Prosody in Contact
Prosodic aspects of language contact are understudied, even though insights from such research are required to deepen our understanding of resultant language change. There is increasing evidence that ongoing language contact results in intonational variation and change in the speech of bilingual speakers in different ways.
Contact between languages may result in either phonological or phonetic prosodic transfer (Mennen, Reference Mennen, Scobbie, Mennen and Watson2006), influencing the category of phonological tonal events (pitch accents and edge tones) or their phonetic realization. For example, in Buenos Aires Spanish, which was in long-term contact with Italian, prenuclear accents in broad focus declaratives display the Italian early-peak H tone alignment at the beginning/middle of the stressed vowel, rather than the Spanish late-peak alignment in the stressed or the following syllable (Colantoni & Gurlekian, Reference Colantoni and Gurlekian2004). Similarly, in Peru, Lima Spanish speakers who do not have contact with Quechua produce earlier peak alignment in contrastive rather than in broad focus (a pattern found in Peninsular Spanish) while Cuzco speakers who are Spanish-Quechua bilinguals do not consistently differentiate between broad and contrastive focus, something that is attributed to the influence of Quechua (O'Rourke, Reference O'Rourke2012).
Sometimes contact gives rise to novel patterns attested in neither language. Lekeitio Spanish, a contact variety of Basque and Spanish, displays mixed properties of Basque and Spanish intonation, that is, accents in broad focus declaratives are not falls, as in the H*+L of Lekeitio Basque, but rises as in the L*+H or L+H* of Madrid Spanish. On the other hand, the peak alignment of the H tone in the L*+H rises does not appear after the stressed vowel as in Spanish but within the stressed vowel, as in Lekeitio Basque (Elordieta & Calleja, Reference Elordieta and Calleja2005).
In addition, bilingual speakers have been shown to codeswitch in prosody. Queen (Reference Queen2012) reported codeswitched productions in the polar question tunes of German-Turkish bilinguals: when the Turkish question particle /-mI/ was inserted into a German matrix utterance, the question particle was produced with a falling (H*L) Turkish f 0 contour.
Evidence is still lacking on whether and how long such effects persist after contact has ceased, as few studies exist on the diachronic change of intonation (Hualde, Reference Hualde, Auger, Clements and Vance2004). Colantoni and Gurlekian (Reference Colantoni and Gurlekian2004) argue that the alignment patterns still found in Buenos Aires Spanish declaratives almost sixty years after the end of the immigration wave of Italians are due to the covert prestige of Italian. Barnes and Michnowicz (Reference Barnes and Michnowicz2015) report that the contact between Veneto Italian and Mexican Spanish in Chipilo, Mexico resulted in Italian-like patterns of prenuclear peak alignment in broad focus declaratives. They maintain that the influence of Veneto Italian has persisted because speakers identify with Veneto and are proud of their language and heritage.
Similarly lasting effects of contact have been documented in the direction from a dominant to a nondominant language. Bullock (Reference Bullock2009) discusses prosodic patterns in French-English contact in a minority variety of French spoken in Frenchville, Pennsylvania since the 1830s. In the last two remaining fluent heritage speakers in the village, there was adoption of additional structures of the dominant language (i.e., pitch accents used in English but not in French) in the intonation of these French heritage speakers, which have distinct pragmatic uses.
In this paper, we trace the trajectory of intergenerational prosodic change in four generations of speakers of Asia Minor Greek (AMG). AMG patterns are compared with those of four generations of their Turkish-speaking contemporaries to bring to light any similarities that may have remained after the end of AMG-Turkish contact and four contemporaneous generations of Athenian speakers, since AMG speakers have now been living in Greece for almost a century (see Baltazani, Przedlacka, & Coleman, Reference Baltazani, Przedlacka, Coleman and Minematsu2020).
Our approach differs from those cited above in several respects. First, we make a three-way comparison analyzing benchmark data from Athenian and Turkish in addition to AMG, whereas the papers cited above (with the exception of Baltazani et al., Reference Baltazani, Przedlacka, Coleman and Minematsu2020) only analyze data in the contact variety, relying on previously published analyses of the two source languages. Second, we investigate data from four generations, whereas most of the papers cited above use data from just one or two. Third, whereas most studies use small corpora of speech elicited in a laboratory setting, we employ a large corpus of mostly spontaneous and semispontaneous speech because of the stronger influence of the source language on a contact variety in natural than in controlled laboratory speech (Barnes & Michnowicz, Reference Barnes and Michnowicz2015).
Background on Athenian, Turkish, and AMG
Athenian, the Modern Greek variety spoken in Athens, is the standard used for official purposes, in education, and the media. Athenian is thought not to be distinctly marked by any single traditional Greek dialect (Trudgill, Reference Trudgill2003:48). Rather, extensive internal migration from various rural parts of the country to Athens between 1950 and 1980 resulted in today's amalgamationFootnote 1 of different varieties brought by migrants (Allen, Reference Allen1986).
Despite reports on the leveling influence on Turkish of the Istanbul standard used in mass media and the education system since the 1930s (Johanson, Reference Johanson2001:16), there are descriptions of phonological, morphological, and syntactic dialectal features for several regions in Turkey, including the Black Sea (Johanson, Reference Johanson2001), Marmara, Aegean, and Central Anatolia regions (Karlık & Akbarov, Reference Karlık and Akbarov2015). To our knowledge, no descriptions exist about dialectal intonation differences. As we base the analysis of Turkish patterns on recordings from several geographic regions, we conducted a statistical comparison of the intonational parameters in these dialectal recordings (in 3.1), which revealed that they are similar, so for all subsequent analyses we grouped all Turkish data together.
AMG is a variety of Modern Greek previously spoken in Asia Minor by people whose ancestors had been part of the Byzantine Empire until the eleventh century conquest by Seljuk Turks. (For a detailed, well-documented linguistic history, see Karatsareas [2011:11-63] and sources cited there.) The Greek-speaking peoples in Asia Minor mixed culturally and linguistically with Turks for eight centuries in a society where Turkish was the dominant language. There is historical evidence of some linguistically Turkicized Greek communities and of others retaining Greek as their first language (Karatsareas, Reference Karatsareas2011:16-19). In 1923, the cohabitation was forcibly ended due to the Convention Concerning the Exchange of Greek and Turkish Populations. Approximately 1,300,000 Orthodox Christians of the Ottoman Empire were relocated to Greece, in exchange for roughly 360,000 Muslims from Greece to Turkey (Blanchard, Reference Blanchard1925).
AMG is a heritage variety (Polinsky, Reference Polinsky2018) only spoken at home and not dominant at the national level. It survives mostly in northern Greece (Katsapis, Reference Katsapis, Liakos and Gazi2011:71) where currently there are second-, third-, and fourth-generation speakers of AMG who, unlike the first generation, did not grow up in a Turkish-speaking environment. The speakers are bi- or tridialectal, in AMG, local varieties, and Athenian Greek as part of their linguistic repertoire (Janse, Reference Janse2009; Karatsareas, Reference Karatsareas2011). First-generation speakers in this study were born in Cappadocia prior to the 1923 Convention while speakers of subsequent generations are descendants of the Cappadocian refugees and were born in Greece. Refugees from Asia Minor made up more than a quarter of Greece's population in the 1928 census (Katsapis, Reference Katsapis, Liakos and Gazi2011:126-29) and were viewed by many as an economic burden. The already ailing economy and the politically unstable system at the time resulted in the marginalization of these refugees (Gizeli, Reference Gizeli1984), negative attitudes toward them (Kalafati, Reference Kalafati2018), and stigmatization of their language.
Materials and methods
Data, speakers, and annotation
We depart from the controlled laboratory methodology followed in most Autosegmental-Metrical studies of intonation (Ladd, Reference Ladd2008) and instead draw on natural speech corpora, because many of the sociolinguistic parameters affecting the behavior of bilingual speakers are not well understood and cannot be replicated in the laboratory. We extracted 2,977 continuation rise utterances from 111 speakers (seventy-one male, forty female) varying in length, complexity, lexical makeup, syntactic structure, and style from the sources listed in Appendix A. Table 1 presents the number of tokens and speakers analyzed per language variety and generation.
Number of tokens and speakers per language variety and generation
AMG speakers here were divided into four generations based on date of birth and historical circumstances. For consistency with the generational categorization in one of the AMG corpora we used (Janse, Reference Janse2015), we classified speakers born in Turkey before 1923 and their Turkish and Athenian contemporaries as Generation 1. Subsequent generations were divided as follows: second-generation speakers born between 1923 and 1945 (the oldest was in fact born in 1927), third-generation from 1950 to 1975, and fourth-generation after 1978.Footnote 2 The oldest speaker in the recordings across all three varieties was born in 1879, the youngest in 1994, their birthdates spanning over a century.
The first-generation AMG speech was drawn from archival as well as contemporary field recordings, thus some members of this generation were recorded in their youth, others in their old age. For this generation, the shape of the modeled f 0 curves and the location of peaks and troughs in continuation rise tunes in archival recordings were compared to those in contemporary recordings (see Statistical analysis section and Baltazani et al., [Reference Baltazani, Przedlacka, Coleman and Minematsu2020] for details of this method). This comparison revealed no significant differences in f 0 shape or in the location of peaks and troughs due to recording date (Baltazani et al., Reference Baltazani, Przedlacka, Coleman and Minematsu2020), so all the data on first-generation AMG speakers regardless of the recording date are pooled together in the subsequent analysis.
We defined continuation rises in all three varieties as phrases marked with an H tone on their right boundary (in Autosegmental–Metrical terms, H− or H%), indicating that the speaker has not finished speaking (see Analysis of f 0 contours section for details). In the Athenian continuation rise tune there is typically an L* nuclear pitch accent (i.e., an f 0 trough) aligned with the stressed vowel of the nuclear word, followed by an H− phrase-final accent (i.e., the phrase ends in high f 0; Arvaniti & Baltazani, Reference Arvaniti, Baltazani and Jun2005; Baltazani & Jun, Reference Baltazani, Jun, Ohala, Hasegawa, Ohala, Granville and Bailey1999; Figure 1 top). In the Turkish continuation rise tune a H*+L nuclear pitch accent (i.e., an f 0 peak plus a fall) is followed by a H− phrase accent (Ipek & Jun, Reference Ipek, Jun, Campbell, Gibbon and Hirst2014; Özge & Bozsahin, Reference Özge and Bozsahin2010; Figure 1 bottom). The f 0 movement is a simple rise in Athenian but a rise-fall-rise in Turkish.
Representative examples of continuation rise tunes in Athenian (top) [erɣaˈzotane] “ (she was) working” and Turkish (bottom) [maˈsaja oˈturmadan] “Before sitting at the table.” The rectangles near the center of each figure indicate the nuclear vowel, transcribed in bold.
Planned comparisons
For all comparisons, we examined the modeled f 0 curves to find differences in their shape, including location of peaks and troughs (see Analysis of f 0 contours section for details). Two sets of comparisons were conducted: (1) Geographical region comparison (for Turkish only). The Turkish recordings were from several regions, including Istanbul, the Black Sea, the Aegean, and Central Anatolia. (Recordings from the Doegen corpus of Turkish speakers from the territory of the Ottoman Empire in what is now Romania are included as a fifth sample in order to examine whether or not this data is similar to the other varieties); and (2) Diachronic comparison. This was a comparison across the three varieties and four generations to determine the similarities of AMG to Turkish and Athenian, and whether or how their intonation may have changed over the generations.
Analysis of f0 contours
Our quantitative analysis of the shape and relative timing of f 0 contours of continuation rises involves the following steps:
1. Standardization of audio file formats.
2. Identification of utterances containing continuation rises.
3. Estimation of f 0 contours, quality control, and elimination of f 0 tracking errors. This step includes transformation of f 0 to semitones above or below the utterance mean.
4. Functional Data Analysis I: Modeling the f 0 contours of whole utterances, using tenth order polynomials, in order to precisely determine the timing of the trough that is used to compare alignment between the three languages. Alignment parameter τ is estimated in this step.
5. Functional Data Analysis II: Modeling the f 0 contour of the continuation rise portions, using fourth-order polynomials. Shape parameters of the continuation rises are estimated in this step.
For these steps we use a variety of standard signal processing tools: sox, ffmpeg, ESPS, and GNU Octave (Eaton et al., Reference Eaton, Bateman, Hauberg and Wehbring2019), a public-domain package that is similar to Matlab in its syntax and functionality. Subsequent statistical analysis of the modeled contour features was carried out in R.
Standardization of audio file formats.
All our data sources were digital, in a variety of formats (e.g., mp3, mp4, and .wav PCM; 2-channel or monophonic), bit rates or sampling rates (e.g., 44.1 kHz, 22.05 kHz, or 16 kHz). Additionally, some digital recordings made from ¼-inch tape, recorded at different tape speeds, required speeding up or slowing down by a factor of 2 or ½ to restore the correct original recording rate. A small number of such digitized tape recordings ran backwards on one channel as the tape spool had originally been turned over for the second half of a monophonic recording, but it had been digitized as if it were a two-track stereo recording. To permit for the subsequent functional data analysis steps to be performed as batch computations, we converted all the recordings to 16 kHz, monophonic, uncompressed PCM .wav audio files.Footnote 3
Identification of utterances containing continuation rises.
With the assistance of native speaker researchers, we employed pragmatic criteria for choosing the utterances we would analyze in all three language varieties to avoid the circularity that would ensue had we based our selection solely on intonational features. The included phrases were parts of broad focus declaratives in which no constituent carries narrow focus, which were nonfinal in the speaker's turn, and ended in a high boundary that typically (but not always) was followed by a short pause. In some cases, this high boundary tone was followed by a slight fall in pitch, but we took the closeness of the high tone to the end of the phrase as the only intonational criterion; the internal intonational details of the phrase were not used for the selection.
For each variety, the native speaker researchers identified the relevant utterances, orthographically transcribed them, translated them into English, located the nuclear word and manually annotated the beginning and the end of the stressed vowel (“v”) using Praat (Boersma & Weenink, Reference Boersma and Weenink2020) as in Figure 3 (top). The start of this stressed vowel served as the beginning of the “Region of Interest,” that is, the part of the continuation rise tune compared across all three languages extending from the start of the vowel to the end of the utterance.
Estimation and verification of f 0 contours.
For each utterance, f 0 was measured every 10 ms (1 cs) using the ESPS (Entropics Signal Processing System) get_f0 function (Talkin, Reference Talkin, Kleijn and Palatal1995), to obtain an f 0 time series.
To identify f 0 tracking errors, especially octave doubling and halving, and to provide a degree of normalization of between-speaker differences in voice pitch, the f 0 contours of each utterance were converted to semitones above or below the whole utterance mean, f̄ 0, as in (1). This makes every token directly comparable to all the others and goes some way to normalizing for interspeaker differences. If the data had included better information about speaker identities, we might preferably have transformed f 0 to semitones above or below the speaker mean, but we lack that data.
Given this transformation, an octave error is a sudden jump of twelve semitones (or thereabouts; it can be twelve semitones + some small change in f 0), as shown in Figure 3. All such potential octave jumps were individually inspected to check that they were octave errors, not actually occurring large pitch changes; the error portions were then corrected by doubling or halving (as appropriate) the f 0 measurements throughout the mistracked interval. Other large or sudden jumps in f 0 were similarly inspected to determine their cause. Rapid pitch perturbations due to consonantal onsets or offsets were retained unaltered as they are a natural part of f 0 contours. In other cases, rapid jumps could be attributed to environmental noises or to other speakers; such portions were zeroed out in the measured f 0 tracks.
Modeling the f 0 contours of whole utterances.
To determine differences or changes in the shape of continuation rises, we employ techniques of Functional Data Analysis (Ramsay, Hooker, & Graves, Reference James, Hooker and Graves2009), a statistical approach to analyzing continuous data such as curves, signals, or surfaces used in a broad spectrum of disciplines such as physiology (growth curves), demographics (population variables), weather forecasting, and, more recently, speech (Andruski & Costello, Reference Andruski and Costello2004; Aston et al., Reference Aston, Chiou and Evans2010; Chen & Wang, Reference Chen and Wang1990; Grabe et al., Reference Grabe, Kochanski and Coleman2005, Reference Grabe2007; Gubian, Cangemi, & Boves, Reference Gubian, Cangemi and Boves2011; de Ruiter, Reference Ruiter2011; Zellers et al., Reference Zellers, Gubian and Post2010).
Functional data analysis begins with data smoothing and fitting to a selected “basis function,” a process that transforms a time series of discrete, raw data points (in this case measured f 0 values) into a smoothly varying function. This emphasizes patterns in the data by minimizing short-term deviation due to measurement errors or inherent system noise. Functional data also allows information on the shapes of the curves to be obtained, which facilitates comparisons across languages, language varieties, genders, generations of speakers, and other sociolinguistic or phonetic variables. A significant advantage of functional data analysis is that it augments the highly abstract and impressionistic Autosegmental-Metrical analysis of intonation with quantitative, empirically testable models of tunes, allowing comparisons of large numbers of pitch curves of whole utterances or their parts and facilitating the study of melodic variability, co-occurrence of patterns of tone combinations in melodies, and their frequency of occurrence.
Tenth-order polynomials (2) were then fitted to the f 0 contours using the GNU Octave/Matlab polyfit function (Eaton et al., Reference Eaton, Bateman, Hauberg and Wehbring2019).
Tenth-order polynomials were used to fit the f 0 contour of utterances that may be long, with up to nine peaks and troughs (e.g., Figure 2 top). That was sufficient for this dataset; in longer utterances with more than nine peaks and troughs, an even higher-order polynomial could be used.Footnote 4
An example of a tenth-order polynomial fitted to the f 0 contour of an utterance. Top: the smooth modeled curve is superimposed on the observed curve, which is characterized by rapid pitch perturbations, some due to consonantal onsets or offsets. Note the two voiceless stretches in the observed data at around 50 and just before 100 cs. Bottom: The modeled f 0 maxima and minima locations are indicated by stars at the relevant times.
Top: Praat waveform with a pitch track exhibiting several octave errors. Bottom: The observed pitch track (circles), the modeled curve fitted to the pitch track (dashed curve) and the difference between observed data and polynomial model (solid grey line). Such octave errors are indicated by a spike in the difference signal (solid grey line) reaching either of the two faint grey horizontal dashed lines (showing a difference of ±12 semitones). The pitch track shows three octave jumps downwards at around 10, 20, and 70 cs. The large jump upwards of 20 semitones at around 35 cs is a 12-semitone restoration of the previous pitch tracking error, added to a genuine f 0 movement of 8 semitones. The jump upwards at around 75 cs is a return from the previous error at around 70 cs.
Fitting a specific polynomial function to the data also permitted us to find the peaks and troughs in the f 0 contour analytically, by differentiating (2), since they lie at points where its first derivative (3) is zero.Footnote 5
The roots (values of t at which df 0/dt = 0) were found using the GNU Octave/Matlab function real(roots(polyder(a))). These roots provide the times of all the maxima and minima (peaks and troughs) of the intonation contour (Figure 2 bottom). Putting these times back into equation (2) gives the f 0 of those peaks and troughs.
Since there are nine such turning points in a tenth-order polynomial, we manually selected the first local minimum after the start of the nuclear vowel in each continuation rise for the alignment comparison. As this local minimum is present in all the three varieties, this choice ensures crosslinguistic comparability. We determined the alignment (τ) of this local minimum to a segmental landmark, the end of the nuclear vowel; specifically, τ = t(min f 0) – t(V end). τ > 0 means that the trough follows the end of the nuclear vowel (Turkish pattern) and τ < 0 means that the trough precedes the end of the nuclear vowel (Athenian pattern).
Thus, polynomial modeling enables us to calculate very precisely the location of peaks and troughs in the f 0 track. Prior work on intonation has often found it difficult to estimate the location of such turning points due to the presence of voiceless stretches or microprosodic perturbations (e.g., the voiceless stretches in Figure 2), finding recourse instead in specially designed laboratory utterances containing mostly sonorant segments. Simply picking maxima and minima of observed f 0 is a rather questionable and inexact method (Kochanski, Reference Kochanski2010). The location of a high or low f 0 “target” may coincide with a portion of voicelessness in the speech signal, and the observed f 0 contour will not have a measured value at such a point. In contrast, the method used here is able to infer an estimate of the peak or trough location and its modeled f 0 value even during intervals of voicelessness.
Modeling f 0 in the Region of Interest/continuation rise portions.
The Region of Interest, as defined in Identification of utterances containing continuation rises section, contains from one to three syllables, depending on the variety and stress position (antepenultimate, penultimate, or final). To characterize similarities or differences in the overall shapes of the continuation rises in the Region of Interest, we visually inspected the shape of f 0 in this region. The most complex shape involved two peaks and a trough, and therefore the f 0 in this region was modeled in further detail using fourth-order polynomials, an order of polynomial that is necessary and sufficient for a model that has three extrema.
We then modeled the normalized f 0 data using polynomial basis functions, following Grabe et al. (Reference Grabe2007). This process converts discrete data points (f 0 values) into a smoothly varying, continuous function, that is,
for the fourth-order case (Figure 4), one among various possibilities. The values of constants a 0 to a 4 were found using the GNU Octave/Matlab polyfit function.
Fourth-order polynomial fitted to the region of interest of an AMG continuation rise, the f 0 contour from the beginning of the nuclear vowel to the end of the utterance. Above: the smooth modeled f 0 curve (dashed line) is superimposed over the observed data (continuous line). Below: The same fitted curve with axes normalized to the interval [−1, 1].
Disregarding the error term ɛ, the modeled f 0 function in (4) was then converted into the corresponding form (5), the best-fitting sum of Legendre polynomials.
This transformation has the benefit that the c n coefficients of each term are orthogonal, unlike the a n coefficients of an ordinary polynomial such as (4). Low-ranking terms of a polynomial pick out slowly varying properties, and higher-ranking terms pick out successively more rapidly varying properties. Legendre polynomial L0 models the overall level or height (roughly, the average) of the delimited portion of the data, L1 models the slope of that extract, L2 fits a parabola to the data, L3 models the data as an up-down-up (or down-up-down) wavy shape, and L4 as a more complex wavy m- or w-shape. If the sign of the respective c n coefficient is inverted, those components of the pattern are flipped upside down about the horizontal axis (see Grabe et al. [2007] for further details).
We refer to the coefficients of the lowest four components as AVERAGE (i.e., c 0), SLOPE (c 1), PARABOLA (c 2) and WAVE (c 3) (see Grabe et al. [2007]), and coefficient c 4 as M-OR-W. The orthogonality of these components, coupled with the simplicity of their shapes (unlike, for example, Principal Components), makes the physical interpretation and particular contribution to the overall f 0 contour quite straightforward and intuitive. Other basis functions are of course possible, but we consider the independent prosodic transparency of these components to be an appealing feature of this methodology.
Legendre polynomials take values in the range [1, −1], so corrected f 0[semitones] was scaled so that the whole f 0 contour lies within the interval [1, −1], with 0 as the utterance mean and the greatest positive or negative deviation from the mean being 1 or −1, as the case may be:
As a consequence of this step, the normalized average f 0 of every utterance = 0; f 0 [normalized] > 0 means “higher than average f 0”, f 0[normalized] < 0 means “lower than average f 0” (see Figure 4, lower panel, for an example).
The c n coefficients are calculated from the a coefficients through a set of simple formulae, the details of which vary according to the order of the polynomial.Footnote 6 The normalization or scaling needed for the transformation to Legendre polynomials reduces interspeaker variation, to some extent. In particular, it reduces individual differences in mean f 0, f 0 range, and speech rate. But we are not interested in those parameters in this study; the normalization and scaling do not affect interspeaker differences in the shape of the intonation contours, represented by the c n coefficients, and we examine the relative timing of the pitch peaks and troughs using the a n coefficients of the standard polynomial (4), prior to scaling.
Figure 5 presents orthogonal polynomial analysis of prototypical examples of Athenian and Turkish continuation rise contours, showing each of the five polynomial terms independently. The same scale is used for both varieties in order to show their differences in magnitude. The Athenian example, at left, is a typical L* H− contour with a slight initial descent, a low plateau, and a large final rise. The magnitudes of the M-OR-W and WAVE components are therefore almost 0, and those components are almost flat. PARABOLA and SLOPE are much larger; the size of the PARABOLA coefficient c 2 gives a broad and rather shallow bowl shape. The strong overall rising profile of this intonation contour is mostly determined by the positive SLOPE component.
Fourth-order orthogonal polynomial components of typical examples of Athenian and Turkish continuation rise contours.
The Turkish example (Fig. 5 right) is quite different, a typical rise-fall-rise, with a slight deceleration/flattening off at the very end. Consequently, the WAVE component is large, more than ten times the magnitude of the WAVE component in the Athenian example. It is positive, meaning that it is a rise-fall-rise. The PARABOLA component is the largest and is over eight times larger than in the Athenian example, giving this component a narrower trough in Turkish than in Athenian. The M-OR-W component is negative, giving it two peaks rather than two troughs (M-like rather than W-like); the second of those peaks captures the slight flattening-off of the final rise. The AVERAGE component in the Turkish pattern is higher than in the Athenian pattern, because Turkish has two large peaks whereas Athenian has a long low plateau that is mostly a few semitones below the average.
To appreciate the individual contributions of the five components further, appendix B provides further illustrations of the same two examples in which each component is set to zero, one by one.
Hypotheses
Four hypotheses were tested. H1 (geographic region): based on impressionistic analysis, no differences are expected in the intonation patterns of the continuation rise tune between the regional varieties of Turkish. H2 (diachronic development): based on Baltazani et al. (Reference Baltazani, Przedlacka, Coleman and Minematsu2020), the intonation of AMG speakers is expected to display a mixture of Athenian-like and Turkish-like patterns. In addition, H3: first-generation AMG speakers are expected to make more use of Turkish-like patterns and less use of Athenian-like patterns than the subsequent generations. H4: similarities between AMG and Turkish are expected to diminish with each subsequent generation.
Based on the prior literature on continuation rises in Athenian and Turkish, we expect any influence of Turkish on AMG to be manifested in the shape of the modeled curves, through similarity in the polynomial coefficients. For example, because Turkish displays a rise-fall-rise f 0 movement while Athenian displays a simple rise from a trough, we expect Turkish-like continuation rises to have a positive WAVE coefficient that models the data as an up-down-up wavy shape and Athenian-like ones to have a WAVE coefficient around zero, that is, no such wavy shape, though we would expect Athenian-like continuation rises to have a positive SLOPE. In addition, we expect the alignment of the trough in the Region of Interest to be relevant: the nuclear accent in Athenian is typically realized as a trough aligned within the nuclear vowel (τ < 0), while the H*+L nuclear pitch accent in Turkish is realized with an H* tone within the nuclear vowel followed by the trough, a trailing L tone, which typically occurs after the end of the nuclear vowel (τ > 0).
Statistical analysis
Because there were relatively few archival recordings of first generation AMG speakers, we pooled data from archival recordings made in the 1920s and 1930s and contemporary ones made in the 2000s, having first checked that there were no significant differences between the two types. Baltazani et al. (Reference Baltazani, Przedlacka, Coleman and Minematsu2020) tested the hypothesis that the influence of Turkish would be found to be greater in the archival than in the contemporary recordings. Turkish influence was expected to have diminished in contemporary recordings due to longer contact with Greek (eighty years between 1930 and 2011) and absence of contact with Turkish. A Mann-Whitney U test revealed no significant difference in the curve shape (e.g., for c 3, U = 13,452, p = .518; for c 2, U = 12,656, p = .129) or in the alignment (U = 13,317, p = .427) between archival recordings (mean ranks c 3 = 173, c 2 = 166, alignment = 184) and contemporary recordings (mean ranks c 3 = 181, c 2 = 184, alignment = 175).
For the geographic region comparison, six Kruskal-Wallis one-way analyses of variance (Kruskal & Wallis, Reference Kruskal and Allen Wallis1952) tested for differences between the Turkish regional varieties in the five polynomial coefficients (c 4 to c 0) and trough alignment (τ).
For the diachronic development hypothesis, we used a Gaussian mixture model (e.g., Marin et al., Reference Marin, Mengersen, Robert, Dey and Rao2005), which formalized the assumption that the distributions of shape coefficients in the AMG data are either Athenian-like (with a probability of λ) or Turkish-like (with a probability of 1−λ). As ANOVAs and frequentist linear mixed effects models are more widely used in phonetics research, the choice of a (Bayesian) Gaussian mixture model may warrant justification. The main reason is that we were not only interested in whether the coefficients varied by generation or dialect (as an ANOVA would allow us to detect). To test hypothesis 4, we also wanted to determine the relative proportions of Turkish-like and Athenian-like utterances in AMG in each generation, since we had previously found that our first generation of AMG speakers used a mixture of Athenian-like and Turkish-like patterns (Baltazani et al., Reference Baltazani, Przedlacka, Coleman and Minematsu2020).
In consequence, the distributions of coefficients for every AMG speaker were assumed to be a mixture of an Athenian-like component and a Turkish-like component, scaled by the mixture proportion λ, as illustrated in Figure 6 for different examples of mixture distributions with different mixture proportions λ (left, center, and right panels) and different distances between the modes of the two components that constitute the mixture (upper and lower panels). Figure 6 also illustrates that not all mixture distributions are evidently bimodal: when the two mixture components (dotted and dashed lines, respectively) are sufficiently far away from each other relative to their variance, the resulting mixture distribution does have two clearly visible modes regardless of the mixture proportion parameter λ (panels A-C). In contrast, when the mixture components are close, with significant overlap between them, there might be only one local maximum in the mixture distribution (panels D and F). The presence of distinct modes depends on the mixture proportion λ and the distance between the distributions.
Probability density functions of hypothetical mixture distributions (solid lines), and their component distributions (dotted and dashed lines), for different mixture parameters λ (columns) and different distances between the modes of the mixture components (rows).
While the distributions of some coefficients for the AMG data were bimodal (as shown in Figure 9 below), similar to those in panels A-C in Figure 6, some had a single local maximum. Even in such cases, mixture proportions can be estimated if the distributions of the mixture components are known. Thus, we modeled the distribution of AMG coefficients as a mixture of Athenian-like and Turkish-like distributions. To this end, we assumed that the coefficients for Athenian and Turkish tunes were normally distributed with means μA, μT and standard deviations σA, σT, while AMG followed a mixture of the distributionsFootnote 7 N(μA, σA) and N(μT, σT) with different mixture proportions λg for each generation g.
We further assumed that λg represents the proportion of Athenian-like utterances in a given generation rather than the proportion of Athenian-like speakers. This is because most AMG speakers produced continuation rises with both Athenian-like and Turkish-like patterns, as illustrated in the two examples in Figure 7, which were produced by the same speaker.
Examples from the same AMG generation 1 speaker producing a Turkish-like (top) [istoˈria] “…story…” and an Athenian-like (bottom) [taˈmeri] “The places” continuation rise. Rectangles indicate the nuclear vowel, transcribed in bold.
A more detailed description of the model structure is presented in appendix C.Footnote 8 All free model parameters (μA, μT, σA, σT, λ1, λ2, λ3, λ4) were estimated from the data using a Bayesian model implemented in brms (Bürkner, Reference Bürkner2017) and rstan (Stan Development Team, 2022a, 2022b) in R (R Core Team, 2021) with by-speaker random effects for the means of the speaker-specific Athenian-like and the Turkish-like coefficient distributions μA and μT, accounting for the fact that each speaker's scores could be systematically lower or higher than the group averages.
To establish the validity of the Gaussian mixture model, we compared it to a baseline model for each coefficient (c 0 to c 4), and τ, the trough alignment. As a baseline, we used Bayesian linear mixed-effects models (e.g., Gelman & Hill, Reference Gelman and Hill2006; Vasishth & Nicenboim, Reference Vasishth and Nicenboim2016) with generation, dialect, and their interaction as fixed effects, and by-speaker random intercepts. A detailed description of the model structure is presented in appendix D. We compared the models based on their expected log pointwise predictive density (elpd), calculated using PSIS-LOO CV in the R loo package (an implementation of Vehtari, Gelman, & Gabry, Reference Vehtari, Gelman and Gabry2017). The elpd statistic provides an estimate of a model's out-of-sample performance and thus implicitly penalizes excessive model flexibility, thus putting models of different complexity on an equal footing.
Results
Geographic region comparison
There was very strong evidence of differences between the Turkish geographic varieties for four coefficients: M-OR-W (c 4; χ2(4)= 105.31, p < 0.001), PARABOLA (c 2; χ2(4)= 89.46, p < 0.001), SLOPE (c 1; χ2(4)= 14.26, p = 0.007) and AVERAGE (c 0; χ2(4)= 101.93, p < 0.001), adjusted using the Bonferroni correction, but no difference between the varieties for the WAVE coefficient c 3 and the alignment parameter τ.
Each group's mean and median values are also important for the interpretation of these results. As mentioned in the section Modeling f0 in the Region of Interest, the sign of each coefficient is important because the patterns of coefficients with negative values are flipped upside down. The median values for each coefficient in the Turkish data (Fig. 8) have the same sign across the varieties, indicating no difference in shape for the parameters, despite the significant differences in their magnitudes. In view of this, in combination with the fact that all these tokens have the same meaning of continuation rise, we interpret the results of statistical significance as phonetic microvariation. That is, the same phonological pattern for the continuation rise tune is displayed for every coefficient in all varieties (corresponding to the H*+L H− tune), though there are fine phonetic differences, for example, in the breadth of the curvature or the steepness of the slope.
Comparison (from top left to bottom right) of M-OR-W, WAVE, PARABOLA, SLOPE, AVERAGE coefficients and trough alignment in continuation rises produced by Turkish speakers of five different regional varieties (Turkish speakers in the Doegen archive were from the Ottoman Empire, in present-day Romania).
For the subsequent analysis, data from all five varieties were grouped together because no phonological differences were found between them.
Diachronic comparison
Figure 9 shows the distribution and variation of the coefficients and trough alignments for each generation in AMG, Athenian, and Turkish (in each panel, upper, middle, and lower rows, respectively). Vertical dashed lines superimposed on the histograms correspond to the medians of the observations for Athenian and Turkish. The histograms for AMG are overlaid with both the Athenian and Turkish median lines to indicate the approximate position of the expected modes if the mixture were bimodal.
Histogram of coefficients c 1 to c 4 and L tone alignment τ by dialect and speaker generation. Vertical dashed lines correspond to the medians of the observations among speakers of Athenian (light grey) and Turkish (dark grey) over all generations. The histogram for AMG (mid grey) is overlaid with both median lines, for reference.
In Athenian and Turkish, the coefficient medians, for all generations, confirm the impressionistic descriptions of the tunes in 2.1. The positive SLOPE coefficient c 1 for Athenian indicates a rise, but the 0 for Turkish is the average of a rise-fall-rise, the shape of which is captured by other parameters. The positive PARABOLA coefficient c 2 for Turkish models the data as an accelerating f 0 movement, and the 0 for Athenian indicates that this parameter does not contribute much to the contour, mostly a low plateau. The WAVE c 3 is positive for Turkish, modeling the data as a rise-fall-rise f 0 movement, but it is close to 0 for Athenian, indicating that it is not so wavy: it is a plateau plus a rise. The median of the M-OR-W coefficient c 4 is negative in Turkish, reflecting the fact that it has two peaks: an H accent on the stressed vowel followed by a trough and then another peak at the end of the utterance. The median M-OR-W is close to 0 in Athenian as it does not have two peaks. The median alignment parameter τ is negative for Athenian, showing that the L tone is aligned before the end of the stressed vowel (approximately twenty cs), and is positive for Turkish as the L tone is aligned approximately twenty cs after the end of the stressed vowel (Fig. 9).
The AMG histogram reveals a shift from greater use of Turkish-like patterns to greater use of Athenian-like patterns over the generations. The distribution of the SLOPE c 1 coefficient (top row in Fig. 9), has a mode in between the Turkish and Athenian medians. Figure 10 shows that the median SLOPE for AMG changes over the four generations, becoming progressively more Athenian-like. The next two rows in Figure 9 show that the PARABOLA c 2 and WAVE c 3 coefficients have a bimodal appearance in the first-generation. One peak of the AMG distribution is near to the Athenian median and the other is near to the Turkish median. Over the generations, the Turkish-like peak becomes smaller, so that these distributions have an increasingly unimodal appearance as the proportion of Turkish-like values seems to decrease, a pattern like the one modeled in Figure 6F. The M-OR-W coefficient c 4 also changes across the generations: the AMG mode always coincides with the Athenian mode, but the AMG distribution is substantially wider than the Athenian with a tail toward Turkish values, a pattern as in Figure 6D. The Turkish-like aspect of this tail in the first generation is reduced in subsequent generations.
Estimates of λ, the proportion of Athenian-like utterances, for each generation. Circles indicate the median of the posterior distribution, thin horizontal lines represent the 90% credible intervals of each parameter estimate, while thick horizontal lines indicate 60% credible intervals.
The bottom row of Figure 9 gives the visually most striking finding: the distribution of the L tone alignment τ is clearly bimodal in the first three generations, the two peaks in the first generation almost coinciding with the medians of Athenian and Turkish, as in Figure 6B. For this parameter as well, the proportion of Turkish-like values decreases over the generations, giving rise to a more Athenian-like distribution, similar to Figure 6F.
In view of the above, we compared a Bayesian analysis of the Gaussian mixture model with a baseline linear mixed effects model for all five dependent variables as described in 2.6. The results of the model comparison using PSIS-LOO CV are presented in Table 2. They show that the mixture model provided a better description of the data than the linear mixed effects model for all parameters. The mixture model only weakly outperformed the baseline model for c 1 but showed a substantial improvement over the baseline for the rest of the parameters.
Results of the model comparisons between (i) the baseline linear mixed effects model and (ii) the Gaussian mixture model for the coefficients c1−c4, and τ using PSIS-LOO CV estimates of elpd (Vehtari et al., Reference Vehtari, Gelman and Gabry2017). Larger elpdLOO values indicate more parsimonious models. Positive ΔelpdLOO values indicate that the Gaussian mixture model provides a more parsimonious account than the baseline linear mixed-effects model
In the Gaussian mixture model, estimates of the mixture parameter λ (proportion of Athenian-like values, expressed as a percentage) for the remaining parameters are shown in Table 3 and Figure 10. Several trends are revealed for all parameters except SLOPE c 1. First, the median estimates of λ are very close to Turkish values (less than 7% Athenian-like) in generation 1. Second, in generation 2, the median estimates of λ are gradually approaching Athenian (11% - 21% Athenian-like). Third, the median estimates of λ in generation 3 are over 68% Athenian-like. Among all the parameters we examined, only c 1 showed higher Athenian-like values than Turkish-like values. Yet, the rate of this similarity increased gradually from the first-generation to the-fourth generation as well.
Mean estimated proportion (λ) of Athenian-like parameter values in AMG by generation (left column) and 90% credible interval (CI; right column)
All in all, these results reveal a consistent pattern of a change over the generations in the realization of continuation rise tunes. The strong similarity to Turkish in AMG generation 1 weakens over the generations, with Athenian characteristics becoming predominant in generations 3 and 4.
Discussion
In this paper, we examined how long contact effects in intonation persist after contact has ceased. We compared the f 0 patterns in continuation rise tunes of Athenian Greek, Turkish, and Asia Minor Greek (AMG) across four generations. We modeled the sampled f 0 data using Legendre polynomial basis functions to characterize similarities or differences between these varieties in the final stretch of the continuation rises, comprising the nuclear pitch accent and the edge tones. This modeling allowed the analysis of a fairly large dataset of approximately three thousand continuation rise utterances from diverse corpora containing mostly natural speech in conversations and narratives.
Using fitted polynomials for the analysis and comparison of the tunes in the three language varieties captures simple properties of the fitted curves and has an easily understood, cognitively plausible interpretation, such as the average f 0, whether the contour is generally rising or falling, the size and location of intonation peaks and troughs, as well as the number of peaks and troughs in the intonation contour. Furthermore, the functional data analysis can be related to the well-established Autosegmental-Metrical analysis of intonation: the derivative of the quartic polynomial used here has three roots, corresponding to the time-points of the two peaks and the trough, which allow us to estimate their corresponding f 0 more reliably than through the observed peaks and troughs, which are susceptible to noise and mistracking, especially if they occur during voiceless intervals.
The results of the diachronic comparison across four generations of Turkish and Athenian speakers confirmed the realization of the continuation rise tunes reported in the literature for these two languages. The Turkish continuation rise tune is reported as a rise-fall-rise H*+L H−, the H* tone in the H*+L nuclear pitch accent occurring within the nuclear vowel. In our data the median alignment τ of the trailing L tone is 200 ms after the nuclear vowel offset, and the H− phrase accent lies at the right edge of the phrase. The negative median M-OR-W c 4 coefficient in our modeling reflects the fact that the Turkish tune has two peaks, the positive WAVE c 3 captures its rise-fall-rise f 0 movement, and the positive PARABOLA c 2 captures a general rising f 0 movement. The Athenian tune also ends in an H− phrase accent but has a L* nuclear pitch accent that is aligned on average 200 ms before the end of the nuclear vowel. The positive SLOPE coefficient c 1 for Athenian indicates that, in general, it rises while the low plateau from the nuclear vowel to the phrase edge is reflected in the PARABOLA c 2, WAVE c 3, and M-OR-W c 4 coefficients, all of which are close to 0, indicating that the Athenian contour lacks a wavy shape, and that it does not have two peaks.
As for AMG, a previous analysis of this tune in two generations of speakers showed a dual pattern of the L tone alignment, one Athenian- and one Turkish-like. Here we established a more complete picture by showing that the mixed pattern of the data is true for all five parameters through a Gaussian mixture model. The bimodality of the L tone alignment found in the speech of the first-generation AMG speakers decreased in each subsequent generation toward a more Athenian-like alignment. A similarly diminishing proportion of Turkish-like patterns was revealed for the polynomial coefficients c 1 to c 4. While in generation 1 the mixture coefficient λ is less than 8% Athenian-like for four of the five parameters, in generation 2 there is a greater proportion of Athenian-like coefficient values, and in the two youngest generations the greatest proportion (almost 100%) is Athenian-like.
The Bayesian approach gave us the flexibility to define a mixture model that expresses our hypotheses while allowing us to account for speaker-specific deviations from the average in the form of by-speaker random effects (e.g., Gelman & Hill, Reference Gelman and Hill2006; Vasishth, Nicenboim, Beckman, Li, & Kong, Reference Vasishth, Nicenboim, Beckman, Li and Kong2018). This approach enabled us to encode the assumption that the distribution of the AMG coefficients is a mixture of an Athenian-like and a Turkish-like Gaussian distribution, and, at the same time, estimate the mixture parameters and the uncertainty associated with them in datasets with unequal numbers of observations per speaker. For AMG speakers, all coefficients were better described by a mixture of the respective Turkish-like and Athenian-like distributions than by simple linear mixed effects models.
Contact between Greek and Turkish resulted in phonological transfer of the pitch accent found in Turkish continuation rises into AMG. The AMG speakers alternated between the Turkish and the Greek tunes in a way similar to what is reported in Queen (Reference Queen2012), albeit in different proportions depending on the generation. No phonetic changes such as the delayed peaks reported in O'Rourke (Reference O'Rourke2012) and Elordieta and Calleja (Reference Elordieta and Calleja2005) were revealed in the tunes we examined. That is, when the tune was produced with the Athenian L pitch accent, the alignment of the trough was Athenian-like, that is, within the nuclear vowel. Similar results were found for the Turkish-like tune. It is not yet clear whether these two patterns of continuation rise differ in pragmatic interpretation or whether they are codeswitched equivalents. We leave such questions for future investigation.
This paper demonstrates intonational effects of language contact, a generally under-studied area, since so far the knowledge about the results of contact has mainly relied on morphosyntactic or segmental phenomena. We have shown that prosodic characteristics of Turkish have persisted in AMG for close to a century after the cessation of contact, which we attribute to the strong sense of ethnolinguistic identity in the AMG-speaking community. However, usage of the Turkish-like intonation pattern has diminished over the generations due to a complex mixture of factors such as the prestige of Athenian Greek, the stigma that some attach to AMG, and the fact that the younger generations increasingly have less exposure to their AMG heritage variety, at least the Cappadocian variety examined here, than earlier generations did.
Competing interests
The authors declare none.
Acknowledgments
We would like to thank Professor Mark Janse, Dr. Petros Karatsareas, Dr. Dimitris Papazachariou, and the Academy of Athens for permitting us to use their sound recordings of AMG; the Lautarchiv of Humboldt University for Turkish recordings; and native speaker research assistants Mr. Lazaros Kotsanitis and Ms. Clio Takas for their help with annotation of AMG and Athenian utterances respectively. The support of the Economic and Social Research Council (UK), grant ES/R006148/1, is gratefully acknowledged.
Appendix A. Sources of audio recordings
The tables below present the distribution of tokens by source. A star next to the token number indicates sources where the speaker's exact age was not known and where their approximate age and classification to one of the four generations was inferred from characteristics of the speaker's appearance in videos or information about their career. As can be seen in the tables below, a number of tokens were extracted from films,Footnote 9 after having been judged by a native speaker to be natural-sounding.
Athenian Greek
Asia Minor Greek
Turkish
Appendix B. Independent contributions of the five orthogonal polynomial components
In the section Modeling f 0 in the Region of Interest we presented an orthogonal polynomial analysis of prototypical examples of Athenian and Turkish continuation rise contours. Figure 5 showed the contribution of each of the five polynomial terms independently. In order to appreciate the individual contributions of the five components further, Figure B1 shows how the overall polynomial fit in the same two examples is affected when each component is set to zero, one by one. In the Athenian example (Fig. B1, left) setting c 4, c 3, or c 0 to 0 has very little effect on the overall fit (those panels all have a low plateau with a final rise), because those coefficients were close to 0 in any case. Setting c 2 to 0 results in the fit losing its very broad PARABOLA component, so that the fitted contour is now rising rather than gently falling at the start. Since the SLOPE (c 1) component is doing a lot of the heavy lifting in this analysis of the Athenian contour, setting c 1 to 0 results in the fitted curve mostly losing its upward-rising profile at the end.
Fourth-order orthogonal polynomial analysis of typical examples of Athenian and Turkish continuation rise contours (top left panels); asterisks: measured f 0, dashed line: fitted polynomial. The effect of setting each component to zero is shown in each of the other five panels, for each of the two examples.
In the Turkish example (Fig. B1, right), setting the M-OR-W component c 4 to 0 eliminates the two distinct peaks seen in Figure 5. Setting c 3 to 0 eliminates the initial rise, as this WAVE component contributes strongly to the rise-fall-rise contour of the fitted f 0 pattern. In both of these cases, what remains is a falling-rising bowl-like pattern which does not model very well the much more dynamic rise-fall-rise (with final tail-off) of the Turkish pattern. Setting c 2 to 0 results in a fitted curve that does show those two peaks, but now the trough between them is no longer so deep, because of the removal of the PARABOLA component. Setting c1 to 0 has very little effect on the overall fit as it was close to 0 (−0.07) anyway. Setting c 0 to 0 has no effect at all on the overall shape of the fitted curve, as this is just a constant term; the y-axis scales of the two lower-right panels differ by about 2.4 (c 0 = 1.6654), but the shapes are otherwise similar.
Appendix C. Full model specification for Gaussian mixture models
The Gaussian mixture model was based on the assumption that the distributions of the coefficients c 0 to c 4 as well as τ are a mixture of Turkish-like values and Athenian-like values. As formalized in Table C1, we assumed that for each dependent variable, all Athenian observations y S for speaker S are normally distributed with a subject-specific mean $\mu _{A_S}$
and standard deviation σ A, and that the subject-specific means $\mu _{A_S}$
follow a normal distribution around the grand mean μ A with standard deviation σ S (see Table C1 and equation C1). For Turkish, we similarly assumed that each speaker's observations are normally distributed with mean $\mu _{T_S}$
and standard deviation σ T, while subject-specific means $\mu _{T_S}$
follow a normal distribution around the grand mean μ T with standard deviation σ S.
Key assumptions of the Gaussian mixture model of AMG intonation
We further assumed that for each generation g of AMG speakers, each speaker S's observations follow a mixture of the Athenian and Turkish distributions, with λg representing the probability of an Athenian-like observation. This amounts to assuming that each AMG speaker of generation g is capable of producing Athenian-like utterances with probability λ g and Turkish-like utterances with probability 1 − λ g. We further assumed that the subject-specific deviation from the grand mean of the dialect (Turkish and Athenian) is the same for both dialects among AMG speakers.
We assumed that λ g was affected by generation in the way specified in equation C2. We used successive differences contrasts (e.g., Venables & Ripley, Reference Venables and Ripley2002) G (2−1), G (3−2), G (4−3) for the factor generation such that $a_\lambda$
has an interpretation as the average log-odds of producing an Athenian-like utterance across all generations, while b λ,(2−1), b λ,(3−2), b λ,(4−3) represent successive differences in the log-odds of an Athenian-like utterance between generations 2 and 1, 3 and 2, and 4 and 3. Table C2 shows the successive differences contrasts for generation.
Successive differences contrast matrix for generation
All parameters were given weakly informative prior distributions. The same priors were used for all dependent variables. Tables C3 and C4 list the priors for all parameters in the model.
Prior distributions for all model parameters except σ S.
Prior distributions for model parameter σ S.
Appendix D. Full model specification for linear mixed-effects models
The baseline linear mixed-effects models for all dependent variables included fixed effects for generation, dialect, as well as their interaction, and by-speaker intercept as stated in the brms model formula in D1. Generation and dialect were represented using successive differences contrast matrices given in Tables C2 and D1 (e.g., Venables & Ripley, Reference Venables and Ripley2002). Tables D2 and D3 list the prior distributions for the fixed effects and random effects of the model respectively.
Successive differences contrast matrix for dialect
Prior distributions for all model parameters except σ S.
Prior distributions for model parameter σ S.
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