in formant production suggested that their ACF(1) results indicated trial-to-trial adjustments even for speech produced without any auditory perturbation (Sitek et al., 2013). However, the lag 1 autocorrelation of –0.47 in that study was calculated based on differences between pairs of successive trials, thus introducing the problem of overdifferencing that we have discussed above in the Introduction (recall that after differencing even a white noise time series has a lag 1 autocorrelation of –0.5). With regard to the specific perturbation-related questions investigated in the present study, our results (illustrated in Figure 7) showed no statistically significant difference in ACF(1) for the sequences of trials produced in the conditions with Attenuated or Magnified formant feedback variability versus the Control condition with unaltered auditory feedback.

The lack of significant difference in ACF(1) between the Control and experimental conditions (Attenuated and Magnified) is not consistent with work by van Beers (2009). In the latter study, comparisons with a Control condition showed that ACF(1) decreased in a Magnified condition and increased in an Attenuated condition, in keeping with the prediction of a state-space model of adaptive learning based on sensory feedback (Cheng and Sabes, 2006). In fact, in our own study, most of the ACF(1) values for the sequences of productions fell within the 95% confidence interval of a white noise process, suggesting no feedback-based learning. One possible interpretation is of course that the speech control system simply does not modify productions based on auditory feedback from the immediately preceding trial. Although this control system clearly shows adaptation to predictable auditory perturbations (Houde and Jordan, 1998; Villacorta et al., 2007; Shiller et al., 2020), it is possible that such learning mechanisms are inactive in the absence of consistently maintained predictable perturbations (cf. Gonzalez Castro et al., 2014; Herzfeld et al., 2014). However, the statistically significant increase in formant production variability in the Attenuated condition does indicate a previously undocumented form of adaptive learning process during this Variability task.

We therefore speculate that the employed ACF(1) analysis may fail to capture the specific form of feedback-based learning in the Variability task. Several observations support this hypothesis. First, the state-space model of motor control predicts that when the parameter of error sensitivity (also known as adaptation rate) is very low, the ACF(1) of the trial sequence for each of the feedback manipulations implemented in the current experiment would be small, and the trial sequence would resemble a white noise process (van Beers, 2009; van der Vliet et al., 2018). It has been estimated recently that, in comparison with limb motor control studies which generally reported error sensitivity in the range of 30–50% (Baddeley et al., 2003; Cheng and Sabes, 2007; van Beers, 2009; van der Kooij et al., 2015), the error sensitivity for speech auditory-motor adaptation is, on average, as small as 4.8% (Daliri and Dittman, 2019). Second, it is known from previous studies that adaptive learning in speech production can differ between different vowels and words, and a given participant may even adapt for one vowel but follow the perturbation for another vowel (Houde and Jordan, 1998; Max and Maffett, 2015). In the current study’s Variability task, three different target words (“talk,” “tech,” “tuck”) were produced in pseudo-random order. Feedback-based learning under such circumstances may be very complex (e.g., How much does feedback from a trial of “tech” affect the production of “talk”? What is the influence of some trials being preceded by the same word and other trials by a different word?), especially if the history of feedback prior to the last trial is also taken into account (Herzfeld et al., 2014). Such complexity is not captured by the simple ACF(1) index. Third, the statistically significant change in formant production variability during the Attenuated condition of the Variability task indicates that the production sequence may be non-stationary, which renders ACF(1) difficult to interpret. Unfortunately, despite these various disadvantages of ACF(1), it is unclear which alternative measurements may be used to reveal the temporal structure of feedback-based adaptive learning in conditions with altered formant feedback variability.

Immediately after having been exposed to Attenuated or Magnified formant feedback variability, participants completed a conventional speech auditory-motor adaptation task with a predictable upward shift of all formants. This Adaptation task allowed us to assess the potential effect of prior formant feedback variability on formant production learning. If sensorimotor learning is affected by the extent of perceived inter-trial variability (Herzfeld et al., 2014; Wu et al., 2014), then participants’ formant adaptation profiles can be expected to differ after experiencing Attenuated versus Magnified formant feedback variability. On the other hand, if inter-trial variability has no effect on the mechanisms underlying adaptive learning (van der Kooij et al., 2015), then participants’ formant adaptation profiles can be expected to remain unchanged between conditions.

Results shown in Figures 8, 9 indicate that three different measures of formant adaptation—early adaptation extent, early adaptation rate, and final adaptation extent—were all statistically indistinguishable between the Control condition and the two experimental conditions (Magnified or Attenuated feedback variability). In other words, the prior manipulation of formant feedback variability, or the participants’ motor adjustments to this manipulation, had no effect at all on the subsequent formant shift adaptation task. This result aligns with the conclusion of van der Kooij et al. (2015) who conducted a series of visuomotor rotation reach experiments with magnified or attenuated visual feedback errors. Although those authors observed behavioral differences across the feedback manipulation conditions, state-space model estimates of the underlying learning mechanism remained unchanged. In the current study, even the behavioral measures showed no differences at all in each group’s comparison of formant adaptation after the control versus experimental condition of the Variability task. Hence, our results for speech articulation suggest no direct relationship between formant variability perceived in a preceding task and the adaptive learning of formant output adjustments when subsequently exposed to a persistent formant perturbation.

The absence of an effect of formant feedback variability on formant production adaptation may relate to the aforementioned low error-sensitivity parameter in speech auditory-motor adaptation (Daliri and Dittman, 2019). Of course, it is also possible that this outcome is entirely specific to certain methodological aspects of our study. For example, we only implemented a relatively short-term feedback variability manipulation (75 trials), and examined formant-shift adaptation in a subsequent task. Future studies should also address the effect of longer-term variability manipulations and variability manipulations implemented during the auditory-motor adaptation task itself. Moreover, it might prove fruitful to develop methodological approaches that are able to dissociate the effects of manipulations that alter sensory variability (as implemented here) versus direct manipulations of motor variability (which alter both motor and sensory variability).