Secondary stress , intensity and fundamental frequency in Brazilian Portuguese

This paper investigates whether values of acoustical correlates of pretonic syllables adjacent to the one(s) perceived as bearing secondary stress could predict such perception in Brazilian Portuguese (BP) data. In order to pursue this goal, a comparison is made between pretonic syllables perceived as bearing secondary stress and those perceived as not bearing it. According to the results, obtained by application of statistical analyses, it is possible to claim that variation in intensity and in F0 in syllables perceived as bearing secondary stress, as well as in adjacent syllables, can be taken as a robust correlate for data perception regarding secondary stress placement in BP. Variation in intensity and in F0 in syllables perceived as bearing secondary stress and variation in intensity and in F0 in the other adjacent pretonic syllables seem to be complementary information for the perception of secondary stresses by BP speakers. The results point to relevant questions for further work concerning the rhythmic and intonational organization of Brazilian Portuguese. Journal of Portuguese Linguistics, 11-2 (2012), 51-67 ISSN 1645-4537 52 F. F.-Svartman, M. B. M. Abaurre, V. A. G. López & M. C. C Bianchi


Introduction
Primary and secondary stresses define prominent syllables which play an important role in the construction of language rhythmic units.
According to Hulst (1997), primary and secondary stresses must be analysed differently: primary stress is part of the lexical information of the word and secondary stress is assigned post-lexically.While there is a natural relationship between secondary stress and rhythm, primary stress is assigned locally, in the lexicon, and is not determined by rhythm (although it plays an important role in rhythmic organization, since primary and secondary stresses interact in speech).
1 Primary stress is categorical and cannot vary across speakers and language varieties, since its position is lexically fixed and affects the meaning of words, as illustrated by the examples of Portuguese in (1): (1) a. (eu/ele/ela) saBIa b. sabiÁ c.SÁbia 2 "(I/he/she) knew" "type of Brazilian bird" "wise (fem.gender) " On the other hand, secondary stress is variable; its attribution is not categorical, but associated with the rhythmic structure of languages.For instance, different secondary stress implementations are possible in a word as paralelepípedo "parallelepiped; paving stone" in Portuguese, but these variations do not affect the meaning of the word: (2) a. PAraLElePÍpedo 3 b.PAralelePÍpedo c. paraLElePÍpedo According to phonological analyses presented in works as Collischonn (1993Collischonn ( , 1994)), Abaurre & Galves (1998), Frota & Vigário (2000) and Sandalo, Abaurre, Mandel & Galves (2006), Brazilian Portuguese (henceforth, BP) favours the construction of binary rhythmic units in the implementation of secondary stresses.
1 For other authors, working within the framework of Metrical Phonology, the primary stress in BP is assigned by a rule in one of the strata of the lexical component (cf.Bisol, 1992Bisol, , 2000;;Massini-Cagliari, 1995;Lee, 1994;Wetzels, 1997). 2 The syllables with capital and bold letters correspond to the syllables bearing the primary stress. 3The syllables with capital letters correspond to the syllables bearing secondary stress.
Such works have focused exclusively on the phonetic realization of syllables perceived as bearing secondary stress, and, based on experimental data consisting of isolated sentences, the authors claim that no robust acoustical correlate(s) can be associated to secondary stresses perceived by BP speakers.However, given the suprasegmental nature of secondary stress, our hypothesis is that its acoustical correlates can be found predominantly in pretonic syllables adjacent to the one(s) that is(are) linguistically (e.g.rhythmically) assigned as bearer(s) of secondary stress within the prosodic word (PWd). 4aking into account our hypothesis, this paper aims to investigate whether there is a dependence relationship, in the statistical sense, between the acoustical correlate values of the syllable(s) perceived as bearing secondary stress(es) and the acoustical correlate values of adjacent pretonic syllables in the PWd domain, based on data from BP.Therefore, our goal is to investigate whether the acoustical correlate values of pretonic syllables adjacent to the one(s) bearing secondary stress could be taken as predictive values with respect to the values of these last syllables. 5In order to pursue this goal, a comparison is made between pretonic syllables perceived as bearing secondary stress and those perceived as not bearing it.The acoustical correlates specifically investigated in this paper are intensity and fundamental frequency (F 0 ). 6he paper is organized as follows: in section two, we present our data and the adopted methodology of linguistic and statistical analyses; in section three, we present the results of the extraction of intensity and F 0 values from the syllables perceived as bearing secondary stress by BP native speakers and from the other pretonic syllables, as well as the results of the statistical modelling of these two types of values, in order to confirm or discard our hypothesis; and in section four, we present our conclusions.

Speech material
The speech material used in this research is composed of digital recordings of readings of a chronicle, called Complicabilizando, published in a weekly Brazilian magazine (Ricardo Freire, Xongas.Época.Edition 275, 25/08/2003) by 5 BP native speakers, namely: ACS -speaker (1); CTYspeaker (2); FMD -speaker (3); LM -speaker (4); and PA -speaker (5).The BP informants all come from the state of São Paulo, and are speakers of the so-called "paulista dialect" from the interior of the state.They are all from the same age group and educational background (university students).

Methods
The methodology used in this work includes the following steps: (i) presentation of the speech material to BP native speakers for perceptual identification of secondary stress occurrences; (ii) analysis of the acoustical signal, in terms of intensity and F 0 of syllabic nuclei preceding the stressed syllable of PWds identified as bearing of secondary stresses by BP speakers; and (iii) application of statistical analyses to the data.
The auditory perception of secondary stress occurrences was conducted by two native speakers of the paulista dialect of BP (namely, AP and JRM, linguistic students specifically trained on the identification of secondary stress perception, who share the same age group and educational background with the 5 speakers).These two judges worked together in the identification of secondary stresses and, as a result, only one transcription was produced for each reading event.In cases of disagreement about the occurrence of One might be tempted to apply to duration values the same statistical analysis used here for F 0 and intensity.Results thus obtained might the interesting for the discussion concerning the rhythmic on characterization of Brazilian Portuguese as stress-timed, syllable-timed or moraic.We cannot do that, however, because the analytical tools employed in this work were devised to approach prosodic phenomena independent of segmental properties.In the case of duration, it is well known that different vowel qualities, e.g., have different intrinsic duration which would pose a problem for the normalization techniques used here.secondary stress, the judges decided on the existence or not of secondary stress after discussing their perception of the specific token.The acoustical analyses consisted of the extraction of intensity and F 0 values of syllabic nuclei preceding the syllable bearing lexical stress of PWds.For this task, we used the speech analysis software Praat. 7The intensity and F 0 values were always extracted from the more stable part of pretonic vowels, e.g., from the medial part of vowels, as illustrated in Figure 1., in which the cursor marks the approximated intensity and F 0 values of the medial part of the vowel "i" in the syllable "dis" of the prosodic word em disponibilizar "to make available".8

Data pre-processing
The values obtained from the extraction of intensity and F 0 measurements were submitted to the calculation of means.In each one of the PWds, this operation was applied to intensity and F 0 values of each type of pretonic syllables: the ones perceived as bearing secondary stresses and the other pretonic syllables.For instance, in the word deSINcomPAtiBIliZAR, 9 the F 0 mean values for the pretonic syllables perceived as bearing secondary stresses will be: and the F 0 mean values for the other pretonic syllables will be: , where S1 = "de"; S2 = "SIN"; S3 = "com"; S4 = PA; S5 = "ti"; S6 = "BI"; S7 = "li" and F0 (Si) is the fundamental frequency value of syllable "Si".The same procedure was adopted to analyze intensity.10 9 See footnotes 2 and 3. 10 In cases in which only one secondary stress was perceived in the PWd, it was considered the intensity or F 0 absolute value of the nucleus of the syllable perceived as bearing it.
Therefore, we obtained two groups of results for each speaker: (i) the mean intensity or the mean F 0 observed in the syllables perceived as bearing secondary stresses (see Figure 2 Our goal is to eliminate the "speaker effect" which is evident from the plots in Figure 2. The speaker effect is extracted in order to reveal the real process that we need to investigate. 11e extract the effect of the speaker using a random effect model (cf.Fernandes-Svartman, Abaurre & González-López, 2008), assuming fixed effects (see Chambers, 1992 for a complete explanation of the model and R--project environment at http://stat.ethz.ch/R-manual/R-patched/library/stats/html/lm.htmlfor a computational implementation and technical details).This model is presented in (1).Note that the random effect model is the simplest in the statistical sense if the objective is the standardization assuming one effect by speaker (this means 5 effects -see the complete explanation (iv) below) and one global effect (external effects -see the complete explanation (v) below) 12 .
In (1): (i) "l" represents the variable type: Y -nuclei intensity or nuclei F 0 of the pretonic syllables perceived as bearing secondary stresses; X -nuclei intensity or nuclei F 0 of the other pretonic syllables.If l =1, then, (ii) "i" represents the speaker.i = 1 denotes the ACS speaker; i = 2 denotes the CTY speaker; i = 3 denotes the FMD speaker; i = 4 denotes the LM speaker and i = 5 denotes the PA speaker.
(iv) " L " l i represents the speaker influence (or fixed effect).For example: the speaker gender, the type of production (emphatic or neutral productions), etc.
(v) "W0 l " is the independent global effect.It is dependent of external effects that produce some influence on the measures (for example: the quality of recording processes and the semiautomatic process of the extraction of intensity and F 0 values).
12 In order to normalize across speaker effects it is possible to use some linguistic standard techniques, such as in the case of the fundamental frequency used to convert from Hz to ERB scale, as noted by one of the anonymous reviewers of a previous version of this paper.The statistical technique of standardization employed in this paper aims to offer the same methodology for the standardization of different acoustical parameters modelled here: fundamental frequency and intensity. ( represents the goal random process.For example, if , l = 2, it represents the random intensity (or the random F 0 ) process of the pretonic syllables perceived as bearing secondary stress of the "i" speaker.
The real process is our goal because it is the process that could be obtained without the influence of the speaker and without the influence of conditions or quality of recording; consequently, it could be considered a good representation of the phenomenon (intensity or fundamental frequency).This model assumes that W0 l and l i L are fixed effects and could be estimated.Thus, we can concentrate the study on the relation between , where the goal processes are estimated as being W is the observed value (intensity or fundamental frequency), W0 l is estimated and l i L is also estimated.We note that when the process RTX (or the equivalent process

The next table shows the estimated global effects:
shows a decreasing (or increasing) tendency, then the process RTY (or the equivalent process ) shows the same behaviour; this allowed us to enquire about the capacity of prediction that the process , we use copula models, since copula quantifies the dependence.Furthermore, in our hypothesis, the hearer perception is considered as a discrete response, i.e., the hearer may verify or not the secondary stress occurrence.However, the possible acoustical correlates related to this perception may have a discrete or continuous nature.In our case, this hypothesis will be evaluated through continuous random variables, e.g., intensity and F 0 .This choice attributes to the copula model the adequate profile to check the hypothesis, modelling the dependence between the continuous random variables.So, no discretization of the variables is necessary for this approach, since the copula model takes their nature into consideration.In addition, it is possible that the discretization of original measures implies important information loss.If the variables had a discrete nature, other approaches, as ANOVA, discrete copula, etc., could be considered.

Dependence modelling
The copula model is a way to represent the multivariate dependence between random variables, see Rifo & González-López (2012).In general lines, the dependence between random variables could be established using the marginal distribution and the joint dependence (or copula).In particular, the copula does not look at the marginal distribution, but it looks at the joint dependence and exposes the dependence quantified by a mathematical model.If we have the random vector (Z 1 ,Z 2 ) with paired observations (z 11 ,z 21 ), (z 12 ,z 22 ),…(z 1n ,z 2n ), the copula C is the joint cumulative distribution of the ranks of the observations (u 11 ,u 21 ), (u 12 ,u 22 ),…(u 1n ,u 2n ).This means that the copula fits the dependence between the observations corrected by its order, related to the marginal sample.This kind of model has two extremal situations (when we restrict the attention to positive dependence): on the one hand, the model C(u 1 ,u 2 )=u 1 *u 2 means that the random variables Z 1 and Z 2 are independent (Tau-Kendall measure equals to 0), on the other hand, we can find the perfect dependence quantified by the copula C(u 1 ,u 2 )=min{u 1 ,u 2 } that happens when one random variable is a perfect predictor of the other random variable (Tau-Kendall measure equal to 1).As an illustration, we show the next picture with simulations of two situations.In both cases ((a) and (b) from Figure 5.), we test whether the variables are independent.We use a new test appropriated for copula model, developed recently in Bianchi (2008).The results are presented on the next plots (Figure 6.) and they show that the supposition of independence is rejected.
Since we note that the processes for intensity and F 0 values are not independent, we fit the Gumbel, Frank and Clayton copula models to identify the type of dependence.Using the maximum likelihood method to measure the adequacy of the models it was possible to detect the best one among the previous options.The next plots are related to the selection.We use the tests from Bianchi (2008) to verify if the best model (indicated by the maximum likelihood method) is rejected or not, and we show that at level 95% the selected model (in each case) was not rejected.In the intensity case, the best model selected by the method was the Frank model with tau=0.314(see Figure 7. (a)).On the other hand, in the F 0 case, the best model selected by the method was the Gumbel model with tau=0.498(see Figure 7. (b)).In both cases the tau measure reveals a positive association between the processes, as expected.Therefore, it is possible to claim effectively that the variation in intensity and in F 0 in syllables perceived as bearing secondary stress, as well as in adjacent syllables, can be taken as a robust correlate for data perception regarding secondary stress placement in BP.
The models show that the relationship is not corresponding with the extremal cases of dependence (independence and perfect dependence).This means that the random variables are not equal in the probabilistic sense or that some aspects (part of the information) of the 2 ij(i) e process may not be predicted by the 1 ij(i) e process.

Conclusions
In this paper we confirm our initial hypothesis that secondary stress acoustical correlates can be found predominantly in pretonic syllables adjacent to the one(s) perceived as bearer(s) of this type of stress within the PWd.
According to our results obtained by the application of the copula statistic model, it is possible to claim effectively that the variation in intensity and in F 0 in syllables perceived as bearing secondary stress, as well as in adjacent syllables, can be taken as a robust correlate for data perception regarding secondary stress placement in BP.The variation in intensity and in F 0 in syllables perceived as bearing secondary stress and in the other adjacent pretonic syllables are complementary information for the perception of secondary stresses by BP speakers.
The results presented here raise relevant questions concerning the rhythmic and intonational organization of Brazilian Portuguese that shall be undertaken in future work.The first of these questions refers to possible implications of our results for the characterization of BP as a language that has a binary rhythm.The results point to a regular alternation involving prominent and non prominent syllables, but further research is needed in order to exclude a possible positional effect (beginning of a prosodic word) on secondary stress placement.
The second question refers to the implications of the results for the characterization of BP intonational structure.The analysis presented in this paper was based, among other things, on the extraction of F 0 values, but no intonational analysis of the data was conducted.Since it is well known that a correlation exist between F 0 rising and occurrence of an H tone, we can hypothesize that H tones occurring in pretonic syllables might be associated to secondary stress perception, as has already been pointed out in Tenani (2002), Fernandes (2007), Fernandes-Svartman (2009), Vigário & Fernandes--Svartman (2010), among others.

Figure 1 .
Figure 1.F 0 contour (top line) and intensity (bottom line) of the PWd em DISponibiliZAR ("make available"), produced by a BP speaker (PA).
Figure 2. (a) Mean intensity of pretonic syllables perceived as bearing secondary stress (axis Y) and mean intensity of other pretonic syllables (axis X).(b) Mean F 0 of pretonic syllables perceived as bearing secondary stress (axis Y) and mean F 0 of other pretonic syllables (axis X).

Figure 3 .
Figure 3. (a) Mean residual intensity of pretonic syllables perceived as bearing secondary stress (dotted line -RTY process) and mean residual intensity of other pretonic syllables (full line -RTX process).(b) Mean residual F 0 of pretonic syllables perceived as bearing secondary stress (in red -RTY process) and mean residual F 0 of other pretonic syllables (in blue -RTX process).

Figure 5 .
Figure 5. Dependence modelling between X and Y processes relative to (a) 1 ij(i) e

Figure 6 .
Figure 6.Comparative test Tau-plots using a 95% confidence level.(a) Dependence between intensities fitted by Independence copula.(b) Dependence between fundamental frequencies fitted by Independence copula.

Figure 7 .
Figure 7. Comparative test Tau-plots using a 95% confidence level.(a) Dependence between intensities fitted by Frank copula.(b) Dependence between fundamental frequencies fitted by Gumbel copula.

Table 1 .
Global intensity and F 0 values.