Not crazy after all these years? Perceptual grounding for long-distance vowel harmony

Long-distance (or ‘transparent’) vowel harmony systems have frequently been considered ‘unnatural’ and analyzed as ‘crazy rules’ (Bach & Harms, 1972) because they violate the principle of strict locality. Articulatory explanations for the phonetic grounding of vowel harmony are unable to extend to non-local processes, and attempts to re-analyze cases of transparent harmony as strictly local have been largely unsuccessful. In this paper, I present experimental evidence suggesting that vowel harmony may be perceptually (as well as articulatorily) grounded, and that this source of phonetic grounding does in fact extend to long-distance as well as local harmony. In a series of four experiments, subjects were presented with a nonsense word followed by an isolated vowel, and asked to report whether the isolated vowel had occurred in the preceding word. Subjects were consistently faster and more accurate in nonsense words which exhibited vowel harmony along the relevant feature dimension, regardless of locality. A fourth experiment included a task requiring subjects to identify whether the vowel occurred in a specific syllable, and here too they showed better performance on items with vowel harmony along the relevant feature dimension. I argue that strict locality is not a necessary component of a phonetically grounded theory of vowel harmony, suggesting that long-distance harmony can be analyzed as an explicitly non-local process without abandoning phonetic grounding.


Introduction
Vowel harmony-the requirement that all vowels within a prosodic or morphological domain must agree with respect to some feature-is commonly cited as an example of a 'phonetically grounded' or 'natural' process (see in particular Archangeli & Pulleyblank, 1994;Ohala, 1994). There is no general consensus regarding the precise criteria against which a process can be judged to be natural, but there is broad agreement that phonetically grounded processes either confer some advantage (usually to the speaker, in the form of reduced articulatory effort) or arise through sound changes that are plausibly attributable to channel bias in generational transmission.
Harmony processes are typically considered natural because their prevalence is attributable to articulatory factors: Assimilation reduces the number of articulatory gestures necessary to execute a phonological form. For example, harmony along the Front/Back dimension in Finnish (1) means that only a single fronting or backing gesture is required for the entire word.
(1) Finnish: Front/Back Harmony (Local) a. pøytae-nae 'table-ess' *pøytae-na b. pouta-na 'fine weather-ess' *pouta-nae This assumption has been implicit in much of the literature on vowel harmony (Archangeli & Pulleyblank, 1994;Bakovic, 2000;Gafos, 1999;Ni Chiosain & Padgett, 2001, and others), but see e.g., Boersma (1998); Riggle (1999) for explicit analyses based on articulatory ease. Another perspective on the same source of explanation can be found in Evolutionary Phonology (Blevins, 2004;Ohala, 1994, and others), where the genesis of harmony is attributed to listeners' misinterpretation of gradient coarticulation as categorical assimilation. An explanation of harmony as an articulatorily grounded process necessarily entails a commitment to the principle of strict locality: An inviolable restriction which limits phonological dependencies to adjacent segments. This follows from articulatory grounding because assimilation only reduces gestural transitions among articulatorily adjacent segments, so agreement among distant segments (without assimilation of intervenors) provides no articulatory advantage. Likewise, gradient vowel-to-vowel coarticulation is a local phenomenon, so the effects it introduces should also be local.
Strict locality is an attractive principle, and has enjoyed a privileged analytical status in phonological theory. Recent work, however, has questioned its axiomatic status, showing that there are in fact instances where harmony results in non-adjacent dependencies-as in Finnish (2), where harmony takes place across 'neutral' vowels [i] and [e] (see Section 2.1 for further discussion of non-adjacent dependencies). Consequently, a number of different approaches to harmony have adopted explicitly non-local representations: See in particular Agreement by Correspondence (Hansson, 2001;Rose & Walker, 2004;Rhodes, 2012, and others) and Trigger Competition (Kimper, 2011) for theoretical developments in this area.
(2) Finnish: Front/Back Harmony (Non-Local) a. puhe-han 'speech-emph' *puhe-haen b. tsaari-na 'car-ess' *tsaari-nae This creates something of an impasse. The existence of non-local dependencies in harmony seems to be at odds with phonetic grounding, which requires strict locality. One analytical strategy to resolve the impasse has been to introduce theoretical machinery which produces surface non-locality via strictly local phonological operations, either through derivational opacity or tier-or contrast-based definitions of locality (Clements, 1977;Kiparsky, 1981, and others). These approaches, however, ultimately lose contact with the phonetic grounding that motivates the strict locality they seek to maintain, and still fall short of full empirical coverage. See Section 2.1 for further discussion. It is possible, of course, to abandon phonetic grounding entirely: That is, to treat nonlocal harmony as a 'crazy rule' (Bach & Harms, 1972), an accident of diachrony in which a sequence of separate phonetically motivated sound changes has resulted in an unnatural synchronic alternation. However, non-local harmony is robustly typologically attested across a genetically diverse range of languages and with a number of different features; 1 treating it as aberrant misses important generalizations about the nature of harmony itself.
However, if non-locality in harmony is to be reconciled with phonetic grounding, the first requirement is a plausible source of grounding which does not depend on strict locality. In this paper, I argue that it may in fact be possible to maintain both phonetic grounding and explicitly non-local representations. I present experimental evidence demonstrating that harmony confers a perceptual advantage, even when it is non-local. The paper is organized as follows. Section 2 provides a discussion of the empirical difficulties faced by strict locality, as well as an overview of previous work discussing perceptual approaches to vowel harmony; Sections 3-7 present a series of experiments designed to probe the perceptual effects of harmony among both adjacent and non-adjacent vowels; and Section 8 discusses potential connections between the perceptual asymmetries found in those experiments and phonetically grounded theories of phonology.

Against strict locality
In this context, the strict in strict locality refers to its inviolability. This applies both to the set of possible phonological representations-e.g., the "no line crossing constraint" in autosegmental phonology (Goldsmith, 1976), or Archangeli and Pulleyblank's (1994) "precedence principle"-and to the possible computations performed on those representations, preventing e.g., con in Optimality Theory (Prince & Smolensky, 2004) from containing constraints which assign violation marks in ways that involve dependencies between non-adjacent segments.
There are a number of ways to define adjacency for the purpose of assessing strict locality. The definition most closely tied to phonetic grounding-articulatory adjacency (Gafos, 1998)-serves as a useful starting point for the discussion. According to this definition of locality, vowel harmony is free to disregard consonants, since vowel gestures overlap articulatorily regardless of intervening consonants. It should not, however, apply across intervening vowels.
A number of potential examples of long-distance harmony can be understood as still maintaining strict articulatory locality. In Kinande tongue root harmony, the [-atr] vowel [a] lacks a contrastive [+atr] counterpart; it has been described as transparent, allowing harmony to take place across it (Schlindwein, 1987). However, Gick et al. (2006) provide ultrasound evidence showing that [a] in Kinande covertly undergoes tongue root harmony and surfaces as [ʌ] in [+atr] harmonic domains. Additionally, Gafos (1998) notes that, in apparent cases of long-distance consonant harmony, coronal features like anteriority can be manifested articulatorily on intervening vowels and non-coronals without interfering with their realization. Both of these seemingly long-distance processes, then, can credibly be interpreted as articulatorily local.
However, while some cases may yield to reanalysis, a strong case can be made that this version of strict locality is not empirically tenable. One well-studied case of harmony resulting in non-adjacent surface dependencies is Hungarian palatal harmony (Vago, 1976;Kiparsky, 1981;Hayes & Londe, 2006;Hayes et al., 2009, and many others), which may apply across certain intervening vowels. The data in (3) illustrate the general process; suffix vowels alternate to agree with the stem, with front stems selecting a front suffix vowel and back stems selecting a back suffix vowel. (3) Hungarian: Suffix vowels agree with back/front stems a. hɔd hɔd-nɔk 'army (-dat)' b. kuːt kuːt-nɔk 'well (-dat)' c. toek toek-nεk 'pumpkin (-dat)' d. fyst fyst-nεk 'smoke (-dat)' The non-low, front, unrounded vowels [i] and [e] have no back counterparts in the inventory, and do not alternate in harmony. When these vowels intervene between Kimper: Not crazy after all these years? Perceptual grounding for long-distance vowel harmony Art. 19,page 4 of 37 another stem vowel and a suffix vowel, they behave as transparent: They are skipped over by harmony, and the suffix vowel is determined by the preceding stem vowel. This is illustrated in (4).
(4) Hungarian: High front [i,i:] is transparent a. ɡumi ɡumi-nɔk 'rubber (-dat)' (*ɡumi-nεk) b. pɔpiːr pɔpiːr-nɔk 'paper (-dat)' (*pɔpiːr-nεk) While phonemic descriptions of the relevant data are not in dispute, the actual transparency of these intervening vowels should not be taken for granted from these descriptions: [i] and [e] lack contrastive back counterparts, and it's conceivable that they could be realized as something closer to [ɯ] and [ɤ] in back harmonic domains. Can a case be made that Hungarian, like Kinande, does not involve true transparency? Benus and Gafos (2007); Benus (2005) provide articulatory data (electromagnetic articulography and ultrasound) which suggest that front [i] and [e] are realized with less extreme articulatory gestures in a back-harmonic context-however, their results show that these segments are still articulatorily front. This is consistent with acoustic evidence from similar transparent vowels in Finnish (Gordon, 1999). Likewise, consonant harmony processes cannot all be explained by appealing to gestural locality. See Hansson (2001) for a discussion of a broader range of harmony processes than is addressed by Gafos (1998), and see Gallagher (2010) for a careful acoustic analysis demonstrating the non-locality of laryngeal co-occurrence restrictions in Quechua.
Benus and Gafos argue that the gradient coarticulation seen in Hungarian is sufficient to predict the backness of a following suffix vowel. In their analysis, long-distance harmony consists of two processes: One where a back vowel triggers gradient retraction on a following front vowel (in particular [i] and [e], which are not able to surface as fully back), and one where a slightly retracted front vowel triggers categorical backness on a following vowel. It is this latter process, needed to maintain strict locality, which loses touch with the phonetic grounding it seeks to preserve. What's missing from this account is an explanation of how following a slightly retracted front vowel with a categorically back vowel constitutes an articulatory improvement over following it with another categorically front vowel. Szeredi (2012) also provides experimental evidence that the size of the effect that Benus and Gafos found falls below the 'just noticeable difference' threshold, meaning that Hungarian speakers are not able to meaningfully perceive or make use of this level of acoustic detail.
Furthermore, Kimper (2011) notes that splitting long-distance harmony into separate processes in this way is typologically undesirable, since they would then be predicted to occur independently. This means that a front vowel which is gradiently retracted for reasons having nothing to do with vowel harmony-the coarticulatory effects of a uvular consonant, for example-could potentially trigger categorical backness on a following vowel. To my knowledge, no language exists which instantiates this predicted pattern.
Articulatory adjacency is not, of course, the only way of defining locality, and rejection of the principle on the basis of the most stringent proposal alone would constitute an argument against a straw man. However, as we will see, adopting alternative definitions of adjacency does not particularly improve the situation.
One common approach is to assess adjacency in terms of phonological tiers, usually based on contrastive features (Kiparsky, 1981, and others). 2 Dependent segments must be adjacent on their tier, and material that is not part of that tier is disregarded. In Kiparsky's (1981) analysis of Hungarian, for example, the relevant tier consists of those segments which are contrastively specified for [±back]; because [i] and [e] lack back counterparts, and their feature value is fully predictable, they are unspecified. Since unspecified segments are not part of the relevant tier, they can be skipped: No association lines are crossed, and these representations do not run afoul of strict locality.
The central predictions of this approach are that (a) only unspecified segments can be skipped, and (b) specified segments which do not undergo harmony will necessarily block it. However, Kimper (2013) notes that there are exceptions to both of these generalizations. In Khalkha Mongolian (Kaun, 1995) (Pulleyblank, 1996). Regardless of how phonological contrast is determined, Ifẹ and Ọyọ should behave identically; the fact that one dialect exhibits transparency and the other exhibits opacity suggests that defining locality in terms of feature tiers is unsuccessful.
An alternative approach attempts to maintain strict locality (at least at the phonological level) by appealing to derivational opacity. 3 Transparent segments first undergo strictly local harmony, and subsequent neutralization reverts their feature specification, resulting in disharmony (Clements, 1977;Walker, 1998;Bakovic, 2000). This falls victim to the same problems as contrast-based approaches-because a derivationally opaque analysis of non-locality requires a process of absolute neutralization, only segments which do not contrast for the spreading feature can be transparent. As we have just seen, this is not the case.
It seems, then, that the empirical predictions of strict locality are not borne out: Segments which are non-adjacent, however adjacency is defined, may nonetheless exhibit phonological dependency in vowel harmony. This is, of course, not to suggest that locality plays no role in phonological processes; the choice here is not between strict locality and 'anything goes.' While non-local vowel harmony does exist, it is subject to an implicational hierarchy: Any language with non-local vowel harmony also has local harmony, but not vice versa, and local harmony is more typologically frequent. A successful locality restriction, then, will need to predict that locality is preferred, but violable; a number of current proposals, including Agreement by Correspondence (Hansson, 2001;Rose & Walker, 2004) and Trigger Competition (Kimper, 2011), build this into phonological theory. It may also be possible to attribute a preference for locality to processes that occur in learning, for example an attentional bias privileging adjacent dependencies.
The central question at issue in this paper is whether the arguments against strict locality also constitute an argument against phonetic grounding: Does a representational system that can encode non-local harmony necessarily divorce itself from the phonetic precursors to or motivations for local harmony? The following section discusses the potential role of perceptual (rather than exclusively articulatory) grounding factors in harmony, which are not necessarily limited to strictly local application.

Perceptual grounding for harmony
The idea that harmony might be beneficial to listeners is not novel. Suomi (1983) proposes that palatal harmony is a way of facilitating the perception of F2 contrasts, as it renders feature values predictable outside of psycholinguistically prominent positions (in his examples, initial syllables). Kaun (1995), building on Suomi's (1983) proposal, argues that extending the duration of realization of a particular feature (by realizing it across multiple segments) provides the listener with greater opportunity to correctly identify that feature value. Kaun builds on an argument from Steriade (1995a), who suggests that positional neutralization processes affecting vowels serve to provide the listener with more robust cues to vowel contrast. Limiting contrasts to prosodic positions with greater duration gives speakers better opportunity to hit the relevant articulatory target, resulting in more robust cues across a longer time-span for the listener. Similarly, Walker (2005) argues that harmony targeting prominent positions (in her examples, stressed syllables) can serve as a form of feature licensing. Gallagher (2010) discusses the perceptual advantages of harmony in terms of maximizing the distinctness of lexical items, drawing connections to Dispersion Theory (Flemming, 1995(Flemming, , 2004(Flemming, , 2006. She argues that assimilatory co-occurrence restrictions on laryngeal features are driven by a pressure for roots to be as discriminable as possible: In a language with laryngeal agreement, words with different feature specifications will consistently differ with respect to that feature on all relevant segments. Since words with multiple segmental differences are more perceptually distinct from one another than words which differ by single segments, maximizing differences by means of assimilation aids in perception. Gallagher supports this claim experimentally, presenting results of several discrimination studies in which subjects made same/different judgements about pairs of CVCV nonce words. Subjects were more accurate when the pairs differed with respect to the laryngeal features of both consonants than when they differed by the features of only one consonant. Kimper (2013) presents results of a similar study, using vocalic tongue root contrasts rather than consonantal laryngeal contrasts. Subjects were faster and more accurate when discriminating between words which differed by both vowels than words which differed by only a single vowel.
In both Gallagher's (2010) and Kimper's (2013) studies, however, dissimilation was also found to be advantageous; dissimilation is, after all, another way of ensuring that words consistently exhibit multiple differences for a particular feature contrast. This mirrors typological patterns for consonantal features, where dissimilatory co-occurrence restrictions are robustly attested; vowel dissimilation is, however, extremely rare. 4 Differences between long-distance consonantal and vocalic assimilation/dissimilation processes are beyond the scope of the present study; however, it is important to investigate whether assimilation presents a perceptual advantage that is distinct from the 'number of differences' effects found in the discrimination studies discussed above.
The experiments that follow aim to address the question of the perceptual advantage of harmony directly by using a modified identification task. Subjects hear a nonsense word, and are subsequently asked to identify whether a particular vowel occurred in that nonsense word. It is hoped that this task, rather than involving a general assessment of distinctness or difference between two perceived stimuli, will probe more specific aspects of the mapping between an incoming signal and the corresponding abstract features or segmental categories.

Experiment 1
The primary aim of Experiment 1 is to investigate whether or not harmony confers a perceptual advantage, and (if so) the extent to which that advantage is locally restricted. If harmony is perceptually advantageous, subjects should be faster and more accurate in identifying whether or not a nonsense word contains a particular target vowel if the nonsense word contains another vowel which shares phonological features with that target. If this advantage is not strictly local, the effect should be found even when the target and 'supporting' vowel are non-adjacent. The net has been cast somewhat broadly here; there are a number of possible forms that a perceptual advantage could take, more than one of which would result in performance differences in the tasks in this (and subsequent) experiments. Further discussion can be found in Section 8.2.
This second hypothesis-that harmony is perceptually advantageous even among nonadjacent segments-is of primary interest because the articulation-only approach to phonetic grounding, which entails commitment to strict locality, can offer no principled explanation of its robust typological attestation. However, there is also an opportunity to examine the potential perceptual basis for other typological asymmetries; in particular, the tendency for harmony to be facilitated among already-similar segments (parasitic harmony; see e.g., Cole & Trigo, 1988;Cole & Kisseberth, 1994;Kaun, 1995). It was also possible to conduct some post-hoc investigation into the relationship between perception and the tendency for particular feature values (in this case [+round]) to be phonologically active in harmony processes (Steriade, 1995b, and others). Both of these tendencies have alternative explanations, either in terms of articulation or in terms of formal representation, but may also be bolstered by perceptual factors. These predictions involve interactions: If similarity-sensitivity in harmony is perceptually grounded, the advantage of harmony should be greater among already-similar vowels; if the phonological activity of [+round] is perceptually grounded, the advantage of harmony should be greater when the target is round.
The results from this experiment show that all four predictions are borne out: Subjects were faster and more accurate in identifying target vowels in harmonic words, even when harmony was non-adjacent. This effect was greater with harmony among already-similar vowels, and greater for trials where the target was round.

Subjects
The data analyzed for this study came from 33 native speakers of North American English (students in introductory linguistics courses at the University of Massachusetts, Amherst who received course credit for their participation). Subjects who took part in the study were excluded from analysis if they reported speech or hearing disorders, were not native speakers, or registered no response on more than 10% of trials. In addition to the 33 subjects who met the criteria for inclusion, 7 subjects participated for course credit but were excluded (4 non-native speakers and 3 insufficient responders). 5 Native speakers of English were chosen for this study, as in Gallagher's (2010) and Kimper's (2013) studies (discussed in Section 2.2 above), precisely because there is no process of vowel harmony in English. Hypotheses about sources of phonetic grounding are by necessity independent of language-particular learned dependencies, and the effect should therefore be present in naïve listeners. This means that native language phonotactic legality is held constant across experimental conditions, 6 elimiting this potential confound.

Stimuli
Stimuli consisted of trisyllabic (CVCVCV) nonsense words, as well as target vowels uttered in isolation. The consonants {h g k} were chosen for the nonsense words because of their low coarticulatory effect; target vowels were given a [ʔ] onset. Each CV syllable was recorded separately, in a neutral frame sentence, read by a phonetically trained native speaker of North American English in a sound-attenuated booth. Using Praat (Boersma & Weenink, 2008), these syllables were equalized for F 0 (221 Hz), intensity (approx. 80 dB), consonant duration (60 ms), and vowel duration (250 ms) before being spliced together to form the nonsense words. This equalization meant that the stimuli sounded somewhat robotic; prior to the experiment, several native speakers listened to samples of the stimuli and reported that they nonetheless sounded like speech. There was no formal debriefing following the experimental task, but in informal debriefing subjects indicated that the stimuli sounded like speech.
For this experiment, only [i] and [u] were used as target vowels. The intention here is for subjects' judgements to reflect the feature dimension relevant to harmony: In other words, for errors to indicate a failure to identify the back/rounding feature that is spreading, in order to examine the effect that harmony has on the recognition of that feature. The vowels {i e a o u} were used to form the nonsense words; a list of the vowel combinations is given in Table 1. Every word contained the low back vowel [a]; this is meant to stand in for non-contrastive transparent vowels found in many non-local harmony systems. 7 Among the remaining vowels, adjacency and agreement for colour 8 and height features were fully crossed.
In the local conditions, the colour-contrastive vowels were adjacent to each other (followed by [a]); in the non-local conditions, [a] intervened. The order in which the colour-contrastive vowels appeared, and whether they were of the same or different height, was counterbalanced. Of the words with vowels of the same height, only those with [i] or [u] were used (words with only [e] and [o] were excluded, because they contained neither of the target vowels). This resulted in 24 different vowel sequences; each appeared with every possible order of the onset consonants {h g k}, resulting in 144 items total.
6 The stimuli used violate English phonotactics by lacking stress cues-which would normally include reduction of unstressed vowels-but this is true across all experimental conditions. 7 It's worth noting here that low vowels are typologically dispreferred as transparent vowels; Finley (2015) found better learning of harmony systems with transparent [i] than with transparent [a], and Kimper (2011) points out that languages with multiple transparent vowels exhibit an implicational relationship between low and high transparent vowels. Since the goal here is to determine whether the perceptual benefits of harmony extend to non-local arrangements, the use of [a] represents in some sense a useful worst-case-scenario for examining that prediction. 8 Here and throughout this paper I use 'colour' as a way of grouping rounding and backness, since the two cannot be clearly distinguished in this task. While this term is borrowed from feature geometry, no specific theoretical commitments accompany its present use.
Kimper: Not crazy after all these years? Perceptual grounding for long-distance vowel harmony Art. 19, page 9 of 37

Task
A nonsense word was presented auditorily, at a comfortable volume followed by a target vowel (after an ISI of 750 ms). Subjects were asked to indicate by pressing a button whether or not the target vowel had been in the preceding word. They were told that they should answer quickly, and responses were cut off after 1500ms. Stimuli were presented in pseudorandom order using Superlab 4, organized into two blocks of 288 trials each.
Brief within-block breaks were offered every 72 trials, with a longer obligatory break between blocks. Subjects heard each item a total of four times, twice with [i] as the target and twice with [u] as the target. Both the format of the task and the length of the ISI are designed to probe judgements related to category membership rather than acoustic detail (see e.g., Pisoni, 1973;Gerrits & Schouten, 2004). Because subjects listened to the entire word before discovering which target they must identify, the task is sensitive to the effects of vowels that follow the target in the word as well as those which precede it. It is assumed that subjects learned from the early trials that [i] and [u] were the two possible targets; responses are taken then to be indicative of identification of the features that mark the difference between the two, namely backness and rounding.

Results
Mixed effects models (with random intercept for subject, and random slope for subject × colour harmony) were fitted to the results by adding relevant factors and their interactions one at a time until there was no further improvement in model fit. 9 Linear models were fitted for response time; 10 logit models were fitted on correct responses. 11 Deviation contrast coding was used throughout; models are given in Table 2. Where simple effects are reported, these are the result of re-running models with the relevant subsets of the data. 12 9 Mixed effects were calculated using the lme4 package (version 1.1.7, Bates et al., 2014) in R (version 3.1.2, R Core Team, 2014). For linear mixed effects models, p-values were supplied by the lmerTest package (version 2.0.11, Kuznetsova et al., 2014) and coefficients and standard errors used in graphs were retrieved from the fitted models using the effects package (version 3.0.1, Fox, 2003). Here and throughout, nonsignificant effects which nonetheless improved model fit are reported in model tables, while non-significant effects which did not improve model fit are omitted. 10 Here and throughout, response times are measured from the stimulus offset. 11 Proportion correct was chosen as the relevant measure of accuracy rather than detection-theoretic measures like d' (Macmillan & Creelman, 2004) because certain experimental conditions consisted of only 'signal' trials; in particular, same-height colour-disharmonic words necessarily contained both targets. Because of the absence of 'noise' trials in these conditions, calculation of d' would require pooling of conditions in a way that would preclude the relevant comparisons. 12 Reported p-values are uncorrected, but correcting for familywise error in planned simple effects does not result in a qualitative change in interpretation.  Figure 1 shows that subjects were faster (p < 0.001) and more accurate (p < 0.001) with stimuli whose contrastive vowels were harmonic for colour features than those whose contrastive vowels were disharmonic: For example, [u] was better identified in hugoka than in hugeka. For response time, there was a significant interaction with locality (p < 0.01)-the difference between hugoka and hugeka was greater than the difference between hugako and hugake-but subjects were faster on harmonic items in both local (p < 0.001) and non-local (p < 0.001) conditions. For accuracy, there was no significant interaction between harmony and locality. On both measures, subjects performed better in non-local conditions across the board; this appears to be an artifact of timing in the task (see Sections 3.3 and 6.3 for further discussion). Figure 2 shows the interaction between colour harmony and height agreement. For both response time (p < 0.001) and accuracy (p < 0.001), there was a significant interaction-the effect of harmony was greater when accompanied by height agreement (i.e., the difference between huguka and hugika was greater than the difference between hugoka and hugeka). For both response time and accuracy, the effect of harmony was still significant for both height-agreeing (p < 0.001) and height-disagreeing (p < 0.001) items. Additionally, subjects were faster overall (p < 0.001) on items where the colourcontrastive vowels agreed in height than those where they disagreed, though the main effect for height agreement was marginal (p = 0.096) for accuracy. Finally, Figure 3 shows the interaction between harmony and trial type. The effect of harmony was greater in trials where [u] was the target vowel than for [i]-trials, for both response time (p < 0.001) and accuracy (p < 0.001). The effect of harmony remained significant in both [u]-trials (p < 0.001) and [i]-trials (p < 0.001) for both accuracy and response time. Trial type did not interact significantly with any factor besides colour harmony, for either response time or accuracy.

Discussion
The central prediction-that harmony confers a perceptual advantage-is supported by the results of Experiment 1: Subjects did indeed show a performance advantage in words with harmony. Furthermore, this advantage was present even when harmonic vowels were non-adjacent, lending support to the claim that perceptual grounding covers longdistance as well as local instances of harmony. This provides support to the claim that  long-distance harmony is a grounded phenomenon rather than a 'crazy rule,' as it offers a potential source of phonetic grounding.
The interaction between harmony and locality-that is, the finding that the advantage of harmony is somewhat diminished among non-adjacent vowels (which reached significance for response time but not for accuracy)-is consistent with a strong typological preference for local harmony. This finding, while consistent with expectations based on typology, is not crucial: Since perceptual factors are not being pursued as the sole source of grounding for harmony, this result simply adds to the already existing articulatory factors motivating the existence of some form of locality preference. Additionally, the fact that subjects performed better overall, regardless of harmony, in non-local conditions should not be taken as indicative of the superiority of non-adjacency in perception. This is likely due to a difference in temporal proximity between the most recent informative cue and the presentation of the isolated target: By necessity, all words in the non-local condition contained a potentially-informative vowel in final position. Words in the local condition, however, did not, adding an additional latency (the duration of the final [a]) between the last informative cue and the presentation of the isolated target. As locality is of interest here not a priori but specifically in relation to perceptual benefits conferred by harmony, this does not interfere with the main result of this study.
Similarly, the finding that harmony was more advantageous among already similar vowels-those which agreed in height-provides an additional source of explanation for phenomena attributed to Kaun's (1995) gestural uniformity constraint. It should be noted that distinguishing between the role of similarity and the role of complete identity is difficult, and in an experimental design with a relatively scarcely-populated vowel inventory the two are conflated; vowels which agree in height and are colour-harmonic are in fact identical. In this case, then, it should be no surprise that harmony is advantageous in the height-agreement condition: It should of course be easier to detect [u] in a word which contains two instances of that very vowel. It is the height disagreeing conditions that are more informative here: That the task of identifying [u] was easier in a word which also contained [o] suggests that it's not merely the frequency of the target that aids in identification-sub-components of the target (either phonological features or more general phonetic properties) are relevant in the decision that subjects are making.
Finally, the finding that harmony was more advantageous for target [u] than target [i] may provide a source of grounding for the tendency for [+round] to be phonologically Error bars represent 95% Confidence Intervals.
active; indeed, it has been claimed that [-round] is never active, and this has been built into the architecture of phonological feature systems (see e.g., Steriade, 1995b

Experiment 2
Experiment 2 was designed to further investigate the effect of distance on the perceptual advantages of harmony. Experiment 1 found that non-adjacent segments showed a slightly diminished but still robust effect of harmony, suggesting both that long-distance harmony may be phonetically grounded and that a preference for locality is supported by perceptual as well as articulatory asymmetries.
The previous experiment only compared vowels in adjacent and non-adjacent syllables, but natural languages distinguish at least one additional degree of distance. In Hungarian, for example, harmony across a single [i] as in (4) is obligatory; however, if multiple nonundergoers stand between trigger and target, harmony becomes variable (see Londe, 2006 andHayes et al., 2009 for further discussion).
This distinction is difficult to explain in articulatory terms. The number of gestural transitions is the same, regardless of the number of non-undergoers involved, so these situations should be equivalent. Can a perceptual account of phonetic grounding in harmony provide an explanation? Experiment 2 largely replicates the previous design, but with the inclusion of an additional non-local condition with two intervenors, to investigate whether increasing degrees of distance further diminishes the advantage of harmony.
The results suggest that this is in fact the case: The main effect of harmony was replicated robustly, and while the interaction was not significant at one degree of distance, it was significant with two intervenors, suggesting that gradient distance effects in harmony may be grounded in the same perceptual factors that motivate longdistance harmony.

Methods
Data for Experiment 2 come from 38 native speakers of North American English (students in introductory linguistics courses at the University of California, Santa Cruz, who received course credit for their participation). As in the previous study, subjects were excluded from analysis if they reported speech or hearing disorders, were not native speakers, or registered no response on more than 10% of trials. In addition to the 38 subjects who met the criteria for inclusion, 28 subjects participated for course credit but were excluded from analysis (7 reported speech or hearing disorders, 17 non-native speakers, and 4 insufficient responders).
Stimuli consisted of quadrisyllabic (CVCVCVCV) nonsense words, using the same vowel inventory as in Experiment 1. As before, two of the vowels in each word contrasted for colour features, and these either agreed or disagreed with each other. These were either adjacent to each other (preceded or followed by two [a] syllables), separated by one [a] syllable (preceded or followed by another), or separated by two [a] syllables. A full list of vowel combinations can be seen in Table 3. Nonsense words were formed by concatenating the same isolated syllables from Experiment 1, with the addition of [sk] as a possible syllable onset (these were recorded and normalized at the same time and in the same way as the other syllables). Likewise, the target vowels [i] and [u] were the same as those in Experiment 1. Vowel combinations were combined with randomly selected subsets of the possible consonant combinations to create a stimulus set with equal numbers of items across each level of distance, height agreement, and harmony. This resulted in a total of 288 items.
The task and presentation of stimuli were the same as in Experiment 1. Subjects heard a nonsense word followed by a target vowel, and were asked to indicate whether or not the target had been in the preceding word. Subjects heard each nonsense word twice, once with [i] and once with [u]. Trials were distributed across two blocks of 288 trials each, with brief within-block breaks every 72 trials and a longer break between blocks.

Results
As in Experiment 1, mixed effects models were fitted for accuracy and response time (with random intercept for subject, and random slope for subject × colour harmony); here Helmert coding was used for distance, and deviation coding was used for all other factors. The full models can be seen in Table 4. As can be seen in Figure 4, the effects seen in Experiment 1 were, broadly speaking, replicated: Subjects were faster (p < 0.001) and more accurate (p < 0.001) with stimuli whose contrastive vowels were harmonic for colour features; there was a significant interaction with height agreement for both accuracy (p < 0.001) and response time (p < 0.001), with the effect of harmony greater among vowels with height agreement. Trial type also interacted with harmony for both accuracy (p < 0.001) and response time (p < 0.01), with [u]-trials showing a greater effect of harmony.
The three-way interaction between height agreement, distance, and colour harmony was significant for accuracy (p < 0.05) and response time (p < 0.05) at a distance of two syllables, but not at a distance of one syllable. For items where colour-contrastive vowels disagreed in height (e.g., skuhogaka vs. skuhegaka) colour harmony had a significant main effect for both accuracy (p < 0.001) and response time (p < 0.01) but no interactions were significant for either measure. For items with height agreement, there was a significant interaction between distance and colour harmony at a distance of two syllables for both accuracy (p < 0.01) and response time (p < 0.05). 13 The effect of harmony was 13 Correction for familywise error in simple effects jeopardizes result for response time, but not accuracy. diminished at this distance-the difference between skuhugaka and skuhigaka was greater than the difference between skuhagaku and skuhagaki-but the effect remains significant for both accuracy (p < 0.001) and response time (p < 0.01). Unlike in Experiment 1, the interaction does not reach significance at a distance of one syllable, but numerical trends are in the expected direction.

Discussion
The main effect from Experiment 1, that harmony confers a perceptual advantage, was replicated in the current experiment. As before, too, this advantage obtained regardless of distance: The effect of harmony was statistically significant, even in the least conducive set of conditions. The prediction at hand in this particular version of the experiment-that the effect of harmony diminished with increasing distance-was borne out, with somewhat of a caveat: The effect was only detectable among identical vowels. As before, harmony had a greater effect in the same-height conditions than in different-height conditions; the small size of the main effect in the different-height conditions may be responsible for the failure of the interaction to reach statistical significance.
Perhaps surprisingly, there was not a significant diminution of the effect of harmony at a distance of one syllable. This is not entirely unexpected, given the mixed results from that interaction from the previous experiment. However, there was a significant diminution of the effect at a distance of two syllables; harmony was less advantageous at this distance. This is consistent with distance effects found in languages like Hungarian.
This result, however, should be interpreted with some caution. The size of the interaction was small, and detectable only among identical vowels. This offers the potential for a perceptual explanation for distance effects, but such an explanation is not the only plausible account; for example, it may very well be the case that biases in learning systematically disadvantage patterns that require associations across increasing distances (see Moreton, 2012;Moreton & Pater, 2012 for more on structural biases in learning).

The previous experiments have used only high vowels [i] and [u] as targets; in this version, additional blocks with mid-vowel [e] and [o]
targets are included. This means that, in addition to investigating the effect of similarity (or identity) on the advantage posed by harmony, it is possible to look more closely at the impact of height itself. In particular, the typology of rounding harmony suggests that mid vowels tend to be preferred as triggers over high vowels; Kaun (1995) argues that this is attributable to the fact that low and mid vowels are less articulatorily and perceptually rounded than their high counterparts (Linker, 1982;Terbeek, 1977). If this is the case, we expect that subjects should perform worse overall when identifying the front/back contrast in mid-vowel blocks than in highvowel blocks.
In addition, inclusion of high-only stimuli in mid-target blocks (and vice versa)-e.g., hogeka in blocks where [i] and [u] are the targets-can help shed light on the extent to which identification is sensitive to either featural or phonetic sub-components of the target segments; this will be further explored in a discussion of error types across all experiments in Section 7.

Methods
Data for Experiment 3 come from 36 native speakers of North American English (students in introductory linguistics courses at the University of California, Santa Cruz, who received course credit for their participation). As in the previous two studies, subjects were excluded from analysis if they reported speech or hearing disorders, were not native speakers, or registered no response on more than 10% of trials. In addition to the 36 subjects who met the criteria for inclusion, 30 subjects participated for course credit but were excluded from analysis (7 reported speech or hearing disorders, 17 non-native speakers, and 6 non-responders).
Stimuli consisted of trisyllabic (CVCVCV) nonsense words, the items from Experiment 1 plus several additional vowel sequences. Local conditions were included where the colourcontrastive vowels appeared following the neutral [a] (cf. Experiment 1, where they always preceded [a]). 14 The full list of vowel combinations used can be seen in Table 5. Each combination was paired with four different consonant sequences, for a total of 136 items.

In addition to target vowels [i] and [u], [e] and [o]
were also used. All material used to create the additional stimuli was recorded at the same time and normalized in the same way as the materials for the previous experiments.
The task and presentation of the stimuli were the same as in the previous experiments. Subjects heard a nonsense word followed by a target vowel, and were asked to indicate whether or not the target had been in the preceding word. Subjects heard each nonsense word a total four times, once with each target vowel. Trials were organized into two blocks of 272 trials each, with brief within-block breaks every 72 trials and a longer break between blocks. Within each block, the height of the target vowels was consistent: [i] and [u] shared a block, with [e] and [o] in a separate block, in order to ensure that the judgement made for each trial primarily represents information about the colour features of the stimulus. The order of the blocks was pseudorandomized for each subject.

Results
For analysis, data from Experiment 3 was divided between block-matched and blockmismatched conditions. Stimuli were block-mismatched if they contained none of the target vowels relevant to a particular block, e.g., stimuli with all high vowels in a midvowel block and vice versa. As mentioned above, this was done to focus more directly on the role of colour harmony on detection of the feature in question: A 'no' response on a trial like hogeka … u reflects a decision about the height of the vowels in the stimulus and may or may not reflect the detection of the relevant back/round feature value. Results for block-matched data are presented here; see Section 7 for a discussion of the blockmismatched data.
As in the previous experiments, mixed effects models were fitted for accuracy and response time (with random intercept for subject, and random slope for subject × colour harmony); deviation contrast coding was used throughout. Full models can be seen in  Table 6. Once again the main effects seen in the preceding experiments were broadly replicated. There was a robust main effect of colour harmony for both accuracy (p < 0.001) and response time (p < 0.001), and significant interactions with height agreement for both accuracy (p < 0.001) and response time (p< 0.05). While the effect of harmony was diminished among stimuli whose colour-contrastive vowels disagreed in height, the effect remained significant for both accuracy (p < 0.01) and response time (p < 0.001). There were no interactions with locality, which departs from the findings of Experiment 1 but is consistent with the results from Experiment 2 (at a distance of one syllable). Unlike in previous experiments, there was no interaction between the colour of the trial ([i] vs. [u] or [e] vs. [o]) and the effect of harmony.
As can be seen in Figure 5, the height of the trials in a block ([i]/[u] blocks vs. [e]/[o] blocks) exhibited a main effect for accuracy (p < 0.001) and response time (p < 0.01), with subjects performing better overall on high stimuli. There was also significant interaction between block height and colour harmony for both accuracy (p < 0.001) and response time (p < 0.05), with the effect of harmony greater in high blocks than in mid blocks. An analysis of just the disharmonic items suggests that the main effect of block type is not driven solely by differences in the benefits of harmony; even with disharmonic words, subjects were somewhat faster (p < 0.05) and more accurate (p < 0.05) in high blocks than in mid blocks. For accuracy there was a three-way interaction with height agreement (p < 0.001)-the increase in the advantage of harmony under height agreement was exaggerated in high blocks, though this interaction was not significant for response time.

Discussion
The results of this experiment again replicate the main result of experiments 1 and 2, which is that harmony confers a perceptual advantage. In addition, findings from the previous experiments-that this advantage still obtains among non-adjacent segments, and is greater among vowels which share other features-were also replicated. This experiment also allows more direct comparison of harmony involving vowels of different height. The first finding here is that subjects performed better across the board in blocks where the targets were high vowels. This provides support for Kaun's (1995) explanation of mid vowels' behaviour as preferential triggers of harmony-subjects' poorer performance in identifying back/round contrasts with mid vowels in this task bolsters the claim that these vowels are in most need of the boost in perceptual salience that comes with harmony. The finding that the advantage of harmony is greater for high vowels than for mid vowels, while it fails to provide any additional support for this line of reasoning, does not necessarily contradict it-while high vowels may stand to gain more from harmony, they have less need for it.

Experiment 4
In the previous three experiments, subjects were tasked with recognizing and recalling the target vowel regardless of its location in the word. In the course of real-world speech perception, however, phoneme/feature recognition is generally localized to specific linear positions. For example, Sanders (2009, 2011) provide evidence from Event-Related Potential (ERP) studies showing that listeners modulate auditory attention over the time-course of speech perception, and that attention is increased in contexts where phonological content is unpredictable.
As discussed in Section 2.2, one of the possible advantages of vowel harmony is that it renders contrasts predictable across a variety of positions-this in turn reduces the burden on listeners' auditory attention. However, predictability is not a unique feature of harmony: Dissimilation provides an equal degree of predictability with no increase in computational complexity. Furthermore, there is no difference in predictability between transparent harmony and articulatorily-preferred opaque harmony. 15 The previous studies suggest that perception of a target vowel is facilitated by the presence of another vowel bearing a relevant feature value; does this effect still obtain in situations more closely resembling the type of attentional modulation required of real-world speech perception? Experiment 4 extends the previous studies to include localized attention, expanding the set of tasks to include attending specifically to initial and final syllables. Initial-syllable identification in particular bears a closer resemblance to the task of speech perception, since initial syllables are psycholinguistically prominent, selectively attended, and license a greater degree of contrast than non-initial syllables (Beckman, 1998)-even in languages where vowel harmony is anticipatory, initial syllables serve as the listener's first cue to the spreading feature value. If harmony represents a true perceptual advantage, this effect should be present in the more realistic task of identifying an initial-syllable vowel.

Methods
Data for Experiment 4 come from 25 native speakers of British English (students in introductory linguistics courses at the University of Manchester who received course credit for their participation). As in the previous studies, subjects were excluded from analysis if they reported speech or hearing disorders, were not native speakers, or registered no response on more than 10% of trials. In addition to the subjects who met the criteria for inclusion, an additional 16 subjects participated for course credit but were excluded from analysis (10 non-native speakers, 1 insufficient responder, and 5 due to data loss resulting from equipment failure). Subjects participated in a sound-attenuated booth in the University of Manchester Psycholinguistics Laboratory; stimuli were presented at a comfortable volume through circumaural headphones, using E-Prime 2.0 Professional (Schneider et al., 2002).
Stimuli were the same as in Experiment 3. As before, subjects heard a nonsense word followed (after an ISI of 750ms) by a vowel in isolation; as in experiments 1 and 2, only [i] and [u] served as the target vowels. Trials were organized into blocks by task, with brief within-block breaks and a longer between-blocks break as in the previous studies. In Any Syllable blocks, subjects were instructed to respond 'yes' if they heard the target vowel anywhere in the nonsense word; in First Syllable blocks, subjects were instructed to respond 'yes' if they heard the target vowel in the first syllable of the nonsense word; in Last Syllable blocks, subjects were instructed to respond 'yes' if they heard the target vowel in the last syllable of the nonsense word. The First Syllable condition is of primary concern; the others are included for reference. Each subject received two blocks; each was selected pseudorandomly from the set of three, sampled with replacement. Each task was distributed equally between Block 1 and in Block 2, though Last Syllable blocks appeared more often than the other two.

Results
As with Experiment 3, data for analysis was divided into block-matched and blockmismatched trials. For Any Syllable blocks, trials were considered block-matched if they contained at least one of the target vowels ([i] and [u]); for First Syllable blocks, trials were considered block-matched if they contained one of the targets in initial position, and for Last Syllable blocks, trials were considered block-matched if they contained one of the targets in final position. Results for block-matched data are presented here, and blockmismatched data are discussed in Section 7.
As in the previous experiments, mixed effects models (with random intercept for subject, and random slope for subject × colour harmony); deviation contrast coding was used throughout. Full models can be seen in Table 7. As in the previous experiments, there was an overall main effect of colour harmony for both accuracy (p < 0.001) and response time (p < 0.001), and a significant interaction between colour harmony and height agreement for both accuracy (p < 0.001) and response time (p < 0.05), with the effect of colour harmony greater for same-height than different-height items. For response time, this was the only statistically significant interaction term-for accuracy, there were also significant interactions for task (p < 0.05) and block (p < 0.05) and a marginal interaction for trial (p = 0.0696). There was also significant main effect of task, for both accuracy (p < 0.001) and response time (p < 0.001).  Figure 6 shows the effect of colour harmony across the three tasks. The Any Syllable blocks repeat the conditions of the previous experiments, and replicate the main effect. In the First Syllable blocks, the effect remains significant for both accuracy (p < 0.01) and response time (p < 0.01). In the Last Syllable blocks, participants were at or close to ceiling across the board; the effect of colour harmony is significant for response time (p < 0.05), but not for accuracy. Figure 7 takes a closer look at the First Syllable blocks, showing the effect of harmony for both same-height and different-height items. For accuracy, we see the combined action of the interactions between colour harmony and height agreement and between colour harmony and task: Different-height items in the First Syllable task are doubly disadvantaged. Regardless, the effect of colour harmony remains significant even in these items (p < 0.05).

Discussion
This experiment again robustly replicated the main result of the previous three. This experiment also provides an opportunity to examine some of the effects of the task. First, we see that speed and accuracy are both greater in the First Syllable and Last Syllable conditions-this is not surprising, since the subjects' attention can be directed at a single point in the stimulus. In the Last Syllable condition, this resulted in a ceiling effect for accuracy-this is consistent with the performance advantage in Experiments 1-3 in conditions where the latency between the most recent informative cue and the isolated target vowel was reduced. In particular, because the length of the stimuli was consistent, subjects are free to disregard material preceding the attended syllable, and may adopt a strategy similar to that of an AX discrimination study. It is worth noting, however, that while accuracy was at ceiling across the board, there was still a significant main effect on response time, suggesting that preceding material may not have been entirely disregarded. The First Syllable condition is the one which most closely resembles the real-world task of speech perception. In this condition, we see the main effect of Experiments 1-3 replicated: Subjects were faster and more accurate on items with colour harmony. As in the previous studies, this effect was more pronounced for items with height agreement (when colour harmony means total identity)-but the effect is still present even when the colour-contrastive vowels disagree in height. In other words, perception of an initial [u] is facilitated by a subsequent back/round vowel, whether that is another [u] or a (non-identical) [o].

Error analysis
The results in Experiments 1-4 raise questions about the types of errors subjects are making, and their distribution across conditions; this section provides a closer look at those errors, beginning with the block-mismatched data from Experiments 3 and 4 in Section 7.1 and continuing on to a comparison of error types in Section 7.2 and a brief discussion of block order in Section 7.3.

Block-mismatched trials
Recall that trials were classified as block-mismatched if they contained neither of the possible target vowels (Experiment 3 and the Any Syllable condition in Experiment 4) in the attended position (the First Syllable and Last Syllable conditions in Experiment 4). Mixed effects models were fitted on these data, with random intercept for subject and random slopes for subject; helmert contrast coding was used for the three levels of stimulus colour, and deviation coding was used elsewhere. Models for both Experiment 3 and Experiment 4 can be seen in Table 8.
Since neither target is present in these conditions, errors are necessarily false alarms. Figure 8 shows the false alarm rate for block-mismatched trials in Experiments 3 and 4. Across both experiments, there was a clear relationship between the colour of the vowels in the stimulus and the rate of false alarms-colour-harmonic items with all front/unround vowels were most likely to elicit false alarms for [i] and [e] trials, and least likely to elicit false alarms for [u] and [o] trials (p < 0.001 for both Experiments 3 and 4), and vice versa (p < 0.001 for both Experiments 3 and 4).
This pattern of false alarms is consistent with either feature-based identification or sensitivity to overall similarity between the whole nonsense word and the target vowel. If subjects are using sub-segmental features to identify the target vowels, the presence of [o] in e.g., hogeka will activate the [back/round] component of the target vowel [u], leading to occasional erroneous perception or recall of [u]-an additional [o] in hogoka will strengthen that activation, and further increase the false alarm rate. If overall similarity is at play, subjects will judge hogeka to be more similar to [u] than hegeka, and will be more likely to erroneously report having heard [u].
Overall similarity is more likely to have an effect in the non-localized conditions (Experiment 3 and the Any Syllable condition of Experiment 4), where the whole word is the domain of attention. However, even in the First Syllable condition of Experiment 4, the effect remains significant (p < 0.001). This is driven in part by the presence of potential stimuli in non-initial syllables, which may serve as distractors-subjects were more likely to make false alarms with a potential target in a non-initial syllable (p < 0.001), but even when there was no potential target present anywhere in the word, the effect remained significant-the false alarm rate increased with the number of vowels in the nonsense word that shared colour features with the target vowel (p < 0.01). This cannot, of course, rule out the possibility that subjects are still using overall similarity as part of their strategy; however, the high success rate of subjects in this condition indicates that they are indeed performing the task of identifying the vowel in the initial syllable, which is a realistic component of natural speech perception. The persistence of this effect in a context where overall similarity is less likely to be relevant or useful (or if it is, where it could plausibly be expected to be relevant and useful in natural speech perception as well) suggests that the effect is unlikely to be driven by an artificially task-induced reliance on whole-word similarity.

False alarms vs. misses
In block-matched data, where at least one of the possible targets is present in the attended location, errors can either be 'false alarms' or 'misses.' The data here is restricted to height-disharmonic items, where both error types are possible-for height-harmonic items (in Experiments 1-3 and the Any Syllable condition of Experiment 4), both error types are possible for items with colour harmony, but colour-disharmonic items contain both possible targets, so only misses are possible. 16 As in previous analyses, mixed effects models were fitted on these data, with random intercept for subject and random slopes for subject × colour harmony; deviation coding was used throughout. Full models can be seen in Tables 9-12. The most relevant fixed effect (in addition to colour harmony) is correct response-errors on trials with a correct response of 'no' are false alarms, and errors on items with a correct response of 'yes' are misses. 16 The analysis presented here was also checked with height-harmonic items included, and it did not result in a qualitative difference to the results.  Figures 9-10 show the effect of colour harmony on the error rate, across both false alarms and misses. In Experiment 1, there was a significant interaction between harmony and correct response (p < 0.05); the effect of harmony was significant in both false alarms (p < 0.001) and misses (p < 0.001). Likewise in Experiment 2; the interaction between harmony and correct response was significant (p < 0.01), but the effect of harmony was    significant for both false alarms (p < 0.001) and misses (p < 0.01). Experiment 3 also showed a significant interaction between harmony and correct response (p < 0.001). In this case, however, the effect of harmony was significant for false alarms (p < 0.01), but interacted with block for misses, where it was non-significant in Block 2 but marginal in Block 1 (p = 0.0577). In Experiment 4, the main effect of harmony was significant (p < 0.01) and did not interact with correct response. False alarms and misses represent distinct categories of error: Responding 'yes' on hugoka … i in the case of the former, and responding 'no' on hugoka … u in the case of the latter. For block-mismatched trials in Section 7.1, we saw that colour harmony was advantageous (compared to disharmony) when the nonsense word and target bore different feature values (leading to fewer false alarms), but disadvantageous when the nonsense word and the target bore the same feature value (leading to more false alarms). Here we see that-even without the total identity offered by concurrent height agreement-harmony results overall in fewer false alarms than disharmony. And with Figure 9: Error rate as a function of colour harmony and error type, height disharmonic items only, Experiments 1 and 2. Error bars represent 95% Confidence Intervals. the exception of Experiment 3, harmony results in fewer misses than disharmony. In other words, harmony serves to both dissuade an erroneous detection and reinforce a successful one. This effect is still consistent with a listener strategy based on overall similarity between nonsense word and target, and once again the persistence of the effect even in the First Syllable condition in Experiment 4 (recall that there was no interaction between harmony and either task or correct response in the error analysis) is suggestive but not conclusive.

Block order
By examining the effects of block order, it's possible to find some indication of the effect of the time-course of the experiment on the error rate. For experiments where block order showed a significant effect, subjects made fewer errors in the second block than in the first (p < 0.05 for Experiment 1, p < 0.001 in Experiment 4). This suggests that errors are not induced by participant fatigue (which would result in greater errors in Block 2); rather, increasing experience with the task likely allowed subjects to develop knowledge of the task (relevant alternatives, etc.) that streamlined their decision process.

General discussion
The primary objective in this series of experiments has been to investigate whether vowel harmony is perceptually advantageous, and the extent to which that advantage persists among non-adjacent vowels.
A summary of the main findings of the four experiments can be seen in Table 13. The most robust finding, replicated across all experiments, is the advantage of harmony: Subjects were consistently faster and more accurate at identifying a colour contrast in words with harmony. Even in conditions where the effect of harmony was diminished-among non-adjacent vowels and among vowels which disagreed in height-it remained consistently statistically significant. There was also a consistently replicated interaction between this effect and height agreement; harmony was more advantageous among vowels of the same height than among vowels of different heights.
Less stable effects included interactions with locality and with Trial Colour. For locality, Experiment 1 found a small but significant interaction between locality and harmony, with the advantage of harmony diminishing at a distance of one syllable. For Experiments 2-4, this interaction appeared as a non-significant trend. In Experiment 2, the effect of Interaction with Trial Height n/a n/a ✓ n/a harmony was further diminished at a distance of two syllables, but only reached statistical significance in height agreement conditions. For Trial Colour, Experiments 1 and 2 found that the effect of harmony was greater for [u] trials than for [i] trials, though this was not replicated in Experiment 3-4. In Experiment 3, the design was expanded to include both high-target and mid-target blocks, and it was found that the advantage of harmony was greater for high targets than for mid targets. In Experiment 4, the design was expanded to include tasks which asked subjects to attend to specific syllables; initial syllables were of particular interest, and the effect of harmony was found to be significant in this task as well.
The remainder of this section discusses the implications that these findings have for a theory of phonetically grounded vowel harmony. Section 8.1 discusses the connections between these results and asymmetries found in the typology of vowel harmony, while Section 8.2 briefly locates these findings within existing proposals about the role of phonetic substance in phonological grammar.

Connections to typology
The findings summarized above provide evidence that harmony confers a perceptual advantage, and that this advantage includes non-local instances. In local cases of harmony, this perceptual advantage can be seen as adding to previously well-established articulatory sources of grounding (rather than seeking to replace them). However, in the case of transparent harmony, the two sources of grounding make disparate predictions. A theory of phonetic grounding based solely on articulatory factors predicts that harmony should only ever be local. Such theories struggle to account for the empirical reality of long-distance harmony. The finding that the perceptual advantage of harmony persists even among non-adjacent vowels provides phonetic grounding for the existence of long-distance harmony processes. In addition, this conflict between articulatory and perceptual sources of grounding helps to explain why long-distance harmony, while attested, is typologically marked: Every vowel harmony process which applies across a distance also applies locally, but not vice versa. Local harmony has both sources of phonetic grounding supporting it, while long-distance harmony relies only on perceptual factors.
Additionally, there is an attested tendency for the likelihood of harmony to decrease across a distance (as in Hungarian, discussed above). This is somewhat difficult to explain articulatorily, since increasing distance between harmony triggers and targets does not alter the number of gestural transitions required to complete the sequence. 17 However, the finding in Experiment 2 that the advantage of harmony is significantly decreased across a distance of two vowels can provide a source of phonetic grounding for this distance effect.
The finding that height agreement has an effect on the advantage of harmony corresponds with cross-linguistic patterns of 'parasitic harmony,' where harmony is only applicable among segments which agree along some other feature dimension (see Cole & Trigo, 1988;Cole & Kisseberth, 1994;Kaun, 1995 for further discussion). Like local harmony, this also has an articulatory explanation, at least for rounding harmony: On the basis of Linker's (1982) articulatory data, Kaun (1995) argues that the rounding gestures involved in executing high and non-high round vowels are qualitatively different, meaning that executing a height-disagreeing sequence of round vowels would require two separate rounding gestures. This would therefore not accomplish the articulatory goals of harmony as well as executing a height-agreeing sequence of round vowels. In this case, again, articulatory and perceptual grounding appear to be in agreement: Harmony is predicted to occur even among height-disagreeing vowels, but should be additionally licensed among height-agreeing vowels.
The finding that subjects perform better at identifying a colour contrast in high vowels than in mid vowels lends support for Kaun's (1995) perceptually-driven explanation of non-high vowels' status as preferential triggers in rounding harmony. This, like the existence of long-distance harmony and distinctions among degrees of distance, finds no explanation from articulatory sources of grounding. In fact, the articulatory extremes of high vowels should result in stronger vowel-to-vowel coarticulation, the precursor to (local) harmony. The study here advances the chain of reasoning where this asymmetry is concerned: Linker's (1982) findings show that non-high vowels are less articulatorily extreme than their high counterparts, and Terbeek (1977) has demonstrated that listeners rate the latter as sounding more extremely round. The results here show that this difference in extremity does in fact have an impact on listeners' success in identifying the relevant feature contrast, and the main effect seen across all three experiments shows that harmony is indeed a way of achieving improvement in feature recognition.
The interaction between harmony and colour may provide a source of grounding for the generalization that [+round] is phonologically active, while [-round] does not ever appear to be. However, this finding should be taken with an appropriately-sized grain of salt: First, the effect did not consistently replicate, and second, if the phonological activity of feature values is an integral part of the structure of feature systems, the effects seen here may be a result of that structure rather than a precursor for it. Indeed, this raises more questions than it provides answers: To what extent can privativity vs. equipollence be predicted from the salience of phonetic cues, and to what extent does the specification of features impact perception? Caution is indicated in interpreting the results discussed above, but at the very least these findings suggest that this could be an interesting avenue for further inquiry.

Possible mechanisms
The connection between the results of these experiments and the typology of vowel harmony raises a pressing question: How might perceptual effects like these shape phonological systems? The role of phonetic grounding in phonological grammar is a longstanding and unresolved issue in phonological theory, and resolution of the question is far beyond the scope of this paper. However, in this section I will briefly attempt to locate these results within current proposals in this area.
In discussion of phonetic grounding or phonetic precursors, most approaches rely on the notion of bias, which can be divided into several broad categories: 'Channel bias' is the systematic distortion in the speech signal itself in the course of articulation and perception, while 'analytic bias' represents a systematic tendency on the part of the learner to preferentially acquire particular types of phonotactic generalizations or phonological rules (Moreton, 2008). Moreton and Pater (2012) further divide analytic bias into 'structural' bias, the preferential learning of computationally simpler patterns, and 'substantive' bias, the preferential learning of patterns which correspond with sources of phonetic grounding.
Setting aside structural bias, 18 most of the results discussed above are compatible with either channel biases in perception or substantive analytic bias in learning.
In a theory based on channel bias, such as Evolutionary Phonology (Blevins, 2004;Ohala, 1994), these systematic effects in perception shape the listener's mental representations of surface phonological forms. The traditional explanation of the precursors of harmony in channel bias has been primarily articulatory: Gradient vowelto-vowel coarticulation results in vowels whose feature values are misperceived, and sequences of vowels with a shared feature value are posited by the listener. The main contribution of this study is to show that misperception can be biased in this direction (towards harmonic sequences) even in the absence of articulatory asymmetries in the speech signal. If systematic misperception is possible even without detectable coarticulation, the traditional explanation for the evolution of vowel harmony is consistent with the existence of long-distance as well as local harmony.
In a theory based on substantive bias, a learner has some sort of knowledge about the phonetic properties of speech-including the relationship between those properties and articulatory ease, perceptual salience, etc.-and that knowledge influences which potential generalizations over the learning data are given priority in learning. The form that this knowledge takes and the mechanisms by which it exerts influence over learning differ among proposals that make use of substantive bias: It can be innate or it can arise through a learner's experience with his or her own articulatory and perceptual organs; it can be a strict limit on possible generalizations or it can contribute to differences in the prior likelihoods of possible generalization (see e.g., Collins, 2013;Bermúdez-Otero & Kersti Börjars, 2006;Wilson, 2006;Hayes & White, 2013 for further discussion). The perceptual asymmetries found in the experiments above, then, would reside in a learner's phonetic awareness; among the patterns given priority by the relevant learning mechanisms would be those which render colour contrasts among vowels more salient, including long-distance harmony.
Another possible mechanism would introduce harmony processes via lexical competition: If words exhibiting vowel harmony are recognized and recalled more effectively than words which do not, those lexical items should accrue over time, and this accrual in the lexicon may lead learners to posit a categorical phonological rule instantiating the generalization. See e.g., Martin (2007) for a proposal for how lexical competition can introduce changes to a phonological grammar.
There is very little here to differentiate between channel bias and substantive analytic bias as a mechanism for connecting this possible source of phonetic grounding to the phonological grammar; as we have just seen, the main result can easily be accommodated in either approach. One potential divergence, though, concerns the status of non-high rounded vowels as preferential triggers. The results here lend support to an explanation of this typological pattern in terms of perceptual salience in a way that is not straightforwardly accounted for by Evolutionary Phonology. 19 In a theory based on substantive bias, knowledge that non-high vowels are perceptually impoverished means that a phonological process which increases their salience should have some learning advantage over a process which boosts the salience of high vowels. Because this depends on the learner prioritizing patterns which benefit the listener-rather than following from the result of mistakes that the learner makes as a listener-it would seem to lend at least some degree of support to theories of substantive bias.

Conclusion
This paper has presented experimental evidence that vowel harmony is perceptually advantageous; and, crucially, that this advantage obtains even among non-adjacent vowels. Across all four experiments, subjects consistently performed significantly better at a feature-based identification task with colour-harmonic nonsense words than with their disharmonic counterparts. The advantage of harmony was diminished across increasing distance, among vowels which disagreed in height, and for trials with non-round targets (mirroring various cross-linguistic tendencies in the typology of vowel harmony), but the effect of harmony was robustly detectable across all conditions. This provides a potential source of phonetic grounding for long-distance (or 'transparent') vowel harmony, which has been described as an 'unnatural' phonological process. This lends support to theories of vowel harmony in phonology which make use of explicitly non-local representations; while locality still has an important role to play in phonological theory, it should not be understood as a strict, inviolable restriction. While theories of phonetic grounding based solely in articulation must hold transparent harmony as an aberration, including perceptual factors allows for both direct and explicit analysis of long-distance harmony and preservation of phonetic grounding.