Evangelia Adamou

Matthew Gordon

Stefan Th Gries

Prosodic and morphological focus marking in Ixcatec (Otomanguean)

This paper presents the first description of the expression of focus in Ixcatec, a nearly extinct language of Mexico. The study is based on experimental tasks carried out with the last three fluent speakers of Ixcatec.

Prosodic analysis shows that in Ixcatec, a language with three lexical tones, contrastive focus is associated with raised F0, lack of focus is marked through lowered F0 and decreased duration, and corrective focus is signaled through various speaker-specific means. Finally, this study shows that morphological and phonetic properties display a complex interaction that contradicts the view that focus may be conveyed through either morphological or phonetic exponents but not both.

Introduction

The aim of this paper is to describe how focus is expressed in Ixcatec, a nearly extinct Otomanguean language spoken in Mexico (State of Oaxaca).

Results of the analysis, which represents to the best of our knowledge the only phonetic study of focus in any Otomanguean language, show that Ixcatec, a language with three contrastive lexical tones (high, mid, and low), makes use of prosody to express focus, as observed in other tone languages such as Chinese [START_REF] Xu | Effects of tone and focus on the formation and alignment of F0 contours[END_REF][START_REF] Chen | Emphasis and tonal implementation in Standard Chinese[END_REF][START_REF] Chen | Post-focus F0 compression -Now you see it, now you don't[END_REF], Yongning Na and Vietnamese [START_REF] Michaud | Information structure in Asia: Yongning Na (Sino-Tibetan) and Vietnamese (Austroasiatic)[END_REF], and Dane-zaa (i.e. Beaver, [START_REF] Schwiertz | Intonation and prosodic structure in Beaver (Athabaskan)[END_REF].

Moreover, Ixcatec combines a focus marker with prosodic marking, unlike other documented "particle languages" [START_REF] Büring | Towards a typology of focus realization[END_REF]) that rely on a specialized focus marker (i.e. a focus marker with no additional meaning, whether restrictive, additive or scalar) rather than prosody to express focus, including Navajo [START_REF] Mcdonough | The prosody of interrogative and focus constructions in Navajo[END_REF], Chickasaw [START_REF] Gordon | The intonational realization of contrastive focus in Chickasaw[END_REF], Gùrùntùm [START_REF] Hartmann | Morphological focus marking in Gùrùntùm[END_REF], and Bole and Fon [START_REF] Fiedler | Subject focus in West African languages[END_REF].

The paper is organized as follows. In 2, we give an overview of how focus is expressed cross-linguistically. We then provide information on Ixcatec in 3. Prosody and its interaction with morphological marking of focus are presented in 4. We conclude with a summary and discussion of the results in 5.

Focus cross-linguistically

Following the theory of focus elaborated by [START_REF] Rooth | A theory of focus interpretation[END_REF], a widelyaccepted definition of focus refers to constituents introducing alternatives into the discourse. Cross-linguistically focus may be expressed through syntactic, morphological, and/or prosodic means. A central component of the prosodic marking of focus is increased prominence, which is variably realized across languages through manipulation of F0 (and its perceptual correlate pitch), duration and/or intensity. However, studies on individual languages have shown that such prominence is not necessary, as is the case in Wolof, a Niger-Congo language that uses no prosodic marking for focus [START_REF] Rialland | The intonational system of Wolof[END_REF]. On a theoretical level, the use of prosodic means, especially intonation, to express focus has been questioned for tone languages [START_REF] Cruttenden | Intonation[END_REF], in which fundamental frequencythe acoustic dimension along which both tone and intonation are manifestedserves the crucial functional role of conveying lexical contrasts in tone. In support of this view, intonation seems not to be used for focus marking at least in Tamang (Tibeto-Burman, [START_REF] Mazaudon | Language Variation: Papers on variation and change in the Sinosphere and in the Indosphere in honour of[END_REF], Yucatec Maya (Mayan, [START_REF] Kügler | On the universality of prosodic reflexes of contrast: The case of Yucatec Maya[END_REF], and Gùrùntùm (Chadic, Hartmann & Zimmerman 2009). Nevertheless, even if fundamental frequency is less available as a phonetic exponent of focus marking in a tone language, there are other prosodic means that could potentially be exploited to cue focus in a language with lexical tone. Duration thus serves to signal focus in many languages, both non-tonal languages such as English (e.g. [START_REF] Turk | The domain of accentual lengthening in American English[END_REF][START_REF] Katz | Contrastive focus vs. discoursenew. Evidence from phonetic prominence in English[END_REF] and Mexican Spanish [START_REF] Kim | An Intonational Study of Focus and Word Order Variation in Mexican Spanish[END_REF][START_REF] De La Mota | Mexican Spanish Intonation[END_REF], as well as tonal languages such as Standard Chinese [START_REF] Chen | Emphasis and tonal implementation in Standard Chinese[END_REF]. Furthermore, a growing body of work shows that F0 range manipulation is used even in tone languages for the expression of focus. [START_REF] Xu | Effects of tone and focus on the formation and alignment of F0 contours[END_REF], for example, shows that in Mandarin Chinese, a language with four contrastive tones, the F0 contour of the focused constituent (in situ) is expanded and the F0 profile of the remaining utterance is compressed (also see [START_REF] Chen | Emphasis and tonal implementation in Standard Chinese[END_REF][START_REF] Chen | Post-focus F0 compression -Now you see it, now you don't[END_REF] for further evidence and discussion). Similar strategies have been described for the tone languages Yongning Na (Sino-Tibetan) and Vietnamese (Austroasiatic) in [START_REF] Michaud | Information structure in Asia: Yongning Na (Sino-Tibetan) and Vietnamese (Austroasiatic)[END_REF], and Dane-zaa (Athabaskan) in [START_REF] Schwiertz | Intonation and prosodic structure in Beaver (Athabaskan)[END_REF]. [START_REF] Hyman | The Interaction between Focus and Tone in Bantu[END_REF] surveys focus mechanisms in Bantu languages, showing that tone may be influenced indirectly through shifts in prosodic phrasing employed in focus marking.

Prosodic rephrasing and suspension of downdrift are thus used to cue narrow focus in the tone Bantu language Nkhotakota Chichewa [START_REF] Kanerva | Focus and Phrasing in Chichewa Phonology[END_REF][START_REF] Downing | Prosody and Information Structure in Chichewa[END_REF].

Syntactic marking of focus is also widespread across the languages of the world. It has been shown that in several languages a change of the canonical word order is required for an item to be focused. For example in Spanish, a non-rigid, verb-medial language, clause-final position is preferred for focus due to its intrinsic prosodic prominence [START_REF] Zubizarreta | Prosody, Focus and Word Order[END_REF]. Such languages fall under the category of "edge languages" in [START_REF] Büring | Towards a typology of focus realization[END_REF] tentative typology, together with languages that mark focus in a position close to the edge. This is the case for verb-final languages such as Turkish, which has a specific, preverbal, focus position [START_REF] Erguvanlı | The Function of Word Order in Turkish Grammar[END_REF].

A theoretical debate to which Ixcatec potentially contributes is the extent to which languages employing a specialized focus marker (i.e. a morpheme with no additional scalar, restrictive or additive meaning) also redundantly use prosodic means to express focus. It has been observed that languages with specialized focus markers characteristically do not rely on prosody to signal focus, as in Navajo (Athabaskan, McDonough 2002), Chickasaw (Muskogean, Gordon 2007), Gùrùntùm (Chadic, Hartmann & Zimmerman 2009), Bole (Chadic) and Fon (Gbe) [START_REF] Fiedler | Subject focus in West African languages[END_REF]. Examples of languages such as Moroccan Arabic [START_REF] Benkirane | Intonation in Western Arabic (Morocco)[END_REF]) with both prosodic and morphological marking of focus are rare in the literature. [START_REF] Büring | Towards a typology of focus realization[END_REF] proposes the category of "particle languages" for languages that make use of a specialized focus marker with no additional prosodic marking. In order to account for the fact that prosodic marking of focus is rarely encountered in particle languages, two analyses are suggested: "It seems straightforward to analyze the focus morpheme as a direct spell-out of the syntactic feature F […]. Alternatively, one could hypothesize that the focus morpheme marks prominence of prosodic units" (Büring 2009: 201). Similarly, [START_REF] Féry | Focus as prosodic alignment[END_REF] considers that "a focus marker often has an additional prosodic role: it delimits the focus, even if it does not have another prosodic correlate like a boundary tone or duration" (Féry 2013: 720). In evaluating the hypothesis of mutual exclusivity of morphological and prosodic marking of focus, it is important to consider evidence from more "particle languages", such as Ixcatec.

Some background on Ixcatec

ʃ h wa²ni³ is an Otomanguean language better known in the literature under the name of Nahuatl origin, Ixcatec (ISO code: ixc). Ixcatec belongs to the Popolocan branch, alongside Chocholtec (or Ngiba and Ngigua), Popoloc (or Ngiga), and Mazatec (see map in Figure 1).

Ixcatec 1 is only spoken in the municipality of Santa María Ixcatlán in the State of Oaxaca, in Mexico. Today the village has some 400 inhabitants but at the time of the arrival of the Spaniards in 1522 it was an important center for the Mixteca zone with an estimated population of 10,000 people [START_REF] Hironymous | Santa Maria Ixcatlan, Oaxaca: From Colonial Cacicazgo to Modern Municipio[END_REF].

Unlike other Popolocan languages, such as Mazatec and Popoloc, which are spoken by several thousands of speakers, Ixcatec is nearly extinct. There are only ten identified Ixcatec speakers; most of them are in their 80s, and only four of them are fluent in Ixcatec. Although Ixcatec has been in contact with the socially and economically dominant language of Spanish for hundreds of years, the current moribund status of the language is a relatively recent development attributed to a rapid shift to Spanish beginning in the early 20 th century.

Previous linguistic research on Ixcatec consists of the phonology and dictionary of Fernández de [START_REF] Fernández De Miranda | Fonémica del ixcateco[END_REF][START_REF] Fernández De Miranda | Diccionario ixcateco[END_REF] Ixcatec is a verb-initial language with accusative alignment. It makes a clear distinction between nouns and verbs. Several adjectives can be used as non-verbal predicates and there are existential/attributive, locative, and possessive predicates that are distinct from verbs in that they do not carry any person morphemes. Ixcatec's phonology is complex and not yet well understood. It has five vowels, which may be oral or nasalized. Depending on the analysis of consonant clusters, it has 24 or 52 consonants, with pre-and post-aspirated as well as pre-and post-glottalized consonants [START_REF] Fernández De Miranda | Fonémica del ixcateco[END_REF][START_REF] Montero | Temporalidad laríngea en las nasales y obstruyentes del ixcateco[END_REF][START_REF] Dicanio | Laryngeal Timing in Ixcatec Consonants[END_REF], 2012). Syllables are all open but may contain a complex onset.

Ixcatec has three tones that contrast in word-final syllables: high (H), mid (M), and low (L). In non-final syllables, the contrast between mid and low tone is neutralized in favor of the mid tone (see DiCanio 2011 for a preliminary phonetic analysis of Ixcatec tone). Stress in Ixcatec typically falls on the penultimate syllable and is associated with increased duration and intensity and higher F0 (DiCanio 2012).

The expression of focus through prosodic and morphological means

Predictions

In keeping with results from other languages discussed in Section 2, we hypothesize that focus will be expressed through one or more of the following acoustic properties: higher F0, greater duration, and/or increased intensity. We also hypothesize that focus may have an asymmetric realization dependent on the stress level and tone of a vowel. This prediction is based on the fact that both stress and tone are conveyed through acoustic properties also used in the signaling of focus: F0 in the case of tone and F0, duration, and intensity in the case of stress. As mentioned in Section 3, unstressed vowels in Ixcatec typically have reduced duration, intensity and F0 relative to their stressed counterparts (DiCanio 2012). We might thus expect unstressed syllables to be poorer sites than stressed syllables for realizing focus phonetically.

Moreover, an optional focus marker -na² is encountered in Ixcatec, and a similar marker is reported for other closely-related languages such as Metzontla Popoloc (Veerman-Leichsenring 2006: 94). To identify focus in Ixcatec, a language for which we have no native speaker's intuitions, we rely on a discourse approach to focus and apply the Question-Answer Congruence principle [START_REF] Büring | Focus and intonation[END_REF], where questions may be explicit or implicit.

Examples in (1) illustrate the use of the Ixcatec focus marker in a corrective focus condition, i.e. involving two exclusive alternatives [START_REF] Büring | Focus and intonation[END_REF]. However, we note that the use of the focus marker is optional and that the last Ixcatec speakers frequently omit it.

[CONTEXT: Due to her age, the speaker has explained on several occasions that she has difficulties hearing during the working sessions. The interviewer also knows that the speaker has a son. The Ixcatec focus marker is also used in the contrastive focus condition, as can be seen in (2a). Similar to the corrective condition, the use of the focus marker is optional. Compare (2b), where the focus marker -na² is used, with (2c), where it is omitted. Note that focus is not marked syntactically, as there are no changes in the canonical word order Numeral-Noun.

[PRECEDING CLAUSE: The sauce takes four peppers that are not spicy. A further hypothesis relevant to the variable realization of morphological marking of focus is that the acoustic marking of focus will be more pronounced in tokens without an overt focus morpheme than in tokens with focus morphology expressed. This prediction is driven by the suggestion raised in the literature (e.g. [START_REF] Büring | Towards a typology of focus realization[END_REF]) that a focus morpheme precludes, or at least discourages, phonetic exponents of focus.

To test these hypotheses, we conducted a phonetic study of the effects of corrective and contrastive focus on the acoustic parameters of duration, mean F0, and mean intensity. In 4.2 we discuss the methodology employed in this study. Section 4.3 presents the results and section 4.4 a discussion of those results.

Methodology

A controlled experiment was designed to investigate which kinds of phonetic expression distinguish different kinds of focus by adapting the Animal Game task [START_REF] Skopeteas | Questionnaire on Information Structure[END_REF][START_REF] Swerts | Intonational Differences between L1 and L2 English in South Africa[END_REF] to the specificities of Ixcatec.

Participants

This study involved three of the four fluent Ixcatec speakers. 3 The participants, two female and one male, are all in their 80s. Only one of them was brought up monolingual in Ixcatec and acquired Spanish at the age of six at school. The other two speakers acquired both Spanish and Ixcatec in their childhood. All of them have received little formal education. They all reside in the municipality of Santa María Ixcatlán (State of Oaxaca) and their everyday language is Spanish.

Stimuli

Thirty-two words were selected based on phonetic properties including tone and number of syllables, semantic field, and origin (only two Spanish-origin words were retained); see Table 4 in the Appendix. To avoid problems with picture-recognition, we used real-life, culturally-adapted objects and simple drawings (e.g. for colors or certain objects); see Figure 2.

3 The fourth fluent speaker was excluded due to a hearing impairment.

14 The objects were presented in a specific order designed to manipulate their discourse status. Three conditions were targeted: non-focus, contrastive focus, and corrective focus, where 'contrastive focus' refers to a constituent that introduces alternatives in the discourse, and 'corrective focus' offers two exclusive alternatives [START_REF] Katz | Contrastive focus vs. discoursenew. Evidence from phonetic prominence in English[END_REF][START_REF] Büring | Focus and intonation[END_REF]. Objects were grouped together by semantic field (colors, objects, food, animals, and numbers) and each series was introduced by an object that was not analyzed.

Note that participants always used isolated words. In the corrective condition, when they used the negative answer particle, 'no', the tokens were discarded from the phonetic analysis. Elicited words in isolation allowed for control of asymmetric declination effects in the various conditions.

For the contrastive condition, the speakers were instructed to name what they saw. For example, pink color would be followed by yellow color on a sheet of a paper, in which case the color term 'yellow' was assumed to be contextually contrastive. See an example in (4).

[The participants were shown a drawing of yellow color. They had just seen a drawing of pink color and described it as '(it is) pink'.]

(4) ['sa²ne²]F yellow '(It is) YELLOW.'
For the corrective condition, the interviewer described the picture in Ixcatec using an inappropriate noun or color term. The speakers then corrected the interviewer, as if they were in a classroom, and proposed the correct term.

See an example in (5).

[The participants were shown a drawing of yellow color. The interviewer suggested a wrong color name in Ixcatec: 'ka¹tse³ 'red?']

(5

) ['sa²ne²]F yellow '(It is) YELLOW.'
Lastly, to elicit the non-focus condition and obtain comparable single-word tokens, the interviewer asked the translation of the target words from Spanish; see an example in (6). To avoid the contrastive focus effect, each word was introduced by a relatively long question with discussion of various related and unrelated topics. This procedure induced speakers to produce words with the default statement-final terminal fall in intonation.

[The participants were shown a drawing of yellow color. The interviewer asked in Spanish: Como se dice en idioma? 'how do you call (this) in your language (Ixcatec)?'] (6) 'sa²ne² yellow 'Yellow.'

In total, the task elicited 576 tokens: 32 words x 3 conditions (contrastive focus, corrective focus, and non-focus) x 3 speakers x 2 repetitions.

Recordings

Elicitation sessions were recorded using a Tascam DR-100 solidstate recorder at a 44.1kHz sampling rate via two microphones, a supercardioid head-worn microphone (Shure beta 54) and an AKGC480b handheld condenser microphone, the former of which provided the signal submitted to acoustic analysis.

Measurements

In order to assess the acoustic realization of different types of focus in Ixcatec, a series of measurements were made of all the vowels in the data set using Praat [START_REF] Boersma | Praat: Doing phonetics by computer (version 5.1[END_REF]. Based on a waveform in conjunction with a time-aligned spectrogram, the beginning and end of each vowel was demarcated. For vowels following a consonant other than a glide, the onset of a visible second formant was taken as the start of the vowel. For vowels preceding a consonant other than a glide, the offset of the vowel as determined by the second formant served as the end point. The start of a steady state second formant was taken as the beginning point for a vowel following a glide and the end of a steady state second formant served as the end point for a vowel preceding a glide. For word-final vowels, the primary criterion for delimiting the right edge of a vowel was the start of non-modal phonation (i.e. breathiness or creakiness) associated with sufficiently irregular pitch pulses to result in a failure of the pitch tracking algorithm.

A script was run within Praat to collect a series of measurements for all the segmented vowels. Measurements included duration, mean intensity and mean F0. 4 For a relatively small number of tokens (most commonly vowels with low tone), F0 values could not be extracted by the pitch-tracking algorithm and were consequently excluded from the analysis. In order to minimize microprosodic effects attributed to adjacent consonants, the window over which F0 was calculated excluded the 10 milliseconds at the beginning and the 10 milliseconds at the end of each vowel.

Statistical analysis and evaluation

For the statistical analysis, 5 we employ multinomial regression modelling in order to assess which properties (i.e. variables) most reliably distinguish between the three different levels of focus with some predictive power. The dependent variable is therefore FOCUS, a categorical variable with 3 levels:

contrastive, corrective, and none. The independent variables (i.e. the variables potentially distinguishing between/predicting focus levels) fall broadly into three groups. First, there are three continuous variables, mean intensity, mean F0, and duration, all of which are possible phonetic exponents of focus.

The second group of independent variables are categorical and include a number of properties that might be expected to interact with the continuous variables. These include tone and stress level, both of which are involved in hypotheses to be tested, as well as other properties that have been shown in studies of other languages to potentially correlate and/or interact with one or more of the continuous variables: vowel quality, location of the syllable 5 All statistical analysis were carried out with the open-source programming language and environment R 3.2.1 (R Core Team 2015), relying most heavily on the base package, but also the packages effects [START_REF] Fox | Effect Displays in R for Generalised Linear Models[END_REF][START_REF] Fox | Effect Displays in R for Multinomial and Proportional-Odds Logit Models: Extensions to the effects Package[END_REF] and nnet [START_REF] Venables | Modern Applied Statistics with S. Fourth Edition[END_REF].

relative to the left edge of the word (equivalent in this study to the utterance given the isolation context in which the words appeared), word length measured in number of syllables, and speaker. An additional variable reflecting the presence vs. absence of the focus suffix is relevant only for the subset of data characterized by corrective focus since the suffix did not occur with contrastive focus in our data. The relationship between the focus suffix and the phonetic realization of focus is statistically explored in section 4.3.3.

Finally, the variable SPEAKER, which has one level for each of our three speakers, was included in the analysis to be able to evaluate speaker-specific differences.

The predictors (i.e. independent variables) employed in the analysis are summarized in Table 1. A key virtue of including all the potential predictors of focus level together in the regression model is that it provides a means for assessing the relative efficacy of the predictors all at the same time, thereby avoiding the possibility of misjudging the predictive capacity of one or more variables, which happens when independent variables are considered in isolation. For example, if DURATION emerged as a reliable predictor of focus level in one analysis and F0MEAN were significant in a separate analysis, it would be unclear how much of the success of each predictor was in fact covertly attributed to the other one. Another benefit to a single regression model encompassing all independent variables is its ability to discover potential interactions between variables that would be missed if variables were evaluated in separate analyses.

As an initial exploratory step, the distribution of data points was inspected. The histogram in Figure 3 provides a visual display of the DURATION (Figure 3a), F0MEAN (Figure 3b), and INTENSMEAN (Figure 3c) data. To provide a better sense of the degree to which the distributions are normal, the data are divided into ten quantiles, each representing 10% of the data points. In order to make its distribution more normal, we logged the values of the variable DURATION. In addition, we z-standardized DURATION as well as

INTENSMEAN and F0MEAN in order to protect ourselves against collinearity (the fact that predictors might be highly correlated with each other, which can give rise to highly unstable regression coefficients) and to be able to evaluate their effects all on the same scale. We then proceeded to explore to what degree the independent variables and their pairwise interactions would predict the variable FOCUS using a multinomial regression analysis. Given that the variable SUFFIXATROOT was deterministically correlated with FOCUS (i.e. all forms with an overt focus suffix were associated with corrective focus), our initial regression approach was only applied to the 772 unsuffixed cases (277 with contrastive focus, 205 with corrective focus, 290 with no focus).

In a first step, we generated the null model, equivalent to a model with only SPEAKER as a predictor (to immediately allow for speaker-specific differences). Then, we employed an automatic stepwise and bidirectional model selection procedure using AIC (Akaike Information Criterion). This approach entails enlisting an algorithm that begins from the smallest possible modelthe one not including only SPEAKERand iteratively adds or subtracts predictors to improve the fit of the model. Goodness of fit is defined in terms of AIC, a criterion that evaluates the fit of a model against its number of parameters (i.e. it effectively integrates Occam's razor into the model selection process). Note that for all numeric predictors we did not merely include the predictor per se, but also implemented it as an orthogonal polynomial to the second degree; this is rarely done but is in fact very useful because it allows the regression algorithm to identify whether (some of) the trends of the numeric predictors in the data exhibit curvature rather than the traditional 'straight regression lines only' approach. This process stops with the discovery of a so-called 'minimal adequate' model, a model that cannot be improved by either adding or deleting a predictor to the model. In other words, predictors that are not encompassed by this final model did not contribute enough to be included. For this minimal adequate model, we then provide summary statistics (to assess overall model quality), classification accuracy (to assess model accuracy), as well as visualizations of the model's effects.

Results

As a first interim result, the automatic model selection process returned a model that was significantly better than the null model. for all coefficients of this model); we are not discussing the effect of VOWEL, which was merely included as a control. Section 4.3.3 presents the relationship between the morphological and phonetic expression of focus.

The main effect of F0

The interactions

The next three effects all involve the predictor SPEAKER; these effects thus involve predictors whose effect on focus is not constant across speakers.

Consider first the relationship between DURATION and FOCUS, which is different across speakers. Figure 5 is a visualization of this interaction. The plots in Figure 5a and 5b show the results for the two female speakers (F1 and F2), the plot in Figure 5c the corresponding effect for the male speaker (M1). The interaction shows that the two female speakers pattern very similarly to each other and very differently from the male speaker.

Specifically, the female speakers are more likely to mark contrastive focus with increased duration and less likely to mark no focus with increased duration, whereas the male speaker uses increased duration for corrective focus. The nature of this effect defies easy characterization: low intensity is associated with corrective focus for F1 and M1 but contrastive focus for F2; medium intensity is associated with no focus for all speakers (though less so for F2); finally, high intensity is associated with contrastive focus and no focus for F1, no focus for F2, and corrective focus for M1. In general, the confidence intervals are highly overlapped at both ends of the scale with one exception: the relationship between high intensity and corrective focus for M1.

Finally, the plots in Figure 7 represent the interaction STRESS : SPEAKER (with predicted probabilities and their confidence intervals). On the whole, this interaction is weak: in most cases, the change from unstressed to stressed results in only small changes of predicted probabilities (and most of the confidence intervals of the predicted values overlap); the main source of significance is that, for the male speaker, stressed is associated significantly more with no focus than unstressed and significantly less with corrective focus than unstressed.

The relationship between the morphological and phonetic expression of focus

In the experimental task, -na² was encountered only in the corrective condition and not in the contrastive condition (e.g. [ju²wa³]F-na² 'green-FOC'). In the analyzed data, the focus suffix appeared in 46.4% (N=26/56) of corrective focus tokens for one female speaker, 22% (N=11/50) for the other female speaker, and none for the male speaker. In order to test the hypothesis that phonetic expression of focus will be stronger in tokens without morphological marking of focus, a regression model was fit to the data for only the tokens with corrective focus. Recall that only corrective focus had the option of morphological marking in our data. In the analysis, SUFFIXATROOT served as the dependent variable and the predictor variables were otherwise the same as those employed in the original model. It should be noted that the coding for the variable STRESS was the same in the suffixed as in the unsuffixed forms since the suffix falls outside the domain of stress and thus does not trigger a rightward shift of stress from the penultimate syllable of the root. Similarly, the coding for SYLLTONE also did not vary between suffixed and unsuffixed forms as the contrast between mid and low tone, which is lost in root non-final syllables (see section 3), is preserved in the final syllable of a root appearing before a suffix.

The minimal adequate model we arrived at indicated a highly significant correlation between the predictors and SUFFIXATROOT (LR-statistic=66.48, df=9, p<10 -10 ), and a medium-sized correlation (Nagelkerke R 2 =0.45), a classification accuracy 81.7%, which is highly significantly better than either baseline and a good C-value of 0.851. The highest-order effects are summarized in Table 3. Before considering the results of primary interest, those involving the continuous phonetic variables of intensity, and duration, there are three other less interesting effects that were included in the model. These were insignificant but included because our model selection process used AIC as a selection criterion. First, there was an effect of vowel quality, such that the non-high vowels /a, e/ were slightly more predictive than the high vowels of the presence of the focus suffix. Second, there was a difference between the speakers such that F1 exhibited a higher occurrence of the focus suffix.

Finally, there was a tendency for lack of stress to predict the presence of the focus suffix.

Turning to the effects that are significant and of particular interest, Figures 8 and 9 depict the predicted probabilities of the focus suffix surfacing as a function of DURATION (Figure 8) and INTENSMEAN (Figure 9); for ease of interpretation, values on the x-axes are unstandardized in both figures.

Figure 8 shows a very salient effect of duration on the probability of the focus suffix being realized: an increase in duration of vowels in the root (as suffixal vowels were not included in the analysis) results in a sharp increase in the likelihood of the suffix occurring.

Discussion

Results of the acoustic study indicate that focused words are phonetically differentiated from their unfocussed counterparts and, further, that corrective and contrastive focus are also acoustically distinguished. This result corroborates the primary hypothesis tested in the phonetic study: that focus has phonetic exponents in Ixcatec, in keeping with the lack of focus marking through word order changes and the only sporadic morphological marking of focus. Most consistently across speakers, higher F0 values are associated with contrastive focus whereas lowered F0 values are associated with lack of focus. Furthermore, decreased duration is predictive of lack of focus for all speakers.

There are, however, other properties that vary between speakers. At the upper end of the spectrum of duration values an increase in duration triggers a greater likelihood of contrastive focus for the two female speakers. The male speaker, on the other hand, employs increased duration as a marker of corrective focus.

Intensity displays the greater interspeaker variation in its behavior and is also generally the least reliable predictor of focus as reflected in its characteristically very broad confidence intervals. For the male speaker (the speaker with the narrowest confidence bands), corrective focus is associated with greater intensity to go along with the increase in duration associated with corrective focus. One of the female speakers (F1) displays greater intensity under the contrastive focus condition in keeping with the increased duration also observed under contrastive focus. The other female speaker (F2) has a divergent pattern characterized by decreased intensity under contrastive focus and increased intensity under lack of focus.

Synthesizing the results by speaker, the male speaker appears to display the clearest phonetic distinctions between focus levels. In his speech, contrastive focus is associated with higher F0, while corrective focus is associated with increased duration and intensity. A reduction in any of the three patterns is predictive of lack of focus. For the two female speakers, increased duration and F0 are both predictive of contrastive focus. For one of the female speakers, increased intensity is also associated with greater probability of contrastive focus. For the other speaker, the increase in duration under contrastive focus is paradoxically accompanied by a decrease in intensity. Interestingly, for both of the female speakers, there is no phonetic dimension along which an increase in the relevant property distinguishes corrective focus from the other two focus conditions. Rather, it is the absence of a reduction in F0 and duration that differentiates corrective focus from lack of focus (and from contrastive focus as well). This result may be due to a ceiling effect, whereby the exploitation of increased F0 and duration to signal contrastive focus renders these phonetic properties less available as markers of corrective focus. In any case, corrective focus is still phonetically distinguishable from a lack of focus by virtue of possessing (relative to the unfocused condition) greater duration and F0.

With respect to stress, its association with lack of focus, on the one hand, supports the claim that Ixcatec possesses stress in addition to tone (DiCanio 2012). On the other hand, its lack of efficacy in predicting focus is plausibly attributed to a ceiling effect whereby the properties used to signal stress are less available to signal focus. These patterns were most apparent for the male speaker, for whom lack of stress was predictive of corrective focus and stress was predictive of the no focus condition. This finding contradicts the hypothesis that focus would have a more robust realization in stressed syllables, which are inherently conducive to supporting the same prominence-lending properties characteristically associated with focus. One interpretation of the present findings is that there is actually more freedom to implement focus phonetically in unstressed syllables relative to stressed syllables, the latter of which already possess certain of the same features that mark corrective focus for the male speaker. In a cross-linguistic study of the acoustic interaction between focus and stress in four languages (Greek, Hungarian, Spanish, and Turkish), [START_REF] Vogel | Prominence, contrast, and the functional load hypothesis: An acoustic investigation[END_REF] find differences between languages in the realization of stress under focus, even observing a reduction in the prominence of stress under focus.

The hypothesis that focus may have a more pronounced realization for certain tones was not corroborated. Phonemic tone did not predict focus condition in the main analysis excluding suffixed forms and also did not reliably predict whether corrective focus was realized with a suffix or not.

Examining the results from a typological lens, the marking of focus Conversely, one might predict intensity to be a more reliable marker of focus by analogy with the important role of intensity in marking stress in tone languages, such as Thai [START_REF] Potisuk | Acoustic correlates of stress in Thai[END_REF] and Pirahã [START_REF] Everett | Acoustic correlates of stress in Pirahã[END_REF].

Our data, however, suggest that F0 does play a role in predicting focus in Ixcatec, especially contrastive focus. F0, in fact, is a more consistent predictor of different focus conditions in Ixcatec than either intensity or duration. The Ixcatec results thus indicate that, although the use of F0 may be constrained in the marking of focus in a tone language, it is certainly not precluded.

Intensity played a more robust role in predicting whether corrective focus was expressed morphologically through a suffix or not: as intensity increased, the likelihood of the focus suffix surfacing decreased, a finding that is consistent with the hypothesis that morphological and phonetic exponents of focus are in complementary distribution. This hypothesis was only partially confirmed, however, since an increase in duration was associated with a greater likelihood of the focus suffix being realized.

One suggestive finding that cannot be explored further is the divergence between the male speaker and the two female speakers, most conspicuously in the relationship between duration and focus, such that increased duration was predictive of contrastive focus for the females but corrective focus for the male. Because there was only one male speaker in our study, it is unclear whether this discrepancy is a function of gender or of idiolect.

Sadly, this confound can never be teased apart as the three consultants studied for this paper are the last fluent speakers of Ixcatec.

Conclusions

The present study of Ixcatec contributes to our understanding of focus in several ways both from a theoretical and a descriptive standpoint. On a descriptive level, the current paper broadens the typological database on focus by providing the first comprehensive analysis of phonetic and morphological features of focus in an Otomanguean language. Furthermore, our work contributes to the extremely meager descriptive literature on focus in severely threatened languages by examining through varied methodological approaches a moribund language that has only a handful of fluent speakers.

In our experimental data, a focus suffix occurs only with tokens associated with corrective focus. More striking is the relationship between the optional focus suffix and the phonetic exponents of focus in Ixcatec. The results of the second regression analysis limited to the corrective focus condition showed that prosodic marking can be used concurrently with the focus marker in corrective conditions. An increase in duration of the root was thus predictive of the occurrence of the focus suffix. This finding appears to contradict the hypothesis that the morphological and prosodic marking of focus is parameterized on a language-specific basis [START_REF] Büring | Towards a typology of focus realization[END_REF]). An extreme interpretation of this position is that the morphological and acoustic expression of focus are mutually exclusive and that a language may employ one but not the other. This view seems unlikely to be true on the basis of not only the Ixcatec data but also based on studies of other languages with both morphological and prosodic marking of focus, such as Moroccan Arabic [START_REF] Benkirane | Intonation in Western Arabic (Morocco)[END_REF]. A less categorical and a priori more defensible version of the hypothesis of mutual exclusivity would be that the degree of reliance on morphological vs. prosodic marking of focus is inversely related: the more a language relies on morphology to cue focus, the less it depends on acoustic cues, and vice versa. Even this position, however, is contradicted by the Ixcatec results, in which morphological and prosodic marking of focus appear to act synergistically, such that the acoustic expression of focus is more salient, at least along the phonetic dimension of duration, in conjunction with the focus suffix than without it.

To complicate matters, intensity displayed a different pattern from duration in our data: morphological marking of focus was associated with lower intensity. The overall picture is thus not one of an unambiguously synergistic relationship between prosody and morphology but rather that focus has a different acoustic realization depending on whether it co-occurs with a suffix or not.

In contextualizing the Ixcatec results, it is important to note that the set of languages subjected to a comprehensive study of both the acoustic and morphosyntactic exponents of focus is still relatively small. Indeed, future typological work on focus might reveal that, similar to Ixcatec, other languages employing morphological marking of focus may also use prosody redundantly to signal focus, in which case it will be necessary to rethink the relationship between prosody and morphology in the expression of focus.

  and the work of Veerman-Leichsenring on pronouns (Veerman-Leichsenring 2000), noun phrases 1 Ixcatec is not to be confused with the Mazatec variety of San Pedro Ixcatlán. 7 (Veerman-Leichsenring 2001a), and word order (Veerman-Leichsenring 2001b). More recently, work has been done on Ixcatec phonetics and phonology (Alarcón Montero 2010, DiCanio 2011, 2012) as well as on syntax and morphology (Adamou & Costaouec 2013, Adamou 2014, Adamou 2017), codeswitching and language contact (Adamou 2016), and spatial language and cognition (Adamou 2017).

Figure 1 .

 1 Figure 1. The languages of the Popolocan branch (including the main

  ANSWER TO THE QUESTION: Is it your son who doesn't hear well?] (1a) [ʔi²na¹na³]F-na² 1SG-FOC '(It is) ME.' {speaker F1_ELIC} [CONTEXT: Since the interviewer's last visit to the village, the speaker began teaching classes of Ixcatec at the middle school. ANSWER TO THE QUESTION: Do you teach at the kindergarten?]

Figure 2 .

 2 Figure 2. Picture of a local preparation of corn for the target word nixtamal

Figure 3a .

 3a Figure 3a. The distribution of data for the continuous variable DURATION

Figure 4

 4 Figure 4 visualizes the effect of F0MEAN on FOCUS: the x-axis represents

Figure 4 .

 4 Figure 4. The effect of F0MEAN on FOCUS

Figure 5a .

 5a Figure 5a. The effect of the interaction of DURATION:SPEAKER on FOCUS for speaker F1

Figure 6b .

 6b Figure 6b. The effect of the interaction of INTENSITY:SPEAKER on FOCUS for speaker F2

Figure 7a .

 7a Figure 7a. The effect of the interaction of STRESS:SPEAKER on FOCUS for speaker F1

Figure 8 .

 8 Figure 8. The effect of DURATION (polynomial, 2) on SUFFIXATROOT

  through a (speaker-dependent) change in duration, intensity and/or F0 is unremarkable typologically, though it has not been quantitatively documented for any Otomanguean languages. There has been very little quantitative work comparing the acoustic reflexes of different types of focus within a single study. Even though at present the main assumption is that all the pragmatic contexts (contrastive focus, corrective focus, answer focus, etc.) trigger a single type of grammatical focus, the possibility that the various pragmatic types of focus could also be considered as distinct grammatical types of focus remains open(Büring 2009: 180). The differences in the phonetic marking of corrective and contrastive focus observed in Ixcatec thus inform the broader typology and contribute to the ongoing discussion in focus theory. The association of lack of focus with a reduction along one or more phonetic dimensions (varying on a speakerspecific basis) conforms, however, to cross-linguistic patterns.Perhaps somewhat unexpected is the role of F0 in marking focus in Ixcatec. A priori one might expect F0 to be less available as a phonetic correlate of focus in Ixcatec due to its use on a lexical level to distinguish different words (seeChen & Gussenhoven 2008: 726 on Standard Chinese).

Table 1 .

 1 Independent variables employed in multinomial logistic regression model

	Variable	Abbreviation	Values
	Duration (in seconds)	DURATION	0.026 to 0.471 seconds
	Mean F0 (in Hz)	F0MEAN	103 to 334 Hz
	Mean intensity (in dB)	INTENSMEAN	40.2 to 83.44 dB
	Vowel quality	VOWEL	a, e, i, u
	Tone	SYLLTONE	low, medium, high, unspecified 6
	Stress	STRESS	stressed, unstressed
	Syllable location	SYLLFROMLEFT 1st, 2nd, 3rd, 4th
	Length of Root	ROOTLENGTH	1, 2, 3
	(in no. of syllables)
	Speaker	SPEAKER	F1, F2, M1
	Focus Suffix (see section	SUFFIXATROOT Yes(=suffix), No(=no suffix)
	4.3.3)

Table 2

 2

	. Overall results of the minimal adequate model (highest-order
	effects)
	Effect	LR-statistic (type II) df	p
	F0MEAN	21.308	2	<0.001
	SPEAKER : DURATION	15.432	4	<0.004
	SPEAKER : poly(INTENSMEAN, 2) 90.5	8	<10 -15
	SPEAKER : STRESS	20.254	4	<0.001
	VOWEL	16.5	6	0.011
	Sections 4.3.1 (Main Effects) and 4.3.2 (Interactions) discuss the relevant

significant highest-order effects of this model (see Table

6

in the appendix

Table 3 .

 3 Overall results of the minimal adequate model (highest-order effects)

	Effect	LR-statistic (type II)	df	p
	SPEAKER	2.303	1	0.13
	STRESS	2.418	1	0.12
	VOWEL	6.365	3	0.095
	poly(INTENSMEAN.zstand, 2)	8.401	2	<0.015
	poly(DURATION.zstand, 2)	20.53	2	<0.001

Table 5 .

 5 The minimal adequate multinomial regression model (Focus ~ …)

		contrastive  corrective contrastive  none
		coef	se	z	coef	se	z
	(Intercept)	-1.187 0.310 -3.829 -0.564 0.232 -2.429
	SPEAKER: female  male	-1.809 0.490 -3.695 0.263 0.390 0.675
	SPEAKER F1  F2	-1.743 0.751 -2.321 0.097 0.512 0.189
	DURATION.zstand	0.536 0.144 3.718 -0.261 0.111 -2.359
	F0MEAN.zstand	0.211 0.143 1.472 -0.408 0.121 -3.370
	STRESS: unstressed ->	-0.401 0.258 -1.554 0.489 0.207 2.368
	stressed
	VOWEL: a  e	-0.127 0.379 -0.334 0.323 0.305 1.058
	VOWEL: a  i	0.207 0.289 0.717 0.413 0.246 1.680
	VOWEL: a  u	0.856 0.279 3.069 0.252 0.240 1.049
	poly(INTENSMEAN.zstand,2)	9.902 7.016 1.411 -1.198 5.238 -0.229
	1
	poly(INTENSMEAN.zstand,2)	5.720 5.247 1.090 -2.244 4.380 -0.512
	2
	SPEAKER: female  male :	1.671 0.506 3.301 -0.567 0.420 -1.350
	STRESS: unstressed  stressed
	SPEAKER: F1  F2 :	0.677 0.645 1.050 0.287 0.499 0.575
	STRESS: unstressed  stressed
	SPEAKER: female  male :	-1.043 0.299 -3.494 -0.301 0.227 -1.329
	DURATION.zstand
	SPEAKER: F1 F2 :	0.280 0.352 0.796 -0.008 0.274 -0.029
	DURATION.zstand
	SPEAKER: female  male :	-16.304 12.671 -1.287 29.635 9.935 2.983
	poly(INTENSMEAN.zstand,2)1
	SPEAKER: F1  F2 :	-40.449 19.069 -2.121 -21.441 13.784 -1.555
	poly(INTENSMEAN.zstand,2)1
	SPEAKER: female  male :	-38.064 10.880 -3.499 -5.191 9.850 -0.527
	poly(INTENSMEAN.zstand,2)2

Table 6 .

 6 The minimal adequate binary logistic regression model (SuffixatRoot ~ …)

	coef	se	z	p

The examples from the texts of Fernández de[START_REF] Fernández De Miranda | Diccionario ixcateco[END_REF] have been adapted to IPA for the sake of consistency with our newly collected data. Note that de Miranda uses both a mid and a high tone for the suffix -na.

Other F0 values taken at different time points (the beginning, middle and end of each vowel) as well as maximum F0 values were also collected but were not included in the statistical analyses reported in

5.2 after inspection suggested that they were not more effective at differentiating focus than a simpler measure of mean F0.

In order not to bias the analysis, the tonal category unspecified was employed for the optional suffix -na, which has been variously transcribed as mid or high tone by Fernández de[START_REF] Fernández De Miranda | Diccionario ixcateco[END_REF].

Acknowledgments

We are grateful to the two anonymous reviewers for their many helpful and insightful comments. We are profoundly indebted to the speakers of Ixcatec who generously shared their language with us. The data collection was funded by the Hans Rausing Endangered Languages Programme "Textual and Lexical Documentation of Ixcatec, a highly endangered Otomanguean language of Oaxaca, Mexico" (MDP 0214, 2010-2013), awarded to Denis Costaouec, and the French National Research Agency through the program "Investments for the Future" (ANR-10-LABX-0083), Strand 3 GD1 "The Typology and Corpus Annotation of Information Structure and Grammatical Relations".

The plots in Figure 6